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Department of Chemical Engineering

SELF-GENERATED DIFFUSIOPHORESIS IN DEAD-END PORES

A Dissertation in

Chemical Engineering

Abhishek Kar

 2015 Abhishek Kar

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2015

The dissertation of Abhishek Kar was reviewed and approved* by the following:

Darrell Velegol Chair of Committee Distinguished Professor of Chemical Engineering Dissertation Advisor

Ayusman Sen Distinguished Professor of Chemistry

Themis Matsoukas Professor of Chemical Engineering

Robert Rioux Associate Professor of Chemical Engineering

Manish Kumar Assistant Professor of Chemical Engineering

Janna Maranas Professor of Chemical Engineering Chair of the Graduate Program

*Signatures are on file in the graduate school.

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ABSTRACT

Dead-end pores are ubiquitous in nature, from extracellular matrix in the brain to fractured porous media present in oil reserves. In many cases one would gain great advantage to be able to design transport in these dead-end pores. However, achieving fluid flows in dead-end pores is not possible through conventional pressure-driven mechanisms. Traditional electrokinetic flows produced by inserting electrodes are also impractical, especially when these pores are located in difficult-to-reach regions. In this thesis we explore whether a subtle but important fluid flow mechanism, called diffusioosmosis, can produce “chemically-driven flows” in dead-end pores, causing transport and exchange of materials. This phenomenon of “transient diffusioosmosis” utilizes the presence of a spatiotemporal ionic gradient across dead-end pores to generate an in situ electric field which drives convection along the charged walls of the pores. Unlike pressure-driven flow mechanisms where the wall acts as a “resistance”, in diffusioosmotic flows the wall acts as a

“pump” with the salt gradient acting as a “localized battery” generating motion.

Following a summary of the relevant literature on diffusioosmosis and diffusiophoresis

(which refers to particle transport coupled with fluid flow), a brief overview of its applicability in geological settings is provided. Surprisingly, we find strong cues of such flows occurring from sudden tectonic movements on earth’s crust as well as during reactive transport phenomena involving dissolution-reprecipitation across rock-fluid interfaces. To illustrate this simple yet important concept, three major scientific questions have been explored:

1) What are the flow rates due to ionic gradients inside dead-end pores, and how far do they extend? Subsequently, how can the transport of mobile species be controlled based on the variation in zeta potentials and other physical parameters?

2) What is the rate at which colloidal fouling can be enhanced or mitigated on membrane surfaces through application of ionic gradients?

3) In pseudomorphic mineral replacement reactions, how do convective flows generated from ionic gradients affect the reaction rate of the system? Consequently, how do these flows enable us to distinguish between reaction and transport limitations along with the quantitative predictions for rate of release of trapped resources from mineral entities?

Remarkably, colloidal migration generated from such chemical energy are found to be orders of magnitude faster than diffusion time scales and are likely to be critical in various technological operations like hydraulic fracking and waste water purification.

The two key results discussed in this thesis are: (a) Electrokinetic flows, e.g. diffusioosmosis, generated from mineral dissolution is a novel way of interpreting mass transfer with the external surrounding, and (b) these flows can drive convective particle migration where other forms of fluid flow are difficult to be set up.

This work constitutes a significant advancement in the field of auto-electrokinetic transport, i.e. diffusiophoresis, and signifies its importance in several physical and geological settings. It proposes an alternate way of driving motion in otherwise inaccessible regions, which can be synergized with synthetic nanomotors and micropumps to induce directionality in micro- and nanoscale transport.

TABLE OF CONTENTS

List of Figures ...... ix

List of Tables ...... xvi

Preface...... xvii

Acknowledgements ...... xviii

Chapter 1 Diffusioosmotic Flows in Natural and Artificial Systems ...... 1

1-1. Motivation: Chemically Driven Fluid Flows ...... 1 1-2. Physics behind Diffusioosmosis and Diffusiophoresis ...... 6 1-3. Research Objectives and Approach ...... 10 1-3-1. Self-generated Diffusioosmotic Flows ...... 10 1-3-2. Transient Diffusioosmosis across Membranes ...... 12 1-3-3. Transient Diffusioosmosis in Dead-end Pores...... 14 1-3-4. Convective Flows in Mineral Replacement Reactions ...... 15 1-4. Outline of the Thesis ...... 17 1-5. References ...... 18

Chapter 2 Mineral Micropumps ...... 22

2-1. Motivation: Self-generated Ionic Gradients ...... 23 2-2. Materials and Methods ...... 25 2-2-1. Chemicals and Instruments Used ...... 25 2-2-2. Calcium and Barium Carbonate Microparticle Synthesis ...... 26 2-2-3. Observing Pumping Behavior of Calcite Microparticles ...... 26 2-2-4. Observation of Pumping Behavior of Natural Rock Samples ...... 27 2-2-5. Zeta Potential Measurements of Latex Particles and Substrate ...... 27 2-2-6. Analysis of Pumping Behavior ...... 28 2-3. Results for Calcium Carbonate Micropumps ...... 28 2-4. Rates of Pumping by Calcite Micropumps ...... 33 2-5. Summary and Future Remarks: Rate-Limiting Step ...... 39 2-6. References ...... 41

Chapter 3 Mitigating Fouling of Membranes through Diffusiophoresis ...... 45

3-1. The Problem: Colloidal Fouling of Membranes ...... 46 3-1-1. Brief Overview of Diffusiophoresis ...... 46 3-1-2. Objectives of the Chapter ...... 48 3-2. Materials and Methods ...... 48 3-2-1. Membrane and Chemicals Used ...... 48 3-2-2. Calcium Carbonate Microparticle Synthesis ...... 49 3-2-3. Salt Gradient in a Closed System ...... 49 3-2-4. Observation and Analysis Tools ...... 50 3-2-5. Determination of Chloride Concentration Profile ...... 51

3-2-6. Zeta Potential Measurements of Latex Beads ...... 51 3-3. Inducing Fouling on Membranes through Salt Gradients ...... 52 3-4. Discussion ...... 56 3-4-1. Development of Transient Salt Gradient ...... 56 3-4-2. Generation of Electric Field ...... 58 3-4-3. Diffusiophoretic Speeds...... 59 3-4-4. Mitigating Fouling through Calcite Micropumps ...... 61 3-5. Conclusion ...... 63 3-6. References ...... 64

Chapter 4 Enhanced Transport in Dead-End Pores ...... 67

4-1. The Problem: Gaining Access to Dead-end Pores ...... 68 4-2. Materials and Methods ...... 69 4-2-1. Chemicals Used ...... 69 4-2-2. Design of Dead-end Capillaries ...... 69 4-2-3. Microscopy Techniques ...... 70 4-2-4. Zeta Potential Measurements of Latex Particles ...... 70 4-2-5. Modeling of Electrokinetic Flows ...... 71 4-3. Results and Discussions ...... 71 4-3-1. Electric Field Generated from Ionic Gradients ...... 71 4-3-2. Exchange of Materials across Dead-End Pores ...... 73 4-3-3. Electrokinetic Model for Transport in Dead-End Pores ...... 76 4-3-4. Extraction of Trapped Oil Emulsions ...... 78 4-3-5. Flows with Divalent Salts ...... 83 4-3-6. Rapid Particle Recirculation ...... 83 4-4. Conclusion ...... 85 4-5. Key Results ...... 86 4-6. References ...... 87

Chapter 5 Convective Flows in Pseudomorphic Mineral Replacement Reactions ...... 92

5-1. The Problem: Diffusion v/s Convective transport ...... 93 5-2. Sample Preparation and Characterization Techniques...... 94 5-2-1. Materials ...... 94 5-2-2. Synthesis of KBr Crystal with Inclusions ...... 95 5-2-3. Design of Batch and Flow-Through Reactor ...... 96 5-2-4. Visualization and Characterization Techniques ...... 97 5-2-5. Sample Preparation for SEM and EDS ...... 98 5-2-6. Sample Preparation for X-Ray Diffraction ...... 99 5-2-7. Analyzing/Tracking of Mineral Replacement Data ...... 99 5-3. Results for Mineral Replacement Reactions ...... 100 5-3-1. The KBr-KCl Pseudomorphic Mineral Replacement Reaction (pMRR) ...... 100 5-3-2. Convective Extraction of Quantum Dots ...... 103 5-3-3. Experiments in a Flow-Through Reactor...... 105 5-3-4. Rate-Limiting Step ...... 108 5-3-5. Electrokinetic Model of pMRR ...... 110 5-4. Conclusion ...... 113 5-5. References ...... 115

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Chapter 6 Conclusion & Future Work ...... 120

6-1. Summary of the Thesis ...... 120 6-2. New! - Internal Mass Transfer enabled by Diffusioosmotic Flows ...... 124 6-3. New! - Concentration Boundary Layer Diffusiophoresis ...... 126 6-4. Simultaneous Propulsion and Pumping of Micromotors ...... 133 6-5. References ...... 137

Appendix A Ionic Gradients in Micropumps...... 139

A-1. Concentration and Diffusiophoretic Velocity Profile ...... 139 A-1-1. Concentration Profile ...... 139 A-1-2. Time to Pseudo-Steady State ...... 140 A-1-3. COMSOL Solution for Concentration Profile ...... 141 A-1-4. Diffusiophoretic Velocity of a Tracer Particle ...... 141 A-2. Impact of Zeta Potential Variation ...... 144

Appendix B Transport Model in Hollow Fiber Membranes ...... 145

B-1. Negligible Osmotic Effects ...... 145 B-2. Model for Salt Gradients across HFM ...... 146

Appendix C Electrokinetic Model for Flows in Dead-End Pores ...... 149

C-1. Horizontal Dead-end Capillary Set-up ...... 149 C-2. Vertical Dead-end Capillary Set-up ...... 149 C-2-1. Impact of Density Driven Flows ...... 150 C-2-2. Transport Profile of Amidine-functionalized PSL Beads ...... 152 C-3. Transport Controlled by the Variation in Zeta Potentials ...... 153 C-4. Other Multi-valent Ionic Gradients ...... 155 C-4-1. Ion gradient from calcium carbonate dissolution ...... 155 C-4-2. Ion gradient from dissolved carbon dioxide...... 156 C-5. Electrokinetic Model to Quantify Observed Speeds ...... 157 C-5-1. Debye Layer inside Dead-end Pores ...... 157 C-5-2. Expression for Fluid and Particle Speed ...... 158 C-5-3. Spatiotemporal Concentration Gradient ...... 159 C-5-4. Transient Diffusioosmotic Flow (TDOF) ...... 159 C-6. Theory behind Exchange of Tracers ...... 160 C-7. References ...... 161

Appendix D Video Analysis in Pseudomorphic Mineral Replacement Reaction ...... 162

D-1. MATLAB Code for Normalized Intensity Calculation ...... 162

Appendix E Vendors ...... 164

E-1. Colloidal Particles ...... 164 E-2. Chemicals ...... 164 E-3. Equipment ...... 165

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E-4. Materials ...... 165 E-5. Experimental Supplies ...... 166

LIST OF FIGURES

Figure 1-1. The triangle representing interconnected fluid flow mechanisms. Different mechanisms for driving fluid flows, such as pressure gradient (p), gradient in electric potential () and concentration gradient (c) are coupled with each other through the participation of ions and charged surfaces in solution. I explain this in detail in Chapter 6 of the thesis...... 4

Figure 1-2. Dead-end pores occurring in various geological and biological systems. Pressure-driven flows are efficient in the main channel, but cannot access the dead-end pores...... 5

Figure 1-3. Increase in oil recovery represented through low-salinity effect (LSE) upon low-salinity waterflooding (LSW) compared to high-salinity waterflooding (HSW) of reservoir core and fluids...... 6

Figure 1-4. Schematic of diffusiophoresis and diffusioosmosis of a charged particle in a concentration gradient. The diffusioosmotic fluid velocity is given by vdo while the diffusiophoretic particle speed is given by udp. The E field generated in the system (from right to left) is due to the difference in diffusion coefficients of the ions involved with the anion diffusing faster than the cation...... 9

Figure 1-5. Schematic of the trajectories for the tracers dispersed in a system with CaCO3 micropumps. The negatively charged tracers are diffusiophoretically attracted towards the micropumps in the bulk; and upon reaching the surface, are diffusioosmotically swept away by the fluid flow emanating radially outwards from the micropump...... 11

Figure 1-6. Salt gradients induce particle deposition on the surface of the hollow fiber membrane. Similar to Fig. 1-4, diffusion of ions across the membrane generates transient E field in the system which attracts charged particles towards the membrane surface. Here, the charged particles are assumed to be carrying a negative charge in solution...... 13

Figure 1-7. Transient salt gradients across dead-end pores result in exchange of materials with oil emulsions being extracted out and colloidal tracers traveling in from the bulk toward the end of the pore...... 14

x substrate using an inverted microscope. Optical microscopy time-lapse images were taken at 40× magnification with overlays every 0.2 s. Scale bars in these images are 10 μm. 29

Figure 2-2. Schematic of microflows for one single CaCO3 particle micropump with sPSL tracers and two images of the same micropump. These systems contained only calcium carbonate pumps (7 μm radius) and 3 μm sPSL tracers in DI water. The inset in (a) shows the axes and the 3-D view of our experimental set-up. Scale bars in these images are 10 μm. (a) x-z plane Tracers in the bulk get attracted towards the pump, some adhere, and the rest get pumped out in to the bulk radially. (b) x-y plane The sPSL tracers are adhered to the surface of the pump, but not permanently. (c) x-y plane A clear exclusion region of tracers develops around the micropump on the glass surface. These tracers, after being ejected, exhibit mostly Brownian motion...... 30

Figure 2-3. Flows near CaCO3 particle micropumps with aPSL tracers. The inset in (a) shows the axes and the 3-D view of our experimental set-up. (a) x-z plane Schematic of flows near a micropump. The chemistry is given, and the E field points outward. The aPSL particles are pushed away from the calcium carbonate micropump by diffusiophoresis, and so the flow lines of these tracers do not approach the micropump, as in Fig. 2-2a. (b) x-y plane The aPSL tracer particles do not aggregate on the surface of the calcium carbonate micropump, as do the sPSL tracers. These systems contained only calcium carbonate pumps (7 μm) and 3.5 μm aPSL microspheres in DI water. Scale bars in these images are 10 μm. (c) x-y plane Two interacting micropumps with no stagnation region of flow. 31

Figure 2-4. Microflows for one single CaCO3 particle micropump and two interacting micropumps. These systems contained only CaCO3 micropumps and 1.4 μm sPSL tracers in DI water. (a, b) vector field for the time-lapse images shown in Fig. 2-1. In the vector field plots, axes are distance in μm. The black circles represent the location of the micropumps, and the vector arrows represent the tracer particle direction and speed in μm/s at the substrate surface. The plots were generated by tracking the movement of 750-1000 particles over 0.3 seconds. (c, d) radial speed plots. In (c), the radial speeds of all sPSL tracers sampled in (b) are plotted against the distance of those tracers from the center of the lone calcium carbonate micropump. In (d), the radial speed of tracer particles within 6 microns of the line between the two micropumps in (b) (boxed area shown) is plotted against the distance of those tracers from the midpoint between the two pumps. In both cases, curves have been fitted using the theoretical radial velocity decay as discussed in Eq. 3-3 in the text. In (d), a 2 parameter superposition of two single particle fits, again with form v ≈ a/(r ± b), was used, assuming no bath concentration of CaCO3. We anticipate that better fits can be achieved by taking the radial varying zeta potentials into account, as shown in Table 2-1. In fact, analysis of the discrepancy between the fitted function and the observed speeds should lead to a better understanding of the concentration dependence of these surface potentials. Fitting curve equations and further discussion can be found in Appendix A...... 32

Figure 2-5. Barium carbonate microparticle pumping 1.4 μm sPSL tracer particles outward, overlays are 0.33 sec apart, scale bar is 20 μm...... 39

Figure 3-1. Salt-gradients induce particle deposition and chemical micropumps mitigate this effect. (a) 50 mM NaCl was concentrated in HFM at t = 0 s, while outside solution contained sPSL ( = 3.0 µm ± 2.1%, w/v = 8%) beads in DI, (b) at t = 150 s, under the influence of NaCl gradients over this time period considerable deposition of particles on HFM wall was observed (also see Fig. 3-2b). (c) Calcium carbonate micropumps prevented this particle deposition...... 53

Figure 3-2. Particle migration under a transient salt gradient due to diffusiophoresis. (a) A transient salt gradient was established with 10 mM NaCl inside the HFM and 3.0 µm sPSL in DI in the capillary. At t ~ 2 mins, sPSL beads are seen to be “concentrated” along the wall of the HFM. (b) In case of 50 mM NaCl inside the HFM, more particles deposited onto the surface of the membrane in the same time frame...... 54

Figure 3-3. Control experiments show negligible effect on particle deposition by gravity or osmotic gradients. (a) For the case with 50 mM NaCl inside the HFM and sPSL in DI water outside (in a vertical setup), particle deposition was similar to (b) in a horizontal setup. (c) For the case with 10 mM NaCl inside the HFM and sucrose (20 mM) with red fluorescent sPSL ( = 4.0 µm ± 2.0%, w/v = 2%,) deposition was similar to (d) with 10 mM NaCl inside HFM and red fluorescent sPSL in DI outside...... 55

Figure 3-4. Quantification of transient salt gradient generated in the system. (a) Lucigenin dye (10 µM) was quenched by chloride ion diffusing out of the HFM. 10 mM NaCl was taken inside the HFM, and the chloride ions upon diffusion, quenched lucigenin (as seen by the dark regions around the HFM).The intensity profile was measured and used in the Stern-Volmer equation to determine concentrations across the entire width of the capillary. (b) Experimental data for salt gradient were plotted along with that predicted from model for t = 1 min. The gradients decayed linearly (for the most part) away from the wall of the HFM...... 58

Figure 3-5. Diffusiophoretic speed of tracers (a) Diffusiophoretic particle velocities (Udp, μm/s) decreases with time and changes with distance as measured and modeled for 10 mM NaCl inside HFM/ 3 μm sPSL beads in DI outside at t~120 s and t ~ 180 s in 1 mm ID capillary and (b) Udp depends on nature of salts as measured and modeled for 10 mM NaCl, 10 mM KCl or 10 mM LiCl inside HFM/ 3 μm sPSL beads in DI outside at t ~ 180 s in 1 mm ID capillary (for NaCl & KCl) and 0.9 mm ID capillary (for LiCl). The symbols represent experimental velocities and the lines represent modeled velocities. The asymmetric velocity profiles show a dependence on physical placement of the HFM within the capillary and the time scales of measurements. The maximum velocity of the particles corresponds to the position where maximum n/n occurs...... 60

Figure 3-6. CaCO3 can be used to prevent particle deposition on the membrane surface. (a) Schematic of aggregation prevention and exclusion zone creation by CaCO3 microparticles as seen experimentally at 4 minutes in (b). (c) shows the same after t =1 min and (d) shows the system after approximately 15 minutes...... 61

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Figure 4-1. Particle transport and exchange of material into and out of dead-end pores due to TDOFs. (a) Experimental setup used to study transport rates of sPSL beads in dead-end pores. Experiments involved a simple vertical sink-reservoir model, containing a smaller capillary that serves as the salt reservoir, within a larger capillary containing only DI water. The solid black arrow indicates the direction of material transport and the black dashed line gives the E-field in the system. Direct visualization of material transport in these dead-end pores was done near the opening of the inner capillary (red open box). (b) The beads were transported upward against gravity both in the center and along the wall of the dead-end pore. Quantitative predictions of tracer speeds from electrokinetic modeling (represented by the curves), at different distances (x) into the dead-end pore are compared with experimental results (represented by open and closed circles) at t = 200 s. ζp = -101 mV and ζw = -65 mV. (c) Lower: 4.0 µm red sPSL beads show diffusiophoretic transport towards the high salt regime both at the center and along the walls. Upper: 2.0 µm green amine-functionalized PSL beads shows diffusiophoretic transport along the wall towards the sink whereas in the center, they move towards the dead-end region containing salt (towards left). (d) Upon adding red sPSL beads in the outside capillary and green amine- functionalized PSL beads in the inside capillary, exchange of material was observed. Near to the side walls of the dead-end pore (inner capillary), the green amine-functionalized PSL beads, initially inside, move towards the sink and eventually out of the pore, whereas the red sPSL beads, initially outside, move in and, eventually, fill up the entire inner capillary...... 75

Figure 4-2. Polydispersity in oil emulsions resulting in transport into or out of dead-end pore. (a) Schematic of the experimental setup used to apply a salt gradient across a dead- end capillary. The solid black arrows indicate the direction of fluid movement. We focus the inverted microscope to the top cross-section of the capillary in order to observe the motion of oil (gray spheres) and sPSL beads (white spheres). Gravity at all times is perpendicular to the direction of motion of oil emulsions. The smaller oil emulsions are found to move out of the capillary, whereas the larger oil emulsions and the sPSL beads are observed to move in. The yellow arrows show this motion of the oil emulsions along the parabolic flow profile (gray) while the white colored parabola indicates the path of sPSL beads. The black dashed lines give the E-field in the system.(b) Time-lapse images showing small emulsion droplets being driven away from the dead end, whereas the sPSL beads (small black circles) are diffusiophoretically transported towards the dead end. Both transport rates are predicted quantitatively by our model (Fig. 4-3). Yellow bars indicate the position of these beads and emulsions before and after 30 s (Movie 4-5). The magnitude of the scale bar is 100 m. (c) When the DI water is inside with salt outside, smaller emulsions ( < 10 m) move towards the dead end and larger emulsions ( > 40 m) move away from it (Movie 4-6) demonstrating the reversible nature of transport...... 80

xiii mostly stationary. Using the diffusiophoretic transport equations, the u for these emulsions was modeled (in b) with the color gradient signifying the direction of motion for these emulsions (negative sign indicates motion towards the sink,while the positive sign shows movement in the opposite direction, towards the dead-end region). In our calculations for b, ζe = -33 mV, ζw = -65 mV, x = 200 µm at t = 300 s. (c,d) The time taken for an emulsion of diameter = 20 µm to exit the dead end pore as a function of its distance from the mouth of the pore (d, mm), as obtained from modeling. Times vary from a few seconds to hours depending on d. Large emulsions are predicted to be stuck in the dead-end pore which is indeed observed experimentally...... 82

Figure 4-4. Transverse transport of beads inside dead-end pores. (a) Tracer particles tracked at z = 0 µm (center plane) entering the dead-end pore containing 10 mM NaCl solution from a DI water sink. (scale bar = 100 µm). The tracers are convected radially towards the walls and then slow down or accumulate along them. (b) The magenta colored dots follow the paths of individual beads entering the pore due to NaCl gradient from a DI water sink. The beads near to the walls of the dead-end pore are seen to execute a curved trajectory in comparison to the ones in the center. The slope of the trajectory increases (i.e. the drift towards the wall increases) for the beads closest to the walls of the dead-end pore. The trajectories are symmetric about the central axis. (c) The purple colored dots track the route followed by individual beads entering the pore due to 10 mM KCl gradient from a DI water sink. The beads are observed to move in a predominantly linear path into the higher salt regime, except for the beads very close to the side walls of the dead-end pore. This observed phenomenon can be explained based the relative contributions of electrophoresis and chemiphoresis to the charged particle movement...... 85

Figure 5-1. Pseudomorphic mineral replacement reaction of KBr crystal in saturated KCl solution. (a, b) Time lapse images of a KBr crystal undergoing replacement in a batch reactor of saturated KCl solution. The darker region around the edges of the crystal, similar in morphology to the parent mineral, exhibits the replacement due to precipitation from the solution.(c) The schematic of the replacement process shows pores developed on the crystal during the reaction which are spatially non-uniform and separated from each other. (d) Surface structure of the crystal after 5 mins under the SEM reveals pores which are roughly 10 – 20 m in width, and (e) cross-sectional view of the crystal shows that these pores penetrate roughly 100 m into the crystal and are dead-end at the dissolution front. (f) XRD analysis of the product specimen after 45 mins of replacement shows that its crystal structure lies in between the pure KBr and the pure KCl lattice orientations. (g) Evolution of crystallographic parameters in the product mineral reveals that as the KBr crystal approaches complete replacement, the disorder in the lattice parameters decrease which is seen through decrease in intensity counts for the crystal. Scale is 100 m...... 102

xiv replacement forming pores through its entire volume. (d) EDS scans for the SEM images of these crystals after fracturing it shows the elemental distribution of bromide ions, and (e) chloride ions within the product phase of the crystal. (f) Line scan through the elemental distribution surface map obtained from EDS reveals that a finite ionic gradient persists for approximately 100 ms across the pores of the mineral. Scale is 100 μm...... 105

Figure 5-3. Flow-through reactors used to enhance mass transfer and extraction of QDs. (a) Rate of change of total normalized intensity of QDs trapped in KBr crystals undergoing replacement. For a batch reactor system, the rate of change is seen to decrease initially and then remain steady for the entire duration of the experiment. In a flow-through reactor system, the rates of change is observed to decrease consistently until all the QDs are extracted from the crystal. (b) SEM images of the crystals in a batch reactor system indicates precipitation on the surface resulting in pores being sealed off after 10 mins into the experiment. Both the inset and the central image confirm that these pores are closed on outside but open within the crystal, and are roughly 180 – 200 μm in width. (c) Flow- through reactor made of polycarbonate sheet being used to study pMRR under a more dynamic set of conditions. Inset to (c) reveals the ionic gradients observed across the pores of the crystal which extend for at least 250 μms in to the crystal lattice. (d) SEM images of the crystals obtained from a flow-through reactor, with a feed rate of solution, Q = 2 ml/min, indicates dead-end pores which are not sealed off on the outside. These images were taken of samples that had undergone replacement for 20 mins...... 107

Figure 5-4. Convective transport rates inside pores during pMRR in a flow-through cell. (a) Time lapse images of sPSL particles getting extracted from a KBr crystal, in roughly 3 minutes, during the pMRR process. The red dots, surrounded by the yellow dashed circles, signify the initial position of the sPSL beads in the KBr crystal. The blue arrow and the yellow arrows indicate the direction of fluid flow (in the outer solution) and particle motion, respectively. (b) The pMRR could be triggered to start or stop depending upon the solution injected into the reactor. While particle extraction is negligible when saturated KBr is flown (indicated by the pink shaded region), extraction can be initiated immediately upon switching the solution to sat. KCl (green shaded region). (c) Rate of progress of the replacement front from the outer rim of the crystal, d (μm) (as shown in the inset), is plotted for various flow rates of solution through the reactor. Since mineral-fluid interface in necessary for the replacement to take place, the tracked rates also signify the fluid speed through the pores of the mineral. Tracking was done from the videos captured under transmission microscope at 4× objective. (d) Velocity of the fluid through the pores was obtained by calculating the slope of the curves in (c). We considered the slope over the region where the curves are linear indicating precipitation from the solution not affecting the replacement process...... 109

Figure 5-5. Slip velocities at the wall of the pore derived through the MPNP and the PNP model agree closely, even at high salt concentrations. The fluid speed near the mouth of the pore is highest at 0.3 μm/s...... 113

Figure 6-1. Calcite dissolution rates measured at 298K and various CO2 partial pressures. At low pH, rates are transport controlled and are not dependent upon CO2 partial pressures, whereas at pH > 3.5, dissolution becomes interface-controlled.3 ...... 125

Figure 6-2. Interrelation between various fluid flow mechanisms and the role of boundary layer diffusiophoresis. (a) At the microscale, different mechanisms for driving fluid flows such as pressure gradient (p), gradient in electric potential () and concentration gradient (c) are coupled with each other through the participation of ions and charged surfaces in solution. This thesis highlights the contributions from diffusioosmosis and boundary layer diffusiophoresis as additional fluid flow and transport mechanisms. (b) The geometry of the concentration boundary layer (CBL) model which extends from the dissolving calcite surface out into the bulk with a thickness of c. The arrows denote the 2+ - - fluxes of Ca , HCO3 and OH from the mineral surface. The difference in diffusion coefficients of these ions generates a steady-state or transient electric field across the CBL leading to BLDP of the dispersed tracers...... 128

Figure 6-3. Unexpected cross-wise motion of particles under a convective flow at moderate Péclet number (Pe  0.5). (a) A self-diffusiophoretic Janus motor undergoes motion upon catalytic decomposition of H2O2 across its active surface (which can be platinum with the inactive site being polystyrene). (b) Upon application of a shear flow, a CBL would be immediately set up across the Janus particle with a thickness varying inversely with respect to the rate at which fluid sweeps its surface. The CBL is expected to be polarized under a shear flow resulting in a cross-wise drift of the particle. (c) CBL formed across the walls of a dead-end pore can induce cross-wise motion of tracers as seen in Fig. 4-4...... 132

Figure 6-4. Coupled behavior of mineral micropumps and catalytic micromotors. (a) Upon using Au/Pt micromotors with CaCO3 micropumps, exclusion regions are created due to the pumping of fluid from the micropump. However, addition of H2O2 to the solution results in complete dissolution of calcite microparticles. (b) BaSO4 micropumps, synthesized through a similar process, are more robust under H2O2 medium and continue pumping tracers away from the mineral surface. (c) A network of BaSO4 micropumps, strategically placed in the system, can enable directional translation of micromotors enhancing our ability to control processes and locomotion at the micro- and nanoscale. Scale is 20 μm...... 136

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LIST OF TABLES

Table 2-1. Zeta potential values (mV) in various solutions ...... 38

Table 6-1. External mass transfer processes v/s Internal mass transfer processes ...... 126

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PREFACE

The dissertation is a compilation of several multi-authored publications in peer-reviewed journals and those in preparation for submission. A list of these publications is listed below.

1. McDermott, J. J., Kar, A., Daher, M., Klara, S., Wang, G., Sen, A., & Velegol, D. (2012).

Self-generated diffusioosmotic flows from calcium carbonate micropumps. Langmuir,

28(44), 15491-15497.

2. Kar, A., Guha, R., Dani, N., Velegol, D., & Kumar, M. (2014). Particle Deposition on

Microporous Membranes Can Be Enhanced or Reduced by Salt Gradients. Langmuir,

30(3), 793-799.

3. Kar, A., Chiang, T. C., Ortiz Rivera, I., Sen, A., Velegol, D. (2015). Enhanced Transport

Into and Out of Dead-End Pores. ACS Nano, DOI: 10.1021/nn506216b

4. Kar, A., McEldrew, M., Mays, B., Stout, R., Khair, A., Velegol, D., Gorski, C. Self-

Generated Electrokinetic Fluid Flows during Pseudomorphic Mineral Replacement

Reactions. to be submitted

5. Kar, A., Guha, R., Velegol, D. Transient Boundary Layer Diffusiophoresis in Natural and

Artificial Systems. in preparation

Patent

(Filed) Velegol, D., Kar, A., Guha, R., Kumar, M. Membrane Fouling Reduction Using

Chemical Micropumps, Assignee: Penn State University, Corresponding Inventor: Darrell

Velegol, December 2014

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ACKNOWLEDGEMENTS

The journey is better than the end

- Cervantes -

I consider myself to be blessed to have a family who have loved and cared for me beyond words could express. Thank you Dad (“Bapa”) for instilling in me the “curiosity” aspect, for believing in me, and for being the best teacher in my life. Thank you Mom (“Mama”) for being the soul behind whatever I do today or in the future. I do what I do to see you happy and proud.

My wonderful sister, Amruta, you have cared for me since the time I could not even manage to stand on my own feet. Till this day when you have your own incredible family, you still call me every day just to check on me. Be it a moment of happiness or frustration, I have found you by my side all the time. Thank you Saroj (brother-in-law) and Omi (nephew) for the wonderful memories over FaceTime and Skype. This thesis is dedicated to my amazing family whom I love with my heart and soul.

I still remember my first day in Penn State. I was walking down the hallway in Fenske when I met Dr. Neetu Chaturvedi (who was then a final year graduate student) and started asking her about her work. After 15 minutes of conversation, I knew I had to get into Prof. Darrell Velegol’s lab.

Since then, I have not looked back. Darrell is the best role model, teacher and friend that one can have. He amazes me every time with how gifted he is in so many things. He is gentle, polite and yet he asks the toughest and the most curios questions one can think of. His levelheaded attitude, his capacity to make you feel smart no matter how dumb you might have acted before him, his ability to always give away the credit for something, his quality of never seeking validation, makes him a standout contributor to the positive experiences I have had in my stay at Penn State. Thank

xix you Darrell for being a great mentor and really teaching me how to ask a good question. At one point, you actually had to write an email to me where you wanted me read out loud the word

“QUESTION” written in it 100 times. Thank you Stephanie and the two little girls, Lauren and

Sabrina, for all the dinners, dinner-table games, basement performances and the opportunity to be a part of your wonderful Velegol family. I will cherish the memories of the time spent with your family lifelong.

I would like to thank Prof. Ayusman Sen for all the wonderful discussions we have had over the years. Thank you for being my committee member, and also making me a part of your extended lab group and Christmas dinner parties. I have thoroughly enjoyed the company of everyone in your lab. I was involved in several collaborations throughout my stay in Penn State, and had it not been for the vision of everyone in the team, I probably would not have come this far. Thank you

Prof. Chris Gorski and Prof. Manish Kumar for all the support, discussions and encouragement.

Thank you Prof. Rob Rioux and Prof. Themis Matsoukas for being my committee members and providing me with useful insights on projects at various levels. Thank you Prof. Ali Borhan and

Prof. Tom Mallouk for helping me navigate through the various questions I would bring to you for guidance.

I had a great time at Penn State because I had some great friends during my stay here. Sonti,

Aabhas, Sub, Dhrmil– thank you guys for listening to my gibberish, ideas about life, dealing with my stupidity, and giving me strength and support during times when I was the most vulnerable.

Thank you Soumalya, Devesh, Jyotsna, Jess, Madhuri, Trivedy, Saurabh, Vinita, Krishna, Guarav,

Sandeep and Isa for the friendship and company. I am still trying to convince Trivedy that he should not be a selfie maniac. Thanks Nishant and Abhijan for being two really good friends since my undergrad days.

I have completely cherished the camaraderie by the people in the Velegol lab group. During my early days, Neetu and Joe helped me grow into my projects while Laura and Tso-Yi were amazing friends and colleagues. Laura and I had one ambitious project which we thought we could get it done in a “single” day. But wisely, we figured out our naivety pretty early. Thanks Laura for the support during my tough times and all the great “maami” stories that you used to tell me regarding how big a fan she is of Shahrukh Khan. Thank you to the newer bunch of people, Sruti,

Astha and Raj. Though Sruti graduated few years back, she infected me with Twitter and blogging, right LadyKedi? Thank you Astha for treating me to some of your excellent home-cooked food.

Unfortunately, I am not a foodie, and so I rarely cook with so much attention to detail. Thank you

Raj for being a collaborator and sharing your strange opinions about winter in Pennsylvania.

During my stay at Penn State, I had the deep privilege to work with some really smart undergraduate students. Mike and Ben, you guys are the whizkids of chemical engineering. More than just working with me, you both have been great friends and I truly cherish that. A special thanks for putting an extra effort on a project during the time when I was in India for two months.

Mike, I am sure someday we will write the movie script on Neanderthals v/s Human beings. Gary

Wang, Kevin Lin, Mike Vilkovoy, Nishant Dani, Kyle Marshall, Mizael Arroyo, Humberto

Gonzalez, and William Weigand – I wish you all the very best in your careers ahead. It was wonderful working with you all.

The staff at Penn State is just brilliant. Their support has been so critical to my stay here. Thank you Blackie, MJ, Roger and Cathy. I hope to bug you people less in future.

Finally, I would like to come back and thank again those key individuals in my life who have helped me immensely to grow as a person and as a researcher over the last few years. Dad, mom, sister and Darrell – thank you again.

Chapter 1

Diffusioosmotic Flows in Natural and Artificial Systems

This thesis deals with fluid flow effects arising from ionic gradients, either from an induced or self-generated source, which can drive transport in otherwise hard-to-reach regions like dead- end pores in reservoir rocks. Here I use both experimental and modeling methods to answer the scientific questions in the thesis. My focus is on the critical knowledge gap that limits our appreciation of salt gradients in a host of problems pertaining to geology, geochemistry, and membrane science. The chapters in this thesis primarily delve into two electrokinetic transport mechanisms – diffusioosmosis and diffusiophoresis – which can generate convective transport of tracers at the micro- and nanoscale without the use of any external pressure or electric field.

Though this mechanism of fluid flow and transport has been around for over 65 years, we demonstrate its relevance to systems like oil reservoirs, mineral-water interactions and fouling of hollow fiber membranes which has not been shown before. This study also broadens our knowledge on how different fluid flow mechanisms are seamlessly coupled with each other which can substantially impact our understanding of transport properties at the micro- and nanoscale.

1-1. Motivation: Chemically Driven Fluid Flows

Microscale fluid flows have emerged as an attractive field of study, both from an industrial and scientific perspective, thanks to the inherent advantages associated with downsizing which requires lesser volume of fluid (e.g. sample and reagent)1,2 and the increase in sensitivity of various

2 operations (e.g. molecular analysis3,4, microelectronics5, DNA sequencing6). Such rapid and explicit benefits offered through microscale fluid manipulation and generation comes at the cost of surfaces playing an active role as compared to the volume of the fluid. At a macro level, fluid flows are typically generated using pressure gradients. However, at micro- and nanoscale, such fluid flow mechanisms are highly inefficient. This can be understood through the Hagen-

Poiseuille’s equation7 for the flow rate of a fluid through a tube given by equation 1-1. We can see that P ~ O(r-4) where P is the pressure gradient across the ends of the tube,  is the viscosity of the fluid, Q is the flow rate, and L and r are the length and the radius of the tube, respectively.

PQ8  (1-1) Lr 4

Hence, pressure gradients required to generate fluid flows increase significantly as the radius of the tube shrinks. As a result, such fluid flows are difficult to control, improve, or tailor to specific applications.

Electrokinetic effects, an alternate way of driving fluid flows, occur in systems wherein ions, electric fields, and surfaces interact to drive fluid and particle motion.8 The flows arising from this interplay has a central role in colloid science9, analytical chemistry10, directed assemblies11, and streaming potential measurements12. Electrokinetic flows can also be generated without the use of any electrodes i.e. through ionic gradients. When ions in a solution diffuse at different rates, a local electric field is generated in order to maintain electroneutrality in the system.

This electric field can in turn act on any charged surface, mobile and stationary, present in a solution driving phoretic and osmotic motion which are analogous to electrophoresis and electroosmosis respectively. Such a transport mechanism is known as diffusiophoresis (for the

3 transport of charged particles) and diffusioosmosis (for the motion of fluid).13-19 Often times in this thesis, we solely refer to diffusiophoresis which actually represents the phoretic speed plus the fluid speed in the system. As we will discuss later (in Chapters 2-5 & Appendices), ionic gradients can be generated through three pathways, i) self-generated through reaction/ dissolution of a species (e.g. a mineral), ii) induced across pore connecting a sink at low salt concentration and a reservoir at higher salt concentration, and iii) across concentration boundary layers developed over a surface swept by a fluid (which is discussed in this thesis with theoretical validation). These gradients could either be steady state or transient in nature.

The primary objective of this thesis is to investigate various such scenarios where ionic gradients induced from either one of the above three mechanisms generate fluid flow and transport in the system.

Holistically, this PhD thesis discusses the coupling between different fluid flow driving mechanisms represented through Fig. 1-1. While each component making up the “fluid flow mechanism triangle” can drive various forms of transport that forms the crux of our knowledge in fluid dynamics, the subtle interconnections between them have been the focus in recent literature.

This thesis delves into the novel concept of boundary layer diffusiophoresis (BLDP) and the known phenomena of diffusioosmosis which are two key transport mechanisms originating across interfaces due to concentration gradients. Note that temperature gradients can also drive flows, and their effect is similar to concentration gradients in the system.

One key hurdle to interpreting diffusiophoresis in porous networks lies in the dominance of advective motion of fluid flow over chemical gradient driven transport. Normally, advection driven transport from pressure gradients nullifies mobility generated from concentration gradients in the system20,21. However, pressure driven flows cease to exist in hard-to-access regions such as dead-end pores (as shown in Fig. 1-2). Conventional electrokinetic driven flows, through inserting electrodes in dead-end pores, are also unrealistic. Such pores are ubiquitous in many geochemical and biological systems and enabling transport through them is a key scientific and industrial challenge.

Accessible pores

Inaccessible dead-end pores

Figure 1-2. Dead-end pores occurring in various geological and biological systems. Pressure-driven flows are efficient in the main channel, but cannot access the dead-end pores.

In light of this, some of the recent operations in oil and gas industries, like the LoSal process22, have highlighted increased productivity obtained through low salinity waterflooding of the core reserves which contains majority of the oil and natural gas trapped in dead-end pores (Fig.

1-3). The scientific challenge lies in determining the exact mechanism behind such an enhanced transport process which far exceeds diffusion time scales (t ~ l2/D, where l is the length of the pore and D is the diffusion coefficient of the material being extracted) for these oil traps. The key to this problem lies in understanding the interaction between transient salt gradients present across such pores with the charged species in the system (e.g. oil emulsions) generating enhanced transport rates out of the pores. Before we dive in toward our research objectives, let us first get a quick overview of the theory behind this chemically driven transport mechanism. The most essential references are discussed below with the goal to provide succinctly the information that is necessary for the reader to understand our scientific questions. There have been many review papers written on diffusiophoresis, and for detailed information the reader is advised to refer to these books and manuscripts.23, 24

Figure 1-3. Increase in oil recovery represented through low-salinity effect (LSE) upon low-salinity waterflooding (LSW) compared to high-salinity waterflooding (HSW) of reservoir core and fluids.22

1-2. Physics behind Diffusioosmosis and Diffusiophoresis

Electroosmotic flows of interest, i.e. diffusioosmosis, arise due to salt concentration gradients near a charged surface or particle, usually in aqueous media. For example, if a gradient of sodium chloride (NaCl) exists across a surface, then as it dissipates, an electric field (E) arises spontaneously in the solution. Since the Cl- ion has a higher diffusion coefficient than Na+ ion, the self-generated E-field helps maintain electroneutrality in the system. Typical values for E-field in solution are 0.1-10 V/cm. Since surfaces in water are almost always charged24,25 with a surface potential (0  zeta potential, ) of magnitude 25-100 mV, they attract counter-ions from the solution building up a diffuse layer around it. This ensures electroneutrality is maintained in the solution and charge build-up is prevented.

7 The diffuse layer (otherwise known as the electrical double layer, EDL) around a surface

-1 12 has a thickness which is given by  with  kBi T() z e c where  is the fluid i permittivity, kB is the Boltzmann constant, T is the temperature, zi is the valence of each ion (+1 for cation and -1 for anion in a z:z electrolyte), e is the proton charge, c is the concentration of ions in the bulk. At low ionic strengths, the Debye length is high resulting in colloidal stability, whereas at high ionic strengths, the Debye length is small leading to short range effects like van der Waals forces dominating over electrostatic repulsion ensuing particle aggregation. The E- field can act on the mobile ions in the diffuse layer making the fluid to slip over surfaces which results in a fluid flow known as diffusioosmosis. The resulting particle motion which is impacted by the fluid flow in the system is called diffusiophoresis. The origin of this subtle yet important transport mechanism has been known in literature for over 65 years since the time when Derjaguin et al.

(1947) argued that the diffuse structure of an interface allows a finite velocity gradient through the interfacial layer resulting in motion of colloids.26,27 The speed (v) of the flows can be estimated by the classic Smoluchowski result, v E /  , where the permittivity of water () is 7.1×10-10

C2/N-m2 and the viscosity () of water at room temperature is about 0.0010 kg/m-s. For typical values of E = 5 V/cm and  = -50 mV, one finds that v = 18 m/s.

So when do we expect diffusiophoretic transport (which includes diffusioosmotic flow) to influence the behavior of fluid and particles in our system? There are certain prerequisites for diffusiophoresis to initiate “chemical locomotion” in a salt solution – a) a finite difference in diffusivities (Di) of the ions present in the salt (i.e. D+ - D-  0), b) a finite surface potential, given by the zeta potential ζ, and c) an electrolyte concentration gradient, n. The first order Poisson’s equation can be used along with the ion migration equation for the flux of ions in the system and

8 with zero net current to yield the self-generated E-field due to an ionic gradient. This E-field is given by equation 1-228

 zi D i c i kTB i E  2 (1-2) e zi D i c i i which simplifies to equation 1-3 upon considering the case of a binary z:z salt solution.

k T D D c E  B    (1-3) e D D  c 

This E-field can act on the counterions surrounding a charged particle or stationary surface driving fluid flow, and hence generating particle motion in the opposite direction (or, commonly referred to as diffusiophoresis) with hydrodynamic retardation forces acting on the particle..

Beside the electrokinetic component arising from the difference in diffusion coefficients of ions, osmotic pressure drop due to ionic gradients can polarize the EDL across charged surfaces.

This induces particle motion due to a related mechanism called chemiphoresis.29 Chemiphoresis always directs a colloidal particle towards the higher salt concentration regime. The magnitude of the chemiphoretic velocity is usually an order lesser than the diffusiophoretic component, and hence is neglected while interpreting our experimental results. However, it is accounted for in the models used throughout this thesis in order to accurately determine the velocity of the fluid or the particle in the system. The diffusioosmotic fluid speed, vdo (Fig. 1-3), which is a combination of the electroosmotic component and the chemiosmotic component, is given by equation 1-4 where

w refers to the -potential of the wall

22   kBB T D D2 k T 2 ze w c vdo  w ln 1  tanh  (1-4)  ze D D z22 e4 k T c  B

The diffusiophoretic speed for colloidal particle, udp, (Fig. 1-4) is identical to equation 1-4 with w replaced by p (referring to the -potential of the particle) and udp = - vdo. The net tracer speed is thus given by u,

u = udp + vdo (1-5)

Unlike conventional electrokinetics where the direction of migration for the particle is relatively straightforward to predict (from the Helmholtz-Smoluchowski’s equation), with diffusiophoresis (referring to equation 1-5) it is an interesting interplay of surface properties and the ionic gradient in the system. As expected, depending on the type of salt used, the surface charges on a particle and the geometry of the channel (which we will discuss in the later sections), we can tune the velocity to match the desired outcome like sorting30, assembly11, pumping31, and even exhibit active matter behavior32.

10 1-3. Research Objectives and Approach

Classical diffusiophoresis is considered to occur when an ionic gradient (of an electrolyte or non-electrolyte) is applied across a dispersed phase of colloids at steady state. But it is also possible to self-generate an ionic gradient through dissolution of a mineral like CaCO3, CaSO4,

BaCO3 or even the commonly available NaCl. Ionic gradients generated from dissolution of sparingly soluble minerals like CaCO3 are sustained for longer periods of time than those produced from dissolution of a simple salt crystal like NaCl. Dissolution of CaCO3 in solution primarily

2+ - - 2+ -9 produces three ions - Ca , HCO3 and OH - whose diffusion coefficients are (DCa =0.792×10

2 - -9 2 - -9 2 m /s, DOH =5.273×10 m /s, DHCO3 =1.185×10 m /s) different from each other. This brings us to the first research objective of this thesis (discussed in Chapter 2)

1-3-1. Self-generated Diffusioosmotic Flows

Do ionic gradients produced from dissolution of CaCO3 microparticles generate diffusiophoretic transport of tracers in the system? And if they do, how does the rate of motion of these tracers vary with space, time and background ion concentration?

In order to measure the diffusiophoretic transport rates produced from dissolution of a sparingly soluble mineral, we synthesized 5 – 10 μm sized CaCO3 microparticles through the precipitation technique (details regarding synthesis and set up used to study these microparticles is provided in Chapter 2). These microparticles, being heavy, settle on to a glass surface. When a quiescent flow of de-ionized (DI) water and colloidal tracer beads are added in the background, they immediately start pumping fluid on the glass surface which carries the particles with it radially

11 outward. This makes these microparticles behave as chemical micropumps whose properties could be tuned by changing solution conditions and tracers in the system (Fig. 1-5). We observed transport rates of tracers to be as high as 50 μm/s close to the surface of the dissolving microparticle. The speeds decreased non-linearly with space and time (for details refer to Chapter

2). While diffusioosmotic flows were directed radially outwards from the surface of the micropump, diffusiophoresis of negatively charged tracers in the bulk was directed inwards and upon advancing close to the glass surface, they were radially swept outward by the fluid flow

(Movie 1-1).

Figure 1-5. Schematic of the trajectories for the tracers dispersed in a system with CaCO3 micropumps. The negatively charged tracers are diffusiophoretically attracted towards the micropump in the bulk; and upon reaching the surface, are diffusioosmotically swept away by the fluid flow emanating radially outwards from the calcite microparticle.

Fluid flows generated from dissolving minerals provides a major breakthrough in the field of diffusiophoretic transport as it implies i) most of the subsurface earth which are newly formed during “disruptions” will produce such electrokinetic flows, and ii) transport at microscale can be precisely controlled by strategic placement of these micropumps. This enables us to use

12 electrokinetic behavior as cues for mineral transformations in geochemical systems, stick-slip motion of faults causing earthquakes, and power nanomaterials for site-specific cargo delivery (see

Chapter 6). We also discuss diffusiophoresis across concentration boundary layers in relation with dissolution from a calcite surface into a reactive stream of fluid (see Chapter 6, Section 6-3). Next we look at how chemical micropumps could be useful in membrane applications.

A common understanding in pressure driven filtration processes is that particle deposition on membrane surfaces occur primarily due to convective flows in the system. This is assumed to be true for flat sheet membranes used in reverse osmosis as well as for hollow fiber membrane

(HFM) modules.33,34 However, it is often ignored that deposition of salt on these membranes over time due to pressure (i.e. concentration polarization) can also cause back diffusion of ions into the bulk producing local electric fields which can generate diffusiophoresis of charged entities in the stream of flow. This can boost cake enhanced concentration polarization (CECP)35 resulting in water flux decline through the membrane surface. As a first step in the process, we conducted experiments with HFM in a quiescent flow to determine if diffusiophoresis indeed plays a role in fouling of membranes (discussed in Chapter 3). The questions we sought to answer are:

1-3-2. Transient Diffusioosmosis across Membranes

Do transient ionic gradients across hollow fiber membranes cause diffusiophoresis of tracers in the system, inducing fouling on the membrane? If it does, at what rate do membranes get fouled, and how can we prevent the fouling from occurring?

As seen in Fig. 1-6, we were able to show experimentally that particle deposition onto membrane surfaces can be enhanced by the presence of an ionic gradient across it (Movie 1-2).

13 The tracer particles, suspended in the bulk, were attracted normal to the membrane surface. The rates of particle motion increased as they got closer to the HFM containing salt since the gradients near the surface were the highest. We measured the required parameters like zeta potential of the colloids, concentration gradients across the membrane using dyes (under a confocal microscope) to determine the rates of particle fouling. We compared our results with the model for the system which used Fick’s 2nd law along with the conventional diffusiophoretic speed for particles (as discussed earlier). Our modeling result for speeds of tracers was consistent with the experimental observations. While these ionic gradients enhanced fouling on the membrane surface, we used

CaCO3 micropumps (as discussed earlier) to mitigate fouling which is discussed in Chapter 3.

While micropumps can generate fluid flows upon disruptions in nature, most of geologic reservoirs containing valuable resources like oil and gas are at steady state with respect to their surrounding fluid. These reservoirs contain dead-end pores that are not accessible through conventional pressure-driven or electrokinetic mechanisms.36-38 However, ionic gradients across

14 these dead-end pores are a common occurrence, which brings us to the third research objective in this thesis (details in Chapter 4)

1-3-3. Transient Diffusioosmosis in Dead-end Pores

What are the flow rates due to ionic gradients inside dead-end pores, and how far do they extend? Subsequently, how can the transport of mobile species be controlled based on the variation in - potentials and other physical parameters?

With this study of transient ionic gradients across dead-end pores, we moved away from the previous studies of diffusioosmosis (and diffusiophoresis) which were conducted for steady- state and uniform concentration gradients. In this work, we were able to create a simple yet robust set up where time-dependent and spatially non-uniform studies of transport of tracers (both oil emulsions and colloidal particles) could be conducted using salt gradients under the microscope.

15 By generating transient diffusioosmotic flows (TDOFs) in the set up, we observed convective transport of oil emulsions and tracers into and out of the dead-end pore (Movie 1-3) thus enabling quantitative exchange of materials. The speeds of the tracers were found to be as high as 50 μm/s close to the mouth of the pore. Our electrokinetic model (which employed the Stokes equations, ion migration equation, continuity equation, Poisson’s equation of electrostatics) combined with the Fick’s 2nd law of diffusion was able to accurately predict the enhanced rates of transport in our system.

The last and final objective of this thesis was to predict the mechanism behind pseudomorphic mineral replacement reactions which is a specific class of transformation occurring through mineral-water interactions. Pseudomorphic mineral replacement reactions (pMRRs) involve one mineral phase replacing another with the product phase inheriting the shape and texture of the parent mineral. These interfacial reactions are important in geochemical systems39 with familiar examples including fossilization and petrification.40 A key aspect of this process is that it generates porosity in the replaced phase which are dead-end in nature. Our interest is in leveraging the pores created during pMRR, chemically, to release trapped natural gas from shale formations during fracking process. However, in order to implement this across a broad spectrum of mineral, we need to address two fundamental interfacial questions:

1-3-4. Convective Flows in Mineral Replacement Reactions

What are the reaction rates and rate of recovery of trapped resources from minerals undergoing pMRR?

If they are transport limited, what is the relevant importance of convective and diffusive transport in such processes?

16 The experiments done for a pMRR of KBr crystal in a saturated KCl solution shows that the KBr completely transforms into KCl crystal upon exposure to a saturated solution of KCl. In doing so, the shape and the texture of the mineral is completely preserved, but it forms pores throughout the volume of the crystal which are dead-end (as shown in Fig. 1-8). To test if this transformation process was surface reaction limited, we conducted experiments in a flow-through cell which showed that the rates of replacement change upon changes in flow rates of saturated

KCl through the reactor. This warrants the reaction to be transport limited.

Figure 1-8. Sketch of pseudomorphic mineral replacement reaction occurring in a system of KBr crystal and saturated KCl solution. The replacement occurs via formation of a solid solution where chloride ions replace the bromide ions in the system forming an intermediate solid solution of K(Br,Cl). When the reaction is allowed to reach completion, the crystal transforms completely into a KCl crystal. This phenomenon is seen to proceed via preservation of shape and size of the parent KBr crystal. Further, in order to investigate the role of convective transport through the pores in the crystal, we used tracers of various sizes which were initially trapped in the KBr crystal. During replacement, these tracers were released in to the KCl solution at rates two orders faster than predictions made from their diffusion in solution. This was a surprising result, and it acts as a cue for presence of electrokinetic flows inside the pores during replacement. Development of a robust theory which explains this process will greatly enhance our understanding of geochemical transformations in nature. We carry forward this discussion in chapter 5 of the thesis.

17 1-4. Outline of the Thesis

The electrokinetic flows in our system are sometimes self-generated and at other times induced to study transport rates of tracers dispersed in the system. While CaCO3 dissolved to produce self-generated ionic gradients causing particle motion (Chapter 2), low concentrations of

NaCl and KCl were used to generate gradients in capillary set-ups. The fabrication details of these set-ups can be found in chapters 3 and 4. In Chapter 5, we operated with saturated solutions of KCl which were also seen to generate electrokinetic transport during mineral-water interactions. The tracers in our experiments were colloidal particles which were few microns in diameter and quantum dots which were 20 nm in diameter. Several sections in chapters 2-5 deal with the background theory behind diffusiophoresis and diffusioosmosis and chapter 6 provides a perspective towards the applicability of this transport phenomena in natural geologic and biologic systems. Appendices at the end give details on the modeling approach for HFM and flows in dead- end pores.

At a much broader level, the primary contribution of this thesis comes from developing simple experimental set-ups and their corresponding model to test the effect of chemical gradients across pores, both in low and high salt concentrations. The results in this thesis are reported from a kinetic standpoint, i.e. rates of motion, for both the fluid and the particle in the systems. Through the chemical energy driven transport process of diffusioosmosis, we were also able to analyze the dynamics behind internal mass transfer during chemical reactions and particle drift close to surfaces. These insights will advance our knowledge in geological mineral transformations (e.g. weathering and metamorphism)41, long-term radioactive waste storage42, carbon sequestration43, ground water remediation44, and mitigating fouling on membranes.

18 1-5. References

1. Whitesides, G. M. The origins and the future of microfluidics. Nature 2006, 442, 368-373.

2. Bocquet, L.; Charlaix, E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 2010, 39 (3),

1073.

3. Sparreboom, W.; Van Den Berg, A.; Eijkel, J. C. T. Principles and applications of nanofluidic transport. Nat. Nano. 2009, 4(11), 713-720.

4. Plecis, A.; Schoch, R. B.; Renaud, P. Ionic transport phenomena in nanofluidics: experimental and theoretical study of the exclusion-enrichment effect on a chip. Nano Let. 2005, 5(6), 1147-

1155.

5. Gijs, M. A. Device physics: Will fluidic electronics take off ?. Nat. Nano. 2007, 2(5), 268-270.

6. Wainright, A.; Nguyen, U. T.; Bjornson, T.; Boone, T. D. Preconcentration and separation of double‐stranded DNA fragments by electrophoresis in plastic microfluidic devices.

Electrophoresis 2003, 24(21), 3784-3792.

7. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport phenomena. John Wiley & Sons. 2007.

8. Lyklema, J. Electrokinetics after Smoluchowski. Coll. Surf. A: Phys. Eng. 2003, 222(1), 5-14.

9. Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions. Cambridge University

Press, 1989.

10. Landers, J. P. Molecular diagnostics on electrophoretic microchips. Anal. Chem. 75 (12),

2919–2927, 2003.

11. Velev, O. D.; Bhatt, K. H. On-chip micromanipulation and assembly of colloidal particles by electric fields. Soft Matt. 2006, 2 (9), 738.

19 12. Revil, A.; Schwaeger, H.; Cathles, L. M.; Manhardt, P. D. Streaming potential in porous media:

2. Theory and application to geothermal systems. J Geo. Res.: Solid Earth (1978–2012) 1999,

104(B9), 20033-20048.

13. Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247-269.

14. Anderson, J. L. Colloid transport by interfacial forces. Ann. Rev. Fluid Mech. 1989, 21(1), 61-

99.

15. Theurkauff, I.; Cottin-Bizonne, C.; Palacci, J.; Ybert, C.; Bocquet, L. Dynamic clustering in active colloidal suspensions with chemical signaling. Phys. Rev. Lett. 2012, 108(26), 268303.

16. Ebel, J. P.; Anderson, J. L.; Prieve, D. C. Diffusiophoresis of latex particles in electrolyte gradients. Langmuir 1988, 4(2), 396-406.

17. Palacci, J.; Abécassis, B.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Colloidal motility and pattern formation under rectified diffusiophoresis. Phys. Rev. Lett. 2010, 104(13), 138302.

18. Abecassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Boosting migration of large particles by solute contrasts. Nat. Mat. 2008, 7(10), 785-789.

19. Ebel, J. P.; Anderson, J. L.; Prieve, D. C. Diffusiophoresis of latex particles in electrolyte gradients. Langmuir 1988, 4(2), 396-406.

20. Anderson, J. L.; Prieve, D. C. Diffusiophoresis caused by gradients of strongly adsorbing solutes. Langmuir 1991, 7(2), 403-406.

21. Frankel, A. E.; Khair, A. S. Dynamics of a self-diffusiophoretic particle in shear flow. Phys.

Rev. E 2014, 90(1), 013030.

22. Morrow, N.; Buckley, J. Improved oil recovery by low-salinity waterflooding. J Petro. Tech.

2011, 63(05), 106-112.

20 23. (a) Yadav, V.; Duan, W.; Sen, A. Diffusiophoretic nano and microscale propulsion and communication. In Engineering of Chemical Complexity II. World Scientific. 2014. Pp. 73-91. (b)

Mitra, S. K., & Chakraborty, S. (Eds.). Microfluidics and Nanofluidics Handbook: Chemistry, physics, and life science principles. CRC Press. 2011.

24. Lyklema, J. Fundamentals of interface and colloid science (Vol. 5). Academic press, 2005.

25. Masliyah, J. H.; Bhattacharjee, S. Electrokinetic and colloid transport phenomena. John Wiley

& Sons, 2006.

26. Hidalgo-Alvarez, R.; Martin, A.; Fernandez, A.; Bastos, D.; Martinez, F.; De Las Nieves, F. J.

Electrokinetic properties, colloidal stability and aggregation kinetics of polymer colloids.

Advances Col. Int. Sc. 1996, 67, 1-118.

27. Derjaguin, B. V.; Sidorenkov, G. P.; Zubashchenkov, E. A.; Kiseleva, E. V. Kinetic phenomena in boundary films of liquids. Kolloidn. Zh. 1947, 9, 335-47.

28. Chiang, T. Y.; Velegol, D. Multi-ion diffusiophoresis. J Coll. Int. Sci. 2014, 424, 120-123.

29. Prieve, D. C.; Gerhart, H. L.; Smith, R. E. Chemiphoresis-A Method for Deposition of Polymer

Coatings without Applied Electric Current. Ind. Eng. Chem. 1978, 17(1), 32-36.

30. Eijkel, J. C.; van den Berg, A. Nanofluidics and the chemical potential applied to solvent and solute transport. Chem. Soc. Rev. 2010, 39(3), 957-973.

31. Ibele, M.; Mallouk, T. E.; Sen, A. Schooling Behavior of Light‐Powered Autonomous

Micromotors in Water. Ang. Chem. Int. Ed. 2009, 48(18), 3308-3312.

32. Sengupta, S.; Ibele, M. E.; Sen, A. Fantastic Voyage: Designing Self‐Powered Nanorobots.

Ange. Chem. Int. Ed. 2012, 51(34), 8434-8445.

33. Song, L.; Elimelech, M. Particle deposition onto a permeable surface in laminar flow. J. Col.

Int. Sci. 1995, 173, 165-180.

21 34. Sun, S.; Yue, Y.; Huang, X.; Meng, D. Protein Adsorption on Blood-Contact Membranes. J.

Mem. Sci. 2003, 222, 3-18.

35. Hoek, E. M.; Elimelech, M. Cake-enhanced concentration polarization: a new fouling mechanism for salt-rejecting membranes. Environ. Sc. & Tech. 2003, 37(24), 5581-5588.

36. Bear, J. Dynamics of Fluids in Porous Media; American Elsevier Publishing Company; New

York. 1972. pp 44-45.

37. Fuerstman, M. J.; Deschatelets, P.; Kane, R.; Schwartz, A.; Kenesis, P. J. A.; Deutch, J. M.;

Whitesides, G. M. Solving Mazes Using Microfluidic Networks. Langmuir 2003, 19, 4714-4722.

38. Goodknight, R. C.; Klikoff, W. A.; Fatt, I. Non-steady-state Fluid Flow and Diffusion in

Porous Media Containing Dead-end Pore Volume 1. J. Phys. Chem. 1960, 64, 1162 – 1168.

39. Putnis, A. Mineral replacement reactions: from macroscopic observations to microscopic mechanisms. Min. Magazine 2002, 66(5), 689-708.

40. Pewkliang, B.; Pring, A.; Brugger, J. The formation of precious opal: clues from the opalization of bone. The Canadian Min. 2008, 46(1), 139-149.

41. Glikin, A. E. Polymineral-metasomatic crystallogenesis. New York, NY : Springer Dordrecht:

Dordrecht, 2008.

42. Putnis, C. V. Direct observations of pseudomorphism: compositional and textural evolution at a fluid-solid interface. American Mineralogist. 2005, 90:1909-1912.

43. Putnis, A., Materials science. Why mineral interfaces matter. Science. 2014, 343:1441-1442.

44. Prieto, M.; Astilleros, J. M.; Fernandez-Diaz, L.; Environmental Remediation by

Crystallization of Solid Solutions. Elements. 2013, 9:195-201.

Chapter 2

Mineral Micropumps

The work in this chapter is adapted from the author’s paper: Joseph J. McDermott, Abhishek Kar,

Majd Daher, Steve Klara, Gary Wang, Ayusman Sen, and Darrell Velegol. "Self-generated diffusioosmotic flows from calcium carbonate micropumps." Langmuir 28, no. 44 (2012): 15491-

15497. A majority of the work was done by Dr. Joseph McDermott while my main contribution was towards validating few critical experimental concepts and re-writing the manuscript.

This chapter discusses a new paradigm in fluid flows driven solely from mineral dissolution. Conventionally, dissolution of a highly soluble mineral like borax (Na2B4O7·10H2O) or sylvite (KCl) is considered to be transport-limited as compared to low-solubility minerals like cinnabar (HgS) which are likely to be reaction limited. This is easier understood through varying the pH of the background solution. Transport-limited processes exhibit changes in rate of reaction upon changes in pH. On the contrary, rates of interfacial reaction limited processes are unaltered by variations in pH of the solution. However, minerals like calcite (CaCO3) exhibit both these properties at various pH values of the solution. Calcite is understood to be transport-limited at lower pH value while at higher pH values, diffusion across boundary layers is considered to be faster than surface reaction and hence the process is surface-reaction limited (further details in chapter 6).

The following work shows that at higher pH values, the transport mechanism that dominates over interfacial surface reaction is not diffusion but is rather electrokinetic flows

23 originating spontaneously in the system. These flows originate from differences in diffusion coefficients of ions emanating from a CaCO3 surface. Under these conditions, the concentration on the surface and the local solution concentration are almost identical which leads to dissolution and reprecipitation occurring on the mineral surface. This preserves the shape and size of the mineral in the system. The focus of the work is to understand the electrokinetic flows generated due to calcite dissolution.

2-1. Motivation: Self-generated Ionic Gradients

An increasing demand for the miniaturization of devices has led to a need for better control of pumping, mixing and moving of fluids to meet the desired needs.1 Since pressure driven mechanisms work poorly in tight or dead-end spaces, a need for an alternative mechanism for driving such flows is required.2-5 The advent of colloidal motors6-10 and micropumps11-13 provides alternative ways of attaining flows in micro and nanochannels through chemistry-based mechanisms. Electroosmotic pumping for applications in narrow channels has also been explored in the literature.14-17 However, there arises a significant limitation: electroosmotic pumps need an external power source that is not feasible in many difficult-to-reach spaces; for example, placing electrodes in tight geometries can be challenging. On the other hand, diffusiophoresis is a transport mechanism that operates based on the existence of a gradient of ion concentrations; no electrodes are needed. This mechanism has seen relatively little technological application, although it has recently been used in connection with DNA translocation and entrapment18 and colloidal transport.19-21

24 Diffusiophoresis converts the free energy of dissolution, precipitation, or chemical reactions into a directed motion of fluid and tracers. The flow mechanism of diffusioosmosis has been studied using both modeling22-24 and experiments25-27 using imposed salt gradients in 1- dimensional systems at steady-state. However, self-generated ionic gradients can be established when a solid dissolves into ions into an unsaturated solution. Such dissolution can occur when the thermodynamic equilibrium between the mineral and the surrounding water is disturbed, such as when new surfaces become exposed, allowing further dissolution of the minerals into surrounding aqueous regions. This physical phenomenon produces local ion gradients originating at the mineral surface. The gradients in turn drive microflows and particle movement along charged surfaces and pores by the mechanism of diffusiophoresis.

In this chapter, we show that the simple dissolution of calcium carbonate microparticles – a material ubiquitous in natural geologic formations – can self-generate electric fields of roughly

0.1-10 V/cm that pump fluids and tracer particles over distances many times greater than the carbonate particle radius. We also find that even for simple model systems, the interplay between the chemistry and fluid dynamics is complex, providing significant opportunities in designing flows and transport in regions that were previously inaccessible. In our systems we observe mesoscale flows with speeds reaching as high as 40 m/s. In short, the dissolution of the mineral particles provides a type of “localized battery”, while the charged surfaces provide the “pump” – even though surfaces act as a resistance to flow. Thus, we can use diffusioosmosis to drive flows in regions where pressure-driven flows cannot access.

25 2-2. Materials and Methods

2-2-1. Chemicals and Instruments Used

We synthesized our own CaCO3 and BaCO3 microparticles for experimental purposes. For calcium and barium carbonate microparticle synthesis, sodium carbonate (Na2CO3), calcium chloride (CaCl2), and barium chloride (BaCl2) were obtained from Sigma-Aldrich Chemicals,

USA. Two sizes of surfactant free sulfate-functionalized polystyrene latex microspheres (d = 1.4

μm ± 2.1%, and d = 3.0 μm ± 2.4%, both had w/v = 8.0%) and one batch of surfactant free amidine- functionalized polystyrene latex microspheres (d = 3.5 μm ± 2.1%, w/v = 4%) were purchased from Interfacial Dynamics Corporation, Portland, OR. These microspheres were used as tracers in our experiments to study flow behavior. The latex particles are abbreviated as sPSL for sulfate- functionalized polystyrene latex and aPSL for amidine-functionalized polystyrene latex throughout the entire text. Calcite samples (~1 mm square) were obtained from Petrobras (Rio de

Janeiro, Brazil). Gypsum and barite rock samples (10×2×2 cm, broken into 100 μm shards) were obtained through Amazon.com and are sold through MMP, LLC located in Denver, Colorado,

USA. Deionized (DI) water used in all aqueous solutions came from our Millipore Corporation

MilliQ system, with specific resistance greater than 1 MΩ·cm (due to equilibration with CO2 in air). Negatively charged square glass coverslips (22 mm х 22 mm) and petri dishes (10 cm × 1.5 cm) were obtained from VWR International. Borosilicate glass capillaries of 0.9 mm ID (Part #

8290-050) were obtained from Vitrocom for some of the experiments with natural rock specimen.

26 2-2-2. Calcium and Barium Carbonate Microparticle Synthesis

A simple precipitation synthesis was used to synthesize the calcium and barium carbonate microparticles. In both cases, 25 mL of a 0.33 M solution of CaCl2 or BaCl2 was stirred at high velocity on a magnetic stirrer. An additional 25 mL of 0.33 M Na2CO3 was then rapidly added to the solution, which turned milky white as the carbonate particles precipitated. The solution was stirred for an additional 1 to 2 min, and then quenched with 50 mL of DI water. To remove the

+ - remaining Na and Cl ions, the particle solutions were rinsed by repeated centrifugation and resuspension in DI water using a Sorvall Biofuge Primo Centrifuge from Kendro Laboratory

Products. The rinsing procedure was typically repeated for 2-4 times, with additional rinsing steps significantly affecting the microparticle size through carbonate dissolution. Using optical microscopy, the CaCO3 particles were found to be roughly spherical, with a polydispersity of

~50% and average radius 7-10 μm. They were found to be stable to aggregation for at least a day.

The BaCO3 particles were found to be smaller (d  1.5 μm, polydispersity ≈ 50%), and more shard- like.

2-2-3. Observing Pumping Behavior of Calcite Microparticles

To observe the pumping behaviour, the carbonate microparticles and tracers were imaged using a Nikon Eclipse TE2000-U inverted optical microscope, typically at 10 and 20 magnification. First, the concentrated carbonate particle solution was diluted to the desired concentration using DI water and using an ultrasonicator (model 550T) along with a Mini Vortexer

(with Speed Control), both obtained from VWR International, and then the microparticles were re- suspended in the solution. 500 μL was quickly pipetted into a glass-bottomed petri dish. An

27 additional 500 μL 0.1% w/v solution of tracer sPSL and aPSL particles was then added to the dish and the solutions mixed and observed.

2-2-4. Observation of Pumping Behavior of Natural Rock Samples

Similar to the procedure in the previous section, calcite (CaCO3), barite (BaSO4), and gypsum (CaSO4 • 2H2O) rock samples were placed in DI water in a glass bottomed petri dish.

Then, 0.1 vol.% tracer particle solutions were added and the resulting movement observed using optical microscopy. In certain cases, the experiments were performed in open capillaries that contained the tracer particle solution, to simulate the effect of dissolution into a microchannel or pore.

2-2-5. Zeta Potential Measurements of Latex Particles and Substrate

For zeta potential (ζ) measurements of sPSL and aPSL particles, we used a Zetasizer Nano

ZS90 (Malvern, MA, Model # ZEN3690). For measuring the ζ-potential of the glass substrate, we used a SurPASS device (Anton Paar, VA) for streaming potential. The ζ-potentials of particles were measured at 298 K using Disposable cuvettes (DTS1061) at ionic strengths of 0.1 mM – 50 mM and pH of 5.8. For ζ-potentials measurements of particles in salt solutions, the latex particles were first soaked in the salt bath for 15 minutes before the measurements were taken. The ζ- potential of walls was measured under various salt conditions and pH values to observe consistency.

28 2-2-6. Analysis of Pumping Behavior

Particle velocimetry was used to generate the plots in Fig. 2-4. Particle tracking of tracer particles was done by using ImageJ for a given number of video frames. To produce the velocity vector field plots in Figs. 2-4a and 2-4b, an appropriate number of tracers (between 700 and 1500) were analyzed over the entire region, encompassing a total analyzed time of ~30 seconds. Fig. A-

1 was prepared by analyzing 10-20 tracers surrounding a single microsphere over the course of

~10 seconds for each value of inter-particle distance. Average inter-particle distances were calculated from the surface fraction of calcium carbonate microspheres. For each sample, tracer velocity vs. radial distance was fitted to an exponential decay function, from which both the maximum tracer speed and decay lengths were taken. In no case did we apply pressure to our system to drive flow.

2-3. Results for Calcium Carbonate Micropumps

In the case of a solitary calcium carbonate “micropump” particles settled onto glass in DI water and surrounded by sPSL tracer particles, the particle flow field was readily observed (Fig.

2-1a and 2-1b). For negatively-charged tracers, the particles were pulled in rapidly from above the plate to the micropump particle surface (Fig. 2-2a). The tracers collected near (Fig. 2-2b) and moved down the surface of the micropump, and upon reaching the substrate, they were rapidly ejected radially outward into the solution (Movie 1-1 & 2-1).

a b

Figure 2-1. Microflows for one single CaCO3 particle micropump and two interacting micropumps. These systems contained only calcium carbonate pumps and 1.4 μm sPSL tracers in DI water. (a,b) time-lapse images. The videos were filmed on a bare glass substrate using an inverted microscope. Optical microscopy time-lapse images were taken at 40× magnification with overlays every 0.2 s. Scale bars in these images are 10 μm.

Movement of sPSL tracers away from the calcium carbonate particles was fast near the micropump’s surface, and decayed with distance until Brownian motion dominated the particle movement 10s of m away. We observed tracers that approached the pump at shallow angles being ejected without ever reaching the micropump surface. During the dissolution process, there appears an exclusion region of tracers near the pump particle on the glass surface. Some negatively-charged tracers adhered to the surface of the calcium carbonate microparticle (Fig. 2-

2b) and were only ejected after complete dissolution of the pump (Fig. 2-2c). These flow fields can be compared with the ones observed for catalytic micropumps28 where there is a recirculating flow pattern around the pump surface originating from similar mechanisms.

(a) 22++ -- -- (a) CaCa ++HHCOCO33 ++OOHH z CaCO3 micropump x y Glass cover slip Microscope Objective - -

CaCO3

Electroosmotic Flow Due to Electrophoresis ofof NegativeNegative Charged Substrate Sulfate Tracer ParticlesParticles

(b) (c)

The aPSL microparticles (3.5 µm diameter) were observed to have different flow paths, as seen in Fig. 2-3. Instead of being attracted from the bulk towards the micropump, these tracers are pushed away from the calcium carbonate surface since they are positively-charged, and so they do not aggregate near the micropump (Fig. 2-3b). However, aPSL particles settle vertically by gravity when they are a few micrometers away from the region defined by the calcium carbonate particle (Fig. 2-3a). They settle until they are near the glass surface, where they then are swept outward by the diffusioosmotic flow caused by the glass. This is in addition to their own

31 diffusiophoretic velocity, which also seeks to move them outward in the self-generated electric field. Very rarely do any of the aPSL tracers settle vertically onto the micropump.

2+ - - (a)(a) 2+ - - Ca + HCO3 +OHH z CaCO3 micropump x y Glass cover slip Microscope Objective + +

CaCO3

ElectroosmoticElectroosmotic Flow Due to Electrophoresis of Positive ChargedCharged Substrate Amidine Tracer Particles

(b) (c)

We used video microscopy to quantify the speeds and directions of the tracers. Fig. 2-4c and Fig. 2-4d were generated from velocity plots generated for a single micropump (Fig. 2-4a) and two interacting pumps (Fig. 2-4b). sPSL tracer speeds were found to decay roughly exponentially to around 1 µm/s at a distance of roughly 100 µm away from a solitary pump.

In the case when two pumps are near enough that their flow fields interact, a stagnation point arises at the midpoint between the pumps (Fig. 2-1b, Movie 2-1) for sPSL tracers. The sPSL tracers ejected from one CaCO3 particle move toward the other, and then escape in a direction

33 orthogonal to the line of centers between the CaCO3 particles. However, this is not the case with aPSL tracers (Fig. 2-3c), where there is no stagnation region between the calcium carbonate micropumps (Movie 2-2). Since the E field points away from pump’s surface, the positively- charged aPSL tracers are pushed away from the particle, and so do not settle near to it.

In our systems the dissolving CaCO3 gives rise to an electric field, and so acts as a type of localized battery. Due to the nature of electrokinetic flows, any charged surface becomes a type of pump. On the lower left of our CaCO3 micropump, there are two large tracer particles attached

(Fig. 2-1b), likely through van der Waals forces. These attached and charged particles generate additional local electroosmotic flow in the solution. That is, the surfaces act as additional pumps rather than hindering flow, and the tracers favor movement along these surfaces. Further experiments (Movie 2-3) confirm the nozzling phenomenon: by adding additional fixed charged surfaces, the flow of tracers can be focused or directed in the solution. This opens the possibility for designing complex flow patterns in dissolving mineral systems. The idea of “surfaces as pumps” can be used to direct flow for any desired application in spaces that are otherwise difficult to access.

2-4. Rates of Pumping by Calcite Micropumps

In trying to identify the mechanism of flow, we have examined the following phenomena:

1) thermally driven density flow, resulting from the heat of dissolution that is not homogeneous throughout the solution; 2) concentration difference density driven29, originating from difference in fluid densities due to the species produced upon dissolution of calcium carbonate into the solution, and 3) diffusiophoresis30, originating from concentration gradients of ionic species produced on

34 dissolution. We do not apply pressure to drive flow in any of our systems. For thermally-driven density changes, we estimate that negligible flows might arise, since the heat of dissolution of calcium carbonate in water is only 427 J/g.31 Over the time that the dissolution occurs, the heat would conduct over more than 1 cm in water. However, a simple heat balance shows that even if this heat were dissipated over a region as small as 1 mm in 20 min the temperature increase would be less than 0.001 C.

For density increases due to dissolved CaCO3, we use scaling estimates from the Stokes equations to evaluate the effect. The Stokes equations are

2 p   u  f (2-1)

.0u where u is the velocity of the fluid, p is the pressure, η is the viscosity of the solution, and f is any external body force acting in the system like gravity (g). Assuming steady state and low Reynolds number for the system, analysis reveals that density driven flow (U) scales as

(2-2)

Our estimate shows that density-driven flows account for a maximum of 1 µm/sec for micron-size particles dissolving into an infinite sink. An interesting consequence of this scaling behavior is the dependence of density-driven flows on the characteristic size of the particle. Because the speed scales as L2, where L is the characteristic dimension of the calcium carbonate microparticle, we expect that density-driven effects will become important as the particle size increases. We in fact see such density effects experimentally when we use mineral chunks (e.g., calcite, barite, gypsum) of roughly 1 millimeter in size, but not for micron size particles.

35 Because the pumping speeds we observe here are not consistent with thermal- or density- driven flow mechanisms, and because there is a dependence of the tracer particle transport on the surface potentials in the system, we now turn to diffusiophoresis and diffusioosmosis to provide an explanation for the observed behavior.

The trajectory of the tracer movement can be changed by changing the magnitude or sign of the particle surface potentials in the system (compare Fig. 2-2 and 2-3). This suggests that our microflows are electrokinetic – here, diffusiophoretic – resulting from the dissolution of CaCO3.

The flow field we see for our system is similar to that of a different problem from the literature: that of an electroosmotic flow field resulting from a lone sphere attached to a flat, charged plate, with an applied normal electric field.32 The circulating hydrodynamic flow lines cause the tracer particles to be pulled in from the top of solution and ejected radially outward along the bottom plate. This similarity in the flow field in parts suggests the electrokinetic mechanism and nature of our micropump CaCO3 particles.

How are our diffusiophoretic flows generated? First, it is important to recognize that in the presence of a large number density of CaCO3 particles, the solution becomes saturated with calcium carbonate, halting further dissolution, and generating no flows. CaCO3 is sparingly soluble in deionized water, with a solubility product constant of 3.3610-9 M2 at 20° C.23 However, when a dilute sample of CaCO3 microparticles exists in DI water, dissolution occurs at the particle surface into the fluid. Although after about 20 minutes the particles disappear from the system, during the dissolution process there is a radial concentration gradient of ions surrounding them which generates the flow.

The concentration profile for these ions can be found from Fick’s second law and can be expressed as (see Appendix A for details)

a  r  a  (2-3) C(r,t)  Cs  Cb  erfc   Cb r  4Dt  where the particle has a radius (a), and distance from the center of the particle is r and with erfc[] representing the complementary error function. D is the overall diffusion coefficient, the bulk concentration being Cb and the surface concentration being Cs. The complementary error function approaches unity at long time intervals (giving rise to steady state condition) with the concentration

2+ - varying as a function of 1/r. The primary ions resulting from this dissolution are Ca , HCO3 and

OH-. These ions contribute to the electric fields generated in the system, due to the differential diffusion described in the next paragraph.33 For the time scales of our observation, the solution acts as a sink as it is unsaturated with the ions produced upon dissolution of CaCO3. In a control test, calcium carbonate micropumps were suspended in saturated 0.5 mM CaCO3 solution with sPSL tracers dispersed in it and the whole sample was placed under a microscope for observation.

By having a saturated solution of the constituent ions, no concentration gradient forms, and the microparticles did not exhibit any pumping behavior on the glass surface, as expected.

The electric field driving the diffusioosmosis arises due to differential diffusion in the usual way. The three ions resulting from each molecule of dissolved calcium carbonate have

34 0 -9 2 -9 2 different diffusion coefficients . At 20 C, D OH = 5.2710 m /s, while D  = 1.1910 m /s and HCO3

-9 2 D Ca 2 = 0.79210 m /s. The ions cannot diffuse freely, however. A spontaneous electric field arises in order to maintain electroneutrality in the system (Fig. 2-2a and 2-3a). Since the hydroxyl ion diffuses 4 times faster than the bicarbonate ion, the electric fields are (along with the concentration gradient) oriented radially outward from the calcium carbonate microparticle surface. This electric field acts not only on the ions, but on any charged colloidal particles or surfaces in the region. This electric field, which in our system is between 1 ~ 10 V/cm, causes the

37 electroosmotic and electrophoretic transport of specimen described earlier. This overall process of an ion gradient effecting an electric field which drives electrokinetic transport is called diffusiophoresis.17

There is a further complexity behind our flow patterns and velocities of tracers. This is due to the chemistry of the system, and the changing particle zeta potentials depending on the local

CaCO3 and other ion concentrations. Table 2-1 below lists the zeta potential measurements of tracers and wall in various solution conditions determined through the Malvern instrument for particles and SurPASS (Anton Paar, VA) for glass cover slips. The diffusiophoretic speed of the tracers depends on ionic strength gradients in the usual way. In addition, the speed also depend upon the absolute local concentration, due to the adsorption of Ca2+ and the resulting change in particle zeta potentials over short distances. For example, the sPSL zeta potential, normally highly

35 negative in DI water, is suppressed in the presence of CaCO3 solution likely due to interactions between the calcium ions and sulfate groups. We found that this change can be manipulated by the addition of KCl ions to the system.36 When the micropump experiments were repeated with a 10 mM KCl solution, the direction of the tracer movement reversed as expected, since now the particle zeta potential had a greater magnitude than the substrate zeta potential (ζp- ζw > 0, Table 1 values).

At higher KCl concentrations (>100 mM), the motion slowed significantly due to ionic screening, which causes the diffusioosmotic flows mechanisms to become small, at least in the timescales of our experiments.

It should be noted here that due to the dynamic nature of calcium ion systems which adsorb on the surface of walls and particles, the zeta potentials could decrease further in magnitude for longer exposure times. Zeta potentials in simple, static systems are well-studied, but dynamic changes in zeta potentials in mixed systems of mineral particles – interacting by dissolution,

38 reaction, and precipitation – are much less well understood. In our system the ionic concentration surrounding the pump changes significantly with radial distance, causing a zeta potential that changes spatially, and since the particles are moving with time, therefore temporally.37 The effect of multivalent ions like Ca2+ on the surface charge of colloidal particles is especially important, as

38 seen for instance in the presence of a fully-dissociated salts (such as CaCl2).

Table 2-1. Zeta potential values (mV) in various solutions

0.5mM CaCO3 + Solution DI water 0.5mM CaCO3 10mM KCl 10mM KCl

3.0 µm sPSL -55 -30 -101 -91

Glass cover slip -70 -35 -62 -54

3.5 µm aPSL +45 +5 +35 +7

CaCO3 particles are not the only ones that drive diffusioosmotic flows. Barium carbonate

microparticles (Fig. 2-5) synthesized in a similar manner to the CaCO3 particles show nearly identical behavior. In fact, the pumping of the tracers is even faster for comparable particle surface fractions, due to the greater disparity in ionic diffusion coefficients between the Ba2+ and OH-.

Figure 2-5. Barium carbonate microparticle pumping 1.4 μm sPSL tracer particles outward, overlays are 0.33 sec apart, scale bar is 20 μm.

2-5. Summary and Future Remarks: Rate-Limiting Step

In conclusion we have shown that self-generated ion gradients resulting from mineral particle dissolution or precipitation can drive significant microscale flows and particle movement in mineral systems. Diffusioosmotic pumping is an effective flow mechanism in micro and nanochannels,28 often superior to pressure-driven flows (see Appendices). Whereas in pressure- driven flow the wall acts as a resistance to flow, in electrokinetic flows a charged wall acts as the pump. Diffusiophoretic flows are µm/sec, and are able to move fluid from very ‘tight regions”

(i.e., small pores, even 1 m or less) – perhaps even over small distances as “tributaries” – into more porous regions where traditional pressure-driven flow can access. Diffusioosmotic flows avoid channeling, where fluid simply goes around low-porosity regions. One application where a better understanding of diffusiophoretic pumping could have an immediate impact is in the geosciences and petroleum engineering. Water injection and rock fracturing are commonly practiced in oil wells39,40 and now in gas shales, and ion gradients will occur as a result. While the

40 overall fracking flows involve high pressures and millions of gallons of water, the mechanism of obtaining the desired petroleum or gas out of tight rock formations could depend significantly on mineral-driven microflows. Thus, diffusiophoretic pumping might contribute to the associated enhanced oil recovery, especially due to flooding with fresh water.41 Furthermore, in geologic events like earthquakes, spontaneous microflows might actively bleed chemical species from micro or nanochannels in rock to larger-scale bulk flows. The directionality obtained from this self-generated flow mechanism opens a new possibility of not only removing material from pores, but also for inserting material into pores These microflows must be considered further as an important area of microfluidics and nanogeoscience.

Beside these microparticles acting as a pump, we also discovered that electrokinetic fluid flows act as an alternate transport mechanism for calcites at high pH enabling mass transfer with the bulk solution. Previously, it has been considered that at high pH values, transport processes are faster than surface reaction, and hence diffusion dominates over the rate of reaction at the fluid- mineral interface.42 Our studies suggest that diffusion of ions actually lead to electrokinetic flows that can be controlled by changing the solution parameters. For example, by introducing a competing ion into the solution, the electrokinetic flows could be halted. This is especially useful as at high pH we can induce either the surface-reaction to be rate limiting or the electrokinetic flows to be rate limiting, giving us control over mineral dissolution properties. This can prove to be immensely helpful in understanding many of the geochemical processes like weathering and metamorphism where the electrokinetic flows are expected to affect the rate of mineral dissolution.

41 2-6. References

1. Whitesides, G.M. The Origins and the Future of Microfluidics, Nature 2006, 442, 368-373

2. Stone, H.A.; Kim, S. Microfluidics: Basic issues, Applications, and Challenges, AIChE J 2001,

47, 1250-1254

3. Stone, H.A.; Stroock, A.D.; Ajdari, A. Engineering Flows in Small Devices: Microfluidics toward a Lab-on-a-chip, Annu. Rev. Fluid Mech. 2004, 36, 381-411

4. Squires, T.M. Electrokinetic Flows over Inhomogeneously Slipping Surfaces, Phys. of Fluids

2008, 20, 092105

5. Eijkel, J.C.T.; van den Berg, A. Nanofluidics: What is it and what can we expect from it?,

Microfluid. Nanofluid. 2005, 1, 249-267

6. Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St. Angelo, S. K.; Cao, Y.; Mallouk, T.

E.; Lammert, P. E.; Crespi, V. H. Catalytic Nanomotors: Autonomous Movement of Striped

Nanorods, J. Am. Chem. Soc. 2004, 126, 13424-13431

7. Paxton, W. F.; Sen, A.; Mallouk, T. E. Motility of Catalytic Nanoparticles through Self-

Generated Forces, Chem. Eur. J. 2005, 11, 6462-6470

8. Paxton, W. F.; Baker, P. T.; Kline, T. R.; Wang, Y.; Mallouk, T. E.; Sen, A. Catalytically

Induced Electrokinetics for Motors and Micropumps, J. Am. Chem. Soc. 2006, 128, 14881-14888

9. Kline, T.R.; Paxton, W.F.; Mallouk, T.E.; Sen, A. Developing Catalytic Nanomotors,

Nanotechnology in Catalysis 2007, 23-37

10. Wang. J. Can Man-Made Nanomachines Compete with Nature Biomotors, ACS Nano 2009, 3

42 11. Kline, T.R.; Iwata, J.; Lammert, P. E.; Mallouk, T. E.; Sen, A.; Velegol, D. Catalytically Driven

Colloidal Patterning and Transport, J. Phys. Chem. B 2006, 110, 24513-24521

12. Solovev, A.A.; Sanchez, S.; Mei, Y.; Schmidt, O.G. Tunable Catalytic Tubular Micro-pumps at Low Concentrations of Hydrogen Peroxide, Phys. Chem. Chem. Phys. 2011, 13, 10131-10135

13. Sen, A.; Ibele, M.; Hong, Y.; Velegol, D. Chemo and Phototactic Nano/Microbots, Faraday

Discuss. 2009, 143, 15-27

14. Harrison, D.J.; Manz, A.; Glavina, P.G. Electroosmoic Pumping Within a Chemical Sensor

System Integrated on Silicon, Solid –State Sensors and Actuators 1991.

15. Manz, A.; Harrison, D.J.; Fettinger, J.C.; Verpoorte, E.; Ludi, H.; Widmer, H.M. Integrated

Electroosmotic Pumps and Flow Manifolds for Total Chemical Analysis Systems,

Transducers’91, International Conference on Solid-State Sensors and Actuators. 1991, Digest of

Technical Papers (Cat. No.91CH2817-5), 939-941

16. Nguyen, N.T.; Huang, X.Y.;Toh, K.C. MEMS-Micropumps: A Review, ASME Trans.—J.

Fluids Eng. 2002, 12, 384-392

17. Laser, D.J.; Santiago, J.G. A review of micropumps, J. Micromec. Microeng. 2004, 14, 35-64

18. Hatlo, M.M.; Panja. D.; Roij, R. Translocation of DNA Molecules through Nanopores with

Salt Gradients: The Role of Osmotic Flow, Phys. Rev. Let. 2011,107, 068101

19. Zhang, L.; Koo, J.M.; Jiang, L.; Asheghi, M.; Goodson, K.E.; Santiago, J.G.; Kenny, T.W.

Measurements and Modeling of Two-Phase Flow in Microchannels With Nearly Constant Heat

Flux Boundary Conditions, J. Microelectromech. Syst. 2002, 11, 12-19

20. Palacci, J.; Abécassis, B.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis, Soft Matter 2012, 8, 980-994

21. Palacci, J.; Abécassis, B.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Colloidal Motility and

Pattern Formation under Rectified Diffusiophoresis, Phy. Rev. Let. 2010, 104, 138302

22. Derjaguin, B.V.; Sidorenkov, G.P.; Zubashchenkov, E.A.; Kiseleva, E.V. Kinetic Phenomena in Boundary Films of Liquids, Kolloidn. Zh. 1947, 9, 335-347

23. Prieve, D.C.; Anderson, J.L.; Ebel, J.P.; Lowell, M.E. Motion of a particle generated by chemical gradients. Part 2. Electrolytes, J. Fluid Mech. 1984, 148, 247-269

24. Anderson, J.L. Colloid Transport By Interfacial Forces, Ann. Re. Fluid Mec. 1989, 21, 61-99.

25. Staffeld, P.O.; Quinn, J.A. Diffusion-induced banding of colloid particles via diffusiophoresis:

1. Electrolytes, J. of Col. and Intf. Sc. 1989, 130, 69-87

26. Ebel, J.P.; Anderson, J.L.; Prieve, D.C. Diffusiophoresis of Latex Particles in Electrolyte

Gradients, Langmuir 1988, 4, 396-406

27. Abécassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Boosting Migration of

Large Particles by Solute Contrasts, Nature Mat. 2008, 7, 785-789

28. Kline, T.R.; Paxton, W.F.; Wang, Y.; Velegol, D.; Mallouk, T.E.; Sen, A. Catalytic

Micropumps: Microscopic Convective Fluid Flow and Pattern Formation, J. Amer. Chem. Soc.

2005, 127,17150-17151

29. Brenner, H. Beyond the no-slip boundary condition, Phys. Rev. Let. E 2011, 84, 046309.

30. Anderson, J.L. Concentration dependence of electrophoretic mobility, J. Colloid Int. Sci. 1981,

82, 248-250

31. CRC Handbook of Chemistry and Physics, 67 ed. Boca Raton 1986, Florida: CRC Press. The heat of dissolution of calcium carbonate in water is 427 J/ gm.

44 32. Solomentsev, Y.; Böhmer, M.; Anderson, J. L. Particle Clustering and Pattern Formation during Electrophoretic Deposition: A Hydrodynamic Model, Langmuir 1997, 13, 6058-6068.

33. Prieve, D.C. Particle Transport: Salt and migrate, Nature Mat. 2008, 7, 769-770

34. Chaturvedi, N.; Hong, Y.; Sen, A.; Velegol, D. Magnetic Enhancement of Phototaxing

Catalytic Motors, Langmuir 2010, 26, 6308-6313

35. Kosmulski, M.; Matijević, E., Formation of the surface charge on silica in mixed solvents,

Colloid Polym. Sc. 1992, 270, 1046-1048

36. Kosmulski, M. Co-adsorption of Mono- and Multivalent Ions on Silica and Alumina, Ber.

Bunsenges. Phys. Chem. 1994, 98, 1062-1067

37. Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions 1989, Cambridge

University Press, New York

38. Elimelech, M.; O'Melia, C. R. Effect of Electrolyte Type on the Electrophoretic Mobility of

Polystyrene Latex Colloids, Colloids and Surfaces 1990, 44, 165-178.

39. Morrow, N. R.; Tang, G.; Valat, M.; Xie, X. Prospects of improved oil recovery related to wettability and brine composition, J. Pet. Sci. Eng. 1998, 20, 267-276.

40. Morgan, N. Less salt, more oil, BP Global Frontiers 2009, 25, 6

41. RezaeiDoust, A.; Puntervold, T.; Strand, S.; Austad, T. Smart Water as Wettability Modifier in Carbonate and Sandstone: A Discussion of Similarities/Differences in the Chemical

Mechanisms, Energy Fuels 2009, 4479-4485.

42. Brantley, S. L. Kinetics of mineral dissolution. In Kinetics of water-rock interaction 2008. pp.

151-210. Springer New York.

45 Chapter 3

Mitigating Fouling of Membranes through Diffusiophoresis

The work in this chapter is adapted from the author’s paper: Abhishek Kar, Rajarshi Guha, Nishant

Dani, Darrell Velegol, and Manish Kumar. "Particle Deposition on Microporous Membranes Can

Be Enhanced or Reduced by Salt Gradients." Langmuir 30, no. 3 (2014): 793-799.

In the previous chapter we observed that the dissolution of a sparingly soluble mineral like calcite (CaCO3) can create fluid flows in the system which are diffusioosmotic in nature. These micropumps generate rapid recirculation of fluid near its vicinity which could be useful in membrane operations like reverse osmosis (RO) and ultrafiltration (UF) processes. The efficiencies of these processes are affected by colloidal fouling (cake deposit) and accumulation of salt (concentration polarization, CP) on the membrane surfaces which cannot be avoided in the current methods of operations. Through experiments in a hollow fiber membrane (HFM) containing salt, we show that fouling of membranes could be enhanced due to diffusiophoresis in the system, with the salt gradient across the membrane acting as a constant source of “fuel” for the phoretic motion of dispersed colloidal particles. Further, the fouling was shown to be mitigated by the use of calcite micropumps which were able to dislodge particles off the HFM surface. Though these observations were carried out in a HFM under quiescent flow, further studies in our research group have indicated that diffusiophoresis could also be active under real RO and UF environment.

46 3-1. The Problem: Colloidal Fouling of Membranes

Colloidal particle deposition onto membranes is frequently cited as the primary cause of fouling in many industrial and scientific processes. The primary mechanism of the deposition for decades has been related to filtration; that is, as fluid is transported toward the membrane, it carries entrained particles that can penetrate into membrane pores or accumulate on membrane surfaces.

Particle-membrane interactions (primarily electrostatic1 and hydrophobic interactions2) then lead to immobilization and flux decline. Here we explore the importance of an additional process, called diffusiophoresis, in causing particle transport towards or away from microdialysis membranes.

Despite the fact that the transport process of diffusiophoresis has been known for over 65 years3-

5, this mechanism has not been examined so far in membrane science to explain particle deposition on membrane surfaces.

Diffusiophoresis is a process of particle transport in a salt gradient6-9. The process has been shown experimentally to cause transport of particles in steady-state salt gradients10, and the experimental results well-explained using electrokinetic modeling11. More recently, dissolving calcium carbonate particles, and other geologic and biologic systems, have been used to create salt gradients that drive particle motion12 through this mechanism.

3-1-1. Brief Overview of Diffusiophoresis

Here we provide a brief description of the mechanism of diffusiophoresis caused by salt gradients (n) present in a system. When a salt gradient exists, it often happens that the ions from the salt diffuse at different rates based on their different diffusion coefficients in the solution. A finite difference in diffusion coefficients of the constituent ions can give rise to a spontaneous

47 electric field (E) in solutions4, which then causes electrophoresis of particles. Furthermore, the particles can also migrate due to a “chemiphoretic” mechanism6-8. The origin of this mechanism is somewhat subtle, but well-known. In essence, within the electrical double layer (EDL), the fluid pressure is higher than in the bulk, and this pressure increases with ionic strength (smaller Debye length). Thus, when a gradient of ionic strength exists, a pressure gradient exists across the surface.

For a symmetric Z:Z electrolyte, the combination of these two effects results in particle motion with a speed (Udp) given by

22  kT D D2 k T2 Ze p n Udp p 22ln 1  tanh  (3-1)  Ze D D Z e4 kT n where e is the proton charge, ε is the permittivity of the medium,  is the solution viscosity, D+ and D- are the diffusivities of cation and anion respectively, ζp is the particle zeta potential, k is the

Boltzmann constant, T is temperature and n is the concentration of the salt. Typically, a charged particle with a zeta potential of order of 2kT/e (~ 50 mV) will move due to electrolyte gradient of

1 M/cm with speeds of several micrometers/sec.

While diffusiophoresis is well-known, it has not been explored as a mechanism that affects colloidal fouling in a membrane system. In many membrane systems, a gradient of ionic strength is produced either through rejection of solutes at the surface (for e.g., reverse osmosis) or by diffusion of salts between feed and permeate streams (for e.g., dialysis). Solute gradients at the membrane surface (concentration polarization) can lead to a build-up of a gel layer (e.g., of proteins), which reduces flux in diafiltration and hemodialysis13-15. In water membrane filtration systems, salt concentration polarization, cake layer build-up and change in ionic strength have been attributed to particle deposition and flux decline16-19.

48 3-1-2. Objectives of the Chapter

Our overarching goal in this article is to show that diffusiophoresis can be an active mechanism for particle migration in membrane modules. The aim of this study is threefold. Firstly, to establish the effect of diffusiophoresis occurring in membrane systems due to transient salt gradients, both numerically and experimentally. Secondly, to demonstrate that the rates of particle migration towards or away from a membrane under applied ionic gradients can be understood through diffusiophoresis. And finally, to show that colloidal fouling in membrane systems can be prevented by strategic placement of chemical micropumps (e.g. calcium carbonate micropumps) which create rapid vortices and fluid flow in the system. With the use of microdialysis membranes and sulfate polystyrene tracers (sPSL) we show that particle migration can be actively controlled by the types of ions present in the system, the ionic gradient and the zeta potentials of tracers. Our study provides new capabilities for controlling and mitigating fouling occurring in membranes during water purification, diafiltration and hemodialysis.

3-2. Materials and Methods

3-2-1. Membrane and Chemicals Used

Our transient salt gradient was generated by using a simple approach of filling a single 13 kDa hollow fiber membrane (HFM) with a salt solution and letting it diffuse out over time. For making the salt solution, we used lithium chloride (LiCl), sodium chloride (NaCl) and potassium chloride (KCl), all obtained from Sigma Aldrich. Various concentrations of these salt solutions were prepared using de-ionized (DI) water obtained from a Millipore Corporation Milli-Q system, with a specific resistance of 1 M.cm (due to equilibration with CO2 in air). We synthesized our

CaCO3 microparticles for experimental purposes using sodium carbonate (Na2CO3) and calcium chloride (CaCl2) which were also obtained from Sigma-Aldrich. Lucigenin dye (mol. weight 511) used to map gradient intensity of chloride ions in the system was obtained from Invitrogen

Molecular Probes (Eugene, OR). Colloidal sulfated polystyrene latex (sPSL) particles ( = 3.0 µm

± 2.1%, w/v = 8%) used for observing transport under salt gradient were procured from Interfacial

Dynamics Corporation (Portland, OR). Red fluorescent sPSL microspheres ( = 4.0 µm ± 2.0%, w/v = 2%, ex/em = 580 nm/ 605 nm) were also used for some confocal microscopy experiments.

Borosilicate glass square capillaries of 0.9 mm size (part # 8290-050) were obtained from

Vitrocom (Mountain Lakes, NJ).

3-2-2. Calcium Carbonate Microparticle Synthesis

Calcium carbonate microparticles were used to mitigate fouling in our systems, by acting as “diffusioosmotic micropumps”. The particles were synthesized using a route described by

20 Volodkin et. al . Using optical microscopy, we found that the CaCO3 microparticles were roughly spherical with an average radius of 7 ~ 10 µm. As explored in our previous chapter these microparticles act as micropumps in a DI water solution containing negatively charged sPSL tracer particles due to an enhanced diffusiophoretic effect.

3-2-3. Salt Gradient in a Closed System

Our gradients were set up by placing a HFM inside of a 1 mm or 0.9 mm square capillary.

We used a single regenerated cellulose microdialysis hollow fiber membrane (HFM) which had a

280 μm outside diameter (OD) and 40 μm wall thickness for each of our experiments. HFM fibers were obtained from Spectrum Labs, Rancho Dominguez, CA. Each HFM was washed with ethanol

50 using one ml syringes (BD Biosciences) fitted with a 21G precision needle before use. HFM was then washed again with 10 mM NaCl (or 10 mM KCl, 10 mM LiCl), loaded with 10mM NaCl and both ends of the hollow fiber were sealed with wax. The sealed HFM was inserted into either a 0.9 mm or 1 mm square glass capillary (Vitrotubes). The capillary surrounding the HFM was filled with DI water containing suspended sPSL beads (< 0.1 % v/v), mounted on a VWR glass microslide (25 mm × 75 mm) and closed at both ends with paraffin wax. Sealed HFMs were used to avoid convective motion across the fiber bore, so that diffusion of ions across the wall was the only way through which charged beads could sense the salt gradient. For observing the motion of tracers in response to CaCO3 micropumps, the CaCO3 microparticles were placed inside the glass capillary which contained the tracer beads.

3-2-4. Observation and Analysis Tools

We used both an inverted light microscope and a confocal microscope to image our systems. Brightfield observation of particle motion was made on a Nikon inverted microscope

(Eclipse TE2000-U) fitted with an optical light source and CCD camera (Q-Imaging). Nikon NIS

Elements Imaging Software (V. 4) was used for particle velocity measurements and tracking. A

Leica TCS SP5 laser scanning confocal microscope (LSCM, Leica Microsystems) was used for dye imaging and experiments with fluorescent beads. Observations were made at 10× magnification for most cases. Image intensity profiles were analyzed using ImageJ software

(National Institutes of Health).

51 3-2-5. Determination of Chloride Concentration Profile

In order to measure the Cl- concentration in our system we used a fluorescence quenching based measurement technique21. We used the fluorescent probe, lucigenin which is commonly used to detect superoxide21 but is also known to be quenched by halide ions and has been employed in assays to detect chloride transport using biological transporters. With restricted illumination from the confocal microscope, we standardized our intensity profile obtained from Lucigenin using the Stern-Volmer equation (Eqn. 3-2) for various concentrations of Cl- in the system.

FFK= 1+ [Cl] (3-2) 0 Cl-- Cl

- - Here, F0 is the fluorescence intensity in the absence of Cl , FCl is the fluorescence intensity in the

- - presence of varying concentration of Cl , KCl is the Stern-Volmer constant and [Cl] is the

- concentration of the salt. By plotting F0/ FCl for various values of [Cl], we obtained KCl to be 365 mM-1 which was then used to find the concentration of Cl- at various measured intensities.

3-2-6. Zeta Potential Measurements of Latex Beads

For zeta potential (ζ) measurements of sPSL tracers (both fluorescent and non-fluorescent), we used a Zetasizer Nano ZS90 (Malvern, MA, model ZEN3690) equipment. The ζ potential of the beads were measured at 298 K using disposable cuvettes (DTS1061) at ionic strengths of 0.1

– 100 mM salt concentration and pH of 5.8. Zeta potential of membrane was not critical to our observation as we measured tracer velocities away from the membrane.

52 3-3. Inducing Fouling on Membranes through Salt Gradients

The hypothesis that diffusiophoresis affects particle deposition was tested under salts of different concentrations using the HFM setup. Fig. 3-1 shows a schematic of the experimental set- up. HFMs were filled with 50 mM NaCl salt solution, then closed at all openings, and placed inside a capillary containing DI water (or the same salt with concentration < 50 mM). The DI water outside the HFM contained negatively charged sPSL tracer beads (Fig. 3-1a). Due to the high ionic gradient near the HFM, rapid deposition of beads onto the membrane surface was observed (Fig.

3-1). Because of the setup time for the experiments, which is typically at least 2 minutes, we were unable to see the initial motion of tracers towards the membrane surface. However, t > 150 s, distinct layers of particle aggregation are observed on the membrane surface (Fig. 3-1b). This physical deposition onto the membrane surface occurs without any external pressure or applied electric field. The chemical energy of the salt gradient is transduced into directed diffusiophoretic transport of the colloidal beads, which results in particle deposition along the membrane surface.

However, by using chemical micropumps, in the form of calcium carbonate microparticles, colloidal deposition can be reduced or even reversed on the membrane surface especially if the micropumps are immobilized close to the surface of the HFM (Fig. 3-1c). The use of CaCO3 reverses the direction of the diffusiophoresis, as explained later. This results in clear exclusion zones of colloidal beads near the surface of the membrane, which grows over time resulting in complete mitigation of particle deposition. Such an auto-electrokinetic effect observed from dissolving minerals, studied in our earlier chapter12, could serve as a motivation for improved designs of hollow fiber modules used in water purification processes in order to disrupt concentration polarization and fouling effects.

54 Previous accounts of diffusiophoretic transport in the literature have primarily focused on steady-state and homogeneous concentration gradients in aqueous systems. However, in our case, a temporal concentration gradient was set-up across the membrane surface due to a finite source

(salt solution) and a finite sink (DI water). This time-dependent and spatially non-uniform salt gradient set up transport of particles towards the higher salt regime, as our images in Fig. 3-2 show.

At a higher NaCl concentration (50 mM) inside the HFM, enhanced particle deposition was observed on the outside wall of HFM (Fig. 3-2b). The deposition thickness increased when the inside salt concentration was changed from 10 mM NaCl (Fig. 3-2a) to 50 mM NaCl.

To account for possible deposition effects induced due to gravitational settling, we switched to a vertical set-up of the HFM. Figs. 3-3a and 3-3b show the same configuration (50 mM NaCl inside the HFM and DI water with latex beads outside) in a vertical and horizontal setup, respectively. The degree of aggregation was observed to be similar in both cases.

Next we sought to distinguish the diffusiophoretic mode of transport from conventional osmotic flow. By using different solutes- NaCl inside and sucrose outside the HFM - we were able

55 to create systems with the same osmotic pressure on both sides of the membrane. Fig. 3-3c displays particle deposition for an isoosmolar set-up with NaCl inside and sucrose (with fluorescent sPSL beads) outside. The aggregation was similar to that observed with 10 mM NaCl inside HFM

(shown in Fig. 3-3d).

Our experimental set-up allowed us to isolate the effect of diffusiophoresis from pressure or osmotic gradient-driven flows that could possibly dominate in conventional membrane testing setups. Next, we moved onto quantifying these observations which would validate our hypotheses.

These are discussed in the following section

56 3-4. Discussion

To the best of our knowledge, no previous studies have connected particle deposition on membranes with diffusiophoresis, however, numerous accounts of electrolyte diffusiophoresis9,10,23,24 and vapor diffusiophoresis25-27 have appeared in literature. The key hypothesis of this chapter is that diffusiophoresis plays an important role in particle transport towards or away from a membrane in the presence of a salt gradient. In the following paragraphs we discuss the development of the salt gradient in the HFM system used, model and measure particle velocities, and describe an approach to mitigate particle deposition on the membrane.

3-4-1. Development of Transient Salt Gradient

Since our membrane had a large molecular weight cut-off (MWCO =13 KDa) compared to the salt solutes used, the solutes diffuse through the membrane surface out into the bulk. With the salt solution inside the HFM and DI water containing tracers outside, a transient salt concentration gradient is set up (dn/dt  0) that is also spatially non-uniform (dn/dr  0). We modeled transient effect using Fick’s second law in cylindrical coordinates with the assumption that the Debye lengths in our system are infinitesimally small, by solving Eqn. 3-3

n( r , t ) 2 n ( r , t ) 1  n ( r , t ) (3-3) D *02   t  r r  r

where D*  2D D /D  D  is the effective diffusion coefficient (also referred to as ambipolar diffusion coefficient) for a Z:Z symmetric electrolyte due to electroneutrality in the system. The

4 rigorous explanation for using D* is reviewed by Anderson . The initial conditions are n(0,r) = n0

57 for r < Rm and 0 for r  Rm. The flux of ions at the center of the HFM and at the capillary wall surface set to zero to form our boundary conditions (see Appendix B).

We compared our model with experimental concentration profiles (Fig. 3-4). After proper calibration, fluorescence intensities were measured at different distances away from the wall of the HFM and plotted as shown in Fig. 3-4b. The experimental results showed a good fit to our modeling predictions. The sidewalls of the capillary posed experimental difficulties when we sought to measure the fluorescence intensity near to it; nevertheless, our data matches our model within 200 µm of the HFM wall. The concentration gradient established was linear near the membrane, but non-linear away from it. Our modeled speeds are consistent with a linear concentration gradient at the particle size scale as described by Khair28. We hypothesize that these calculations for diffusiophoresis will still hold for concentration gradients that are non-linear on the length scale of the particle. This is based on Anderson’s result for electrophoresis29 where he showed that spherical particles in a non-linear E field still translate at Smoluchowski’s electrophoretic speed, if the E field is chosen at the particle center.

3-4-2. Generation of Electric Field

The transient salt gradient gave rise to a spontaneous electric field

E kT/()/() Ze D D  D  D   nn in the system. This occurs due to the difference in

+ + -9 2 diffusion coefficients of the constituent ions, since, a Na (DNa = 1.334x10 m /s) diffuses slower

- - -9 2 than a Cl ion (DCl = 2.032x10 m /s). Difference in diffusion coefficients are quantified by β,

where β = DDDD )(    In cases where the diffusion coefficients of the ions don’t differ

+ - -9 2 by much (e.g. in case of KCl, DK ≈ DCl = 2.032 x 10 m /s), β ≈ 0, the electrophoretic part of

59 Eqn. 3-1 vanishes and the transport is only caused by chemiphoresis. As expected, the particles move at a much slower rate than observed in case of NaCl (where β ≈ -0.207).

3-4-3. Diffusiophoretic Speeds

We show that proper quantification of zeta potentials (ζ) and salt gradients in the system can enable us to perfectly predict the rates of transport of tracers towards the membrane surface.

Fig. 3-5a shows modeled and measured diffusiophoretic speeds of sPSL beads due to a gradient of NaCl. Salt gradient induced by 10 mM NaCl inside the HFM caused particle migration towards the wall with measured speeds in the range of ~ 0.1- 0.3 μm/s after 2-3 minutes. Particle speeds decrease with time as n/n becomes smaller. Initially, when the gradient has not dissipated, diffusiophoretic speeds are estimated to be in the range of 10’s of µm/s. The observed speeds are relatively low compared to convective velocities in membrane systems, however, the gradients utilized here are small and transient.

In modeling the system, inside and outside diffusivities are assumed as solute diffusivity in water. Diffusivity through the membrane was calculated using capillary pore diffusion model accounting for the Stokes radius of each ion30. The effective diffusion coefficient values are provided in the Appendix B. The concentration dilution outside HFM was observed with lucigenin, which also supported modeled concentration in bulk region of capillary, devoid of wall effects.

Fig. 3-5b compares diffusiophoretic speeds of sPSL at t ~ 3 min in presence of LiCl, NaCl

 and KCl gradients, each present inside HFM at 10 mM initial concentration. Since Li ions have

+ + -9 2 + -9 2 lower diffusion co-efficient than Na ions (DLi = 1.03 x 10 m /s and DNa = 1.334 x 10 m /s) and thus βLiCl > βNaCl, a stronger electric field is generated (~ 0.8 V/m for LiCl and ~ 0.45 V/m for

60 NaCl). On the other hand, K+ ions have comparable ion diffusivity as that of Cl-, which leads to very weak electric field of the order of ~0.035 V/m and subsequent sPSL tracer movement mainly through chemiphoretic mechanism with half the speed of NaCl case. Experimental measurements are corroborated by system modeling of diffusiophoretic velocity profiles, both spatiotemporally

(Fig. 3-5a) as well as with different salts (Fig. 3-5b). The particle speeds in our system were not affected by any fluid flow mechanism such as diffusioosmotic flows that can arise on charged surfaces due to salt gradients. These fluid flows were negligible in our case since the salt gradients were orthogonal to the surface of the membrane. Further, the contribution from fluid flows inside the pores of the membrane scaled only as far as 1 µm away from the membrane surface for a 100 nm pore.

61 as measured and modeled for 10 mM NaCl, 10 mM KCl or 10 mM LiCl inside HFM/ 3 μm sPSL beads in DI outside at t ~ 180 s in 1 mm ID capillary (for NaCl & KCl) and 0.9 mm ID capillary (for LiCl). The symbols represent experimental velocities and the lines represent modeled velocities. The asymmetric velocity profiles show a dependence on physical placement of the HFM within the capillary and the time scales of measurements. The maximum velocity of the particles corresponds to the position where maximum n/n occurs.

3-4-4. Mitigating Fouling through Calcite Micropumps

The behavior of particle transport was seen to be altered by changing the positioning of salt in the system. However this effect was most evident when we used CaCO3 micropumps outside

HFM, in the bulk region of capillary which completely reversed the motion of tracers in a NaCl gradient (Fig. 3-6). The difference between effects of calcium carbonate and sodium chloride results in particle motion towards the dominant species in the system i.e. CaCO3 micropumps.

Since the gradient of NaCl dies down rapidly to a more stable value, the system functions similar to a gradient emanating from a single source.

62 at 4 minutes in (b). (c) shows the same after t =1 min and (d) shows the system after approximately 15 minutes.

Reversing the electric field created by a salt gradient using dissolving CaCO3 in the bulk solution can prevent or reverse particle deposition. McDermott et al. showed how CaCO3 microparticles are able to generate strong diffusiophoretic transport during the dissolution process

12 - - 2+ in DI water on glass substrates . The dissolution generates OH , HCO3 ,and Ca ions with

-9 2 -9 2 considerable diffusivity differences (DOH- = 5.27 x 10 m /s, DHCO3- = 1.19 x 10 m /s and DCa2+

= 0.792 x 10-9 m2/s), sufficient to generate a stronger electric field than NaCl owing to the high diffusion coefficient of the hydroxyl ion. When CaCO3 microparticles are kept on the outside surface of the HFM, an electric field towards the membrane and opposite to that generated by the

NaCl is developed. This reverse electric field in conjunction with lower ζp (-67.9 mV) in presence of CaCO3 reduces tracer speeds and eventually removes particles from HFM surface creating an exclusion zone (Figs. 3-6a and 3-6b).

The CaCO3 particles (Fig. 3-6a) create an exclusion region of tracer beads (Fig. 3-6b) next to the membrane surface. This observation supports our idea that we can reduce or reverse particle deposition by controlling the direction of the diffusiophoresis in the system (Movie 3-1). Figs. 3-

6c and 3-6d are a series of time lapse images showing how particle aggregation near to HFM is affected with time in presence of 0.1 mM CaCO3. The resultant electric field in NaCl-CaCO3 system does not allow particle deposition on the membrane. The particles remain stable or relax at a certain distance from the membrane wall (exclusion zone in Fig. 3-6b) and slowly move out towards capillary wall (Fig. 3-6d), possibly because of resultant opposite electric field.

63 3-5. Conclusion

Particle deposition onto membranes causes fouling, and is thus a bottleneck in many membrane processes. In this chapter we have explored the hypothesis that particle deposition occurs not only due to a filtration effect, but also due to a diffusiophoretic transport effect. We investigated a system with induced salt gradients across the wall of a microporous hollow fiber membrane and observed that particle deposition is enhanced by the proposed mechanism of diffusiophoresis. By measuring and modeling all the required parameters (zeta potential, concentration gradient and diffusion coefficients) in the system we observe overall agreement between our t modeled speeds and experimental results to within 17%. With an understanding of the role of this mechanism, we were successful in reducing particle deposition using CaCO3 micropumps. The experiments and analyses presented in this chapter may further our understanding of particle deposition in membrane systems in the presence of salt gradients and provide possible ways of mitigating excessive particle deposition and accompanying flux decline.

64 3-6. References

1. Faibish, R.S.; Elimelech, M.; Cohen, Y. Effect of interparticle electrostatic double layer interactions on permeate flux decline in crossflow membrane filtration of colloidal suspensions: an experimental investigation. J. Coll. Int. Sc. 1998, 204, 77-86

2. Hadidi, M.; Zydney, A.L. Fouling behavior of zwitterionic membranes: Impact of electrostatic and hydrophobic interactions. J. Mem. Sc. 2013, 452, 97-103.

3. Derjaguin, B. V.; Sidorenkov, G. P.; Zubashchenkov, E. A.; Kiseleva, E. V. Kinetic Phenomena in Boundary Films of Liquids. Kolloidn. Zh. 1947, 9, 335-347.

4. Anderson, J.L. Colloidal transport by interfacial forces. Ann. Rev. Fluid Mech. 1989, 21, 61-99.

5. Sharifi-Mood, N.; Koplik, J.; Maldarelli, C. Diffusiophoretic self-propulsion of colloids driven by surface reaction: The sub-micron particle regime for exponential and van der Waals interactions. Phy. Fluids 2013, 25, 012001.

6. Anderson, J.L.; Lowell, M.E.; Prieve, D.C. Motion of a Particle Generated by Chemical

Gradients. Part I: Non-Electrolytes. J. Fluid Mech. 1982, 117, 107-121.

7. Prieve, D.C.; Anderson, J.L.; Ebel, J.P.; Lowell, M. E. Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247-269.

8. Palacci, J.; Benjamin, A.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Colloidal motility and pattern formation under rectified diffusiophoresis. Phy. Rev. Let. 2010, 104, 138302.

9. Abecassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Boosting migration of large particles by solute contrasts. Nat. Mater. 2008, 7, 785-789.

10. Ebel, J. P.; Anderson, J. L.; Prieve, D .C. Diffusiophoresis of latex particles in electrolyte gradients. Langmuir 1988, 4, 396-406.

65 11. Chen, Y. P.; Keh, H. J. Diffusiophoresis and Electrophoresis of a Charged Sphere Parallel to

One or Two Plane Walls. J. Col. Int. Sci. 2005, 286, 784-791.

12. McDermott, J.; Kar, A.; Daher, M.; Klara, S.; Wang, G.; Sen, A.; Velegol, D. Self-generated diffusioosmotic flows from calcium carbonate micropumps. Langmuir 2012, 28, 15491-15497.

13. Sun, S.; Yue, Y.; Huang, X.; Meng, D. Protein Adsorption on Blood-Contact Membranes. J.

Mem. Sci. 2003, 222, 3-18.

14. Ahrer, K.; Buchacher, A.; Iberer, G.; Jungbauer, A. Effects of ultra-/diafiltration conditions on present aggregates in human immunoglobulin G preparations. J. Mem. Sci. 2006, 274, 108-115.

15. Rosenberg, E.; Hepbildikler, S.; Kuhne, W.; Winter, G. Ultrafiltration concentration of monoclonal antibody solutions: Development of an optimized method minimizing aggregation. J.

Mem. Sci. 2009, 342, 50-59.

16. Song, L.; Elimelech, M. Particle deposition onto a permeable surface in laminar flow. J. Col.

Int. Sci. 1995, 173, 165-180.

17. Hoek, E. M. V.; Kim, A. S.; Elimelech, M. Influence of crossflow membrane filter geometry and shear rate on colloidal fouling in reverse osmosis and nanofiltration separations. Environ. Eng.

Sci. 2002, 19, 357-372.

18. Hoek, E. V. M.; Elimelech, M. Cake-enhanced concentration polarization: a new fouling mechanism for salt rejecting membranes. Environ. Sci. Technol. 2003, 37, 5581–5588.

19. Nuang, S.; Ye, Y.; Chen, V.; Fane, A. G. Investigations of the coupled effect of cake-enhanced osmotic pressure and colloidal fouling in RO using crossflow sampler-modified fouling index ultrafiltration. Desalination 2011, 273, 184-196.

20. Volodkin, D. V.; Petrov, A. I.; Prevot, M.; Sukhorukov, G. B. Matrix polyelectrolyte microcapsules: new system for macromolecule encapsulation. Langmuir 2004, 20, 3398-3406.

66 21. Biwersi, J.; Tulk, B.; Verkman, A. S. Long-wavelength chloride sensitive fluorescent indicators. Anal. Biochem. 1994, 219, 139-143.

22. Li, Y.; Zhu, H.; Kuppusamy, P.; Roubaud, V.; Zweier, J. L.; Trush, M. A. Validation of lucigenin (bis-N-methylacridinium) as a chemilumigenic probe for detecting superoxide anion radical production by enzymatic and cellular systems. J. Bio. Chem. 1998, 273, 2015-2023.

23. Staffeld, P. O.; Quinn, J. A. Diffusion-Induced Banding of Colloidal Particles via

Diffusiophoresis 1. Electrolytes. J. Col. Int. Sci. 1989, 130, 69-87.

24. Palacci, J.; Bizonne, C. C.; Ybert, C.; Bocquet, L. Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis. Soft Matter 2012, 8, 980-994.

25. Hidy, G. M.; Brock, J. R. Lung deposition of aerosol- a footnote on the role of diffusiophoresis.

Environ. Sci. Technol. 1969, 3, 563-567.

26. Lehtinen, K. E. J.; Hokkinen, J.; Jokinemi, J.; Gamble, R .E. Studies on Steam Condensation and Particle Diffusiophoresis in a Heat Exchanger Tube. Nuc. Eng. Desi. 2002, 213, 67-77.

27. Grohn, A.; Suonmaa, V.; Auvinen, A.; K. Lehtinen, K. E. J.; Jokiniemi, J. Reduction of fine particle emissions from wood combustion with optimized condensing heat exchangers. Environ.

Sci. Technol. 2009, 43, 6269-6274.

28. Khair, A. S. Diffusiophoresis of colloid particles in neutral solute gradients at finite Peclet number. J. Fluid Mech. 2013, 731, 64-94.

29. Anderson, J. L. Effect of nonuniform zeta potential on particle movement in electric fields. J.

Coll. Int. Sci. 1985, 105, 45-54.

30. Yamazaki, K.; Matsuda, M.; Yamamoto, K.; Yakushiji, T.; Sakai, K. Internal and surface structure characterization of cellulose triacetate hollow fiber dialysis membranes. J. Membrane

Sci. 2011, 368, 34-40.

67 Chapter 4

Enhanced Transport in Dead-End Pores

The work in this chapter is adapted from the author’s paper: Abhishek Kar, Tso-Yi Chiang, Isamar

Ortiz Rivera, Ayusman Sen, and Darrell Velegol. "Enhanced Transport Into and Our of Dead-End

Pores." ACS Nano 28, DOI: 10.1021/nn506216b.

In the previous chapter we saw that a spatio-temporal ionic gradient across microporous hollow fiber membranes could induce particle motion towards or away from it resulting in fouling or exclusion regions, respectively. This study of transient ionic gradient causing phoretic motion of charged tracers in the system is encouraging, especially when we consider the vast scale at which they must be occurring in geological systems undergoing disruptions. Such gradients could be envisioned to arise across the dead-end pores in geological reservoirs containing oil and natural gas trapped in them. Since these pores are dead-end in nature and situated in hard-to-reach regions, driving transport across them is unrealistic through conventional pressure-driven and electrokinetic driven mechanisms. The focus of this chapter lies in exploiting these transient ionic gradients to drive transport and be able to extract trapped oil emulsions into a larger sink where pressure-driven flows are more effective. To do this, we employ a closed two capillary concentric system with salt gradients across them and study the motion of charged particles and emulsions dispersed in the system. The following study highlights the essential contribution of such microscale diffusioosmotic flows in naturally occurring systems undergoing disruptions.

68 4-1. The Problem: Gaining Access to Dead-end Pores

Transport in dead-end micro and nanoscale channels lies at the heart of many geological and biological phenomena. As an example, the introduction of low salinity water into reservoirs, has been shown to result in the enhanced recovery of oil stuck inside dead-end geological channels.1,2 Salt diffusion across these channels appears to be critical for the recovery process.3

Disturbances in the earth’s crust, caused from earthquakes or drilling, have also been found to generate flows across cracks and fissures and have been correlated with the simultaneous observation of spontaneous electric potentials (SP).4-7 In biology, transport in dead end pores has been implicated in extra-cellular diffusion in brain tissue8 and intra-tissue diffusion of water and biomolecules in muscles.9

Transport in dead-end pores through conventional pressure-driven flow is not possible.10-

13 Electric fields can cause flows in channels,14-17 but in remote regions it is difficult to apply an external electric field. Designing conditions for chemically-induced transport and fluid flow18,19 has been challenging. However, the presence of electrolyte gradients (analogous to thermal gradients20) in the systems discussed suggests the critical role of electrokinetics, and specifically diffusioosmosis,21-24 in driving flows in such geometries. In this chapter, we address the question:

Is it possible to harness the presence of salt gradients to drive transport of materials both into and out of such pores? Experimentally, we find ion gradients can simultaneously move material in opposite directions in a cul-desac facilitating exchange of materials. Further, our electrokinetic model allows quantitative predictions that agree with these experimental observations.

69 4-2. Materials and Methods

4-2-1. Chemicals Used

We prepared our salt solutions using the chemicals obtained from Sigma-Aldrich. Sodium chloride (NaCl) and potassium chloride (KCl) were dissolved in DI water (Millipore Corporation

Milli-Q system, with a specific resistance of 1.8 M-cm) to prepare various concentrations of stock solutions. Surfactant-free sulfate-functionalized polystyrene latex beads (sPSL,  = 3.0 µm

± 2.1%, w/v = 8%) and surfactant-free amidine-functionalized polystyrene latex beads (aPSL,  =

1.5 µm ± 2.4%, w/v = 4%) were purchased from Interfacial Dynamics Corporation (Portland, OR).

Fluorescent sPSL beads ( = 4 µm, excitation/emission: 580 nm/605 nm) and fluorescent amine- functionalized beads ( = 2 µm, excitation/emission: 505 nm/515 nm) were used to trace the flow profile under a confocal microscope. Emulsions were prepared by oil-in-water emulsion process using hexadecane (Sigma-Aldrich) with 2% Tween-20 (Sigma-Aldrich) acting as a stabilizer. The polydispersity in the emulsions was varied by changing mixing times and rates of mixing.

4-2-2. Design of Dead-end Capillaries

Our dead-end pore systems were composed of two capillaries, with a smaller one placed inside the larger. Borosilicate square glass capillaries (part #: 8320-050 and 8290-050) used in our experiments were purchased from Vitrocom (Mountain Lakes, NJ) with the larger capillary

(height, h = 0.9 mm) forming the sink and the smaller capillary (h = 0.2 mm) making up the dead- end reservoir in our system. The reservoir mostly contained the salt (sometimes with emulsions) whereas the sink contained DI water with sPSL beads. In order to create the dead-end set-up, the sink was first filled with DI water solution, sealed at one end with paraffin wax and placed on a

70 clear glass slide. The smaller capillary, with the salt solution in it, was then inserted inside the larger closed capillary (see Appendix C for schematic) and waxed across the open ends. The motion of beads and emulsions were observed across the open-end of the smaller capillary under an optical transmission microscope with different magnifications.

4-2-3. Microscopy Techniques

We used both an inverted light microscope and a confocal microscope to image our systems. Brightfield observation of particle motion was made on a Nikon inverted microscope

(Eclipse TE2000-U) fitted with an optical light source and CCD camera (Q-Imaging). Nikon NIS

Elements Imaging Software (V. 4) was used for both particle and emulsion velocity measurements and tracking. A Leica TCS SP5 laser scanning confocal microscope (LSCM, Leica Microsystems) was used for imaging and recording motion of fluorescent particles. Observations were made at

10× magnification for most cases. Image intensity profiles were analyzed using ImageJ software

(National Institutes of Health).

4-2-4. Zeta Potential Measurements of Latex Particles

For zeta potential (ζ) measurements of sPSL tracers (both fluorescent and nonfluorescent), amidine-functionalized PSL tracers and amine-functionalized PSL fluorescent tracers, we used a

Zetasizer Nano ZS90 (Malvern, MA, model ZEN3690) equipment. The ζ-potential of the particles were measured at 298 K using disposable cuvettes (DTS1061) at ionic strengths of 0.1−100 mM salt concentration and pH of 5.8. Zeta potential of the borosilicate capillary, at different ion concentrations, was obtained from the literature.46

71 4-2-5. Modeling of Electrokinetic Flows

To model diffusiophoresis and diffusioosmosis, we used the electrokinetic equations, which consist of the Stokes equations, ion migration equations, continuity equations, and Poisson equation of electrostatics. The concentration gradient (n) was solved using Fick’s 2nd law of diffusion, and it gives rise to an E-field mentioned earlier, due to a difference in diffusion coefficients (Di).

4-3. Results and Discussions

4-3-1. Electric Field Generated from Ionic Gradients

To simulate flows in a laboratory setting, a series of systematic experiments were performed with dead-end pores made of glass capillaries (Fig. 4-1a). We studied transient diffusioosmotic flows (TDOFs) that resulted from imposed salt gradients. To mimic natural systems, our salt gradients were time-dependent25 and arose from both diffusion and convection of ionic species in the system. The gradients give rise to spontaneous electric fields (E, equation

4-1) that generate transport near charged surfaces or of charged particles.21, 26-29

kTDD  n E   (4-1) Ze D D n

Here, k is Boltzmann’s constant, T is temperature, e is the proton charge, Z is the valence of a symmetric Z:Z electrolyte, n is the local salt concentration, and D+ and D- are the diffusion

72 coefficients of the cation and the anion, respectively. At low salt concentrations where the classic electrokinetic theories hold,30 the magnitude of this electric field depends on the difference in diffusion coefficients of the ions and the length over which the gradient is set up. The magnitudes of E can be as high as several V/cm. Aside from the E-field generated in the system that induces fluid and particle motion, double layer polarization due to chemical gradient (usually called chemiphoresis28,31) can also generate transport. The chemiphoretic contribution to transport rates is typically small; however, for completeness we have chosen to include it in our modeling. We explored the above phenomena experimentally using tracer particles (negatively-charged polystyrene latex (PSL) beads with diameters of 4 μm and 2 μm) and oil emulsions. The 4 μm PSL beads were sulfate functionalized (referred to as sPSL beads) whereas the 2 μm PSL beads were amine functionalized. The ion gradients were produced by setting up a source and sink for our salt using concentric square capillaries, each closed at one end. Specifically, this involved a 20 mm x

0.20 mm capillary placed inside another 50 mm x 0.90 mm capillary. Typically the inner capillary was the source (higher salt concentration) and the outer one the sink (lower salt concentration or even deionized water). The tracers were added to the outer capillary. Details are available in the

Methods section. A vertical arrangement of the capillaries allowed us to avoid density-driven convective flows in the system. While electrokinetic flows exhibit a nearly plug-flow profile in open channels, we observed a parabolic flow since our capillaries are closed at opposite ends, causing a pressure-driven back flow.

The E-field generated due to the salt gradient results in an electroosmotic fluid flow near the wall and a concurrent electrophoretic migration of the tracers (Movie 4-1) that is independent of electroosmotic flow.32-34 The net observed transport rate is a combination of these two effects

73 (see equation 4-2 and Appendix C). Knowing E-field, the speeds of the tracers in the system can be predicted quantitatively, and by strategic placement in a salt gradient, we can control their movement towards or away from the salt-rich region. There are three critical parameters controlling the motion: (1) a finite difference in diffusivities of the two ions present in the salt (D+

- D-), (2) a finite surface potential, given by the zeta potential ζ, and (3) an electrolyte concentration gradient, n. Precise control of these parameters can lead to a quantitative exchange of material across dead-end pores.

4-3-2. Exchange of Materials across Dead-End Pores

The speeds of the sPSL beads were analyzed using video microscopy in the xy plane with center of capillary at z = 0 (Fig. 4-1a). In our experiments the E-field is directed from high to low

NaCl concentrations (i.e. along the negative direction of the x-axis). This is readily seen from

-9 2 -9 2 equation 4-1, since DNa+ = 1.334  10 m /s and DCl- = 2.032  10 m /s. The initial speed we measured, up to 55 µm/s, was large close to the mouth of the dead-end capillary and decreased with time and distance as the beads are transported into the smaller capillary. In Fig. 4-1c, the less negative amine-functionalized PSL beads (green), in 10 mM NaCl have a zeta potential (ζp,  -22 mV) lower than that of wall (ζw,  -55 mV), whereas the sPSL beads (red) have a higher zeta potential (ζp,  -100 mV) compared to that of wall (ζw). Thus, the purely electrophoretic migration velocity for the green amine-functionalized PSL beads is lesser than that for red sPSL beads, with the magnitude of electroosmotic velocity near the wall lying in between the two. Hence, electroosmosis dominates in the former while electrophoretic migration controls net motion in the latter. As a result, for sPSL beads, the net movement is towards the higher salt regime, both along

74 the wall and in the center (i.e., in the direction of the dead-end) (Movie 4-2), while the amine- functionalized PSL tracers move towards the sink along the wall of the capillary and towards the higher salt concentration in the center (Movie 4-3). When combined in one set-up, with the amine- functionalized PSL beads inside the dead-end inner capillary (i.e. the smaller capillary) and the sPSL beads on the outside, we found these particles undergo exchange along the wall (Fig. 4-1d,

Movie 4-4). As expected, the rate of exchange varies with space and time due to the transient nature of the gradient. Similar trends are also observed with tracers of different sizes and zeta potentials which confirm our observation of TDOFs in the system. Since the effects in our dead- end capillary system are transient in nature, we do anticipate - potentials to vary in magnitude.

However by using salt solutions at low concentrations in both the sink and the reservoir, we expect the change to be monotonic but small in our system.

a b

E c Inside: 10 mM NaCl, d Outside: 1 mM NaCl t = 0 s

t = 10 s

Figure 4-1. Particle transport and exchange of material into and out of dead-end pores due to TDOFs. (a) Experimental setup used to study transport rates of sPSL beads in dead-end pores. Experiments involved a simple vertical sink-reservoir model, containing a smaller capillary that serves as the salt reservoir, within a larger capillary containing only DI water. The solid black arrow indicates the direction of material transport and the black dashed line gives the E-field in the system. Direct visualization of material transport in these dead-end pores was done near the opening of the inner capillary (red open box). (b) The beads were transported upward against gravity both in the center and along the wall of the dead-end pore. Quantitative predictions of tracer speeds from electrokinetic modeling (represented by the curves), at different distances (x) into the dead-end pore are compared with experimental results (represented by open and closed circles) at t = 200 s. ζp = -101 mV and ζw = -65 mV. (c) Lower: 4.0 µm red sPSL beads show diffusiophoretic transport towards the high salt regime both at the center and along the walls. Upper: 2.0 µm green amine-functionalized PSL beads shows diffusiophoretic transport along the wall towards the sink whereas in the center, they move towards the dead-end region containing salt (towards left). (d) Upon adding red sPSL beads in the outside capillary and green amine-functionalized PSL beads in the inside capillary, exchange of material was observed. Near to the side walls of the dead-end pore (inner capillary), the green amine-functionalized PSL beads, initially inside, move towards the sink and eventually out of the pore, whereas the red sPSL beads, initially outside, move in and, eventually, fill up the entire inner capillary.

4-3-3. Electrokinetic Model for Transport in Dead-End Pores

In order to compare our experimental results quantitatively using the electrokinetic equations, Fig. 4-1b, we modeled the transport of material in a dead-end pore and examined the tracer velocity (u) at any position (x) and any time (t).

u(,t) x v (,t) x Udp (,t) x (4-2)

First we describe how we estimate the flow field (v) within the pore, and later we discuss the additional diffusiophoretic contribution (Udp) from the individual tracers. To evaluate v we model our system as a long, square capillary (Fig. 4-1a) with a particular ζw and known D+ and D- of the ions. With the salt solution at the top (inner capillary) and DI water containing sPSL beads at the bottom (sink, outer capillary) (with no observed contribution to speeds from density gradients), we have temporal salt concentration gradients (n/t  0) that are also spatially non- uniform (n/x  0). We solve numerically for the concentration profile n(x,t) in the system (see

Appendix C) using 1-dimensional, time-dependent Fick’s law of diffusion35 and thus estimating

n(x,t).

In the capillary, v is calculated using the concentration profile n(x,t). First we evaluate vdo near the wall using equation 4-3 which is a combination of both the electroosmotic and the chemiosmotic flow. Both of these flow contributions are analogous to electrophoresis and chemiphoresis, respectively.34

22 kT D D2 k T2  Ze n v   ln 1  tanh w (4-3) do w 22   Ze D D Z e4 kT n

Next, we calculated the complete diffusioosmotic flow profile, different from that of a plug flow in an open channel, which is evaluated using Bowen’s36 result. This result accounts for the fluid dynamics in a closed rectangular channel using the steady-state Stokes equation for the case when there is an electroosmotic slip velocity at the wall surfaces and the net flow across any cross- section of the channel is zero. The flow field has a parabolic shape37 due to the back-pressure built in the dead-end section. In most fluid mechanics problems, the wall resists flow due to the no-slip boundary condition. Here, the finite slip at the wall drives flow – that is, the wall is the “pump” – and this sets up a flow field within the entire capillary.

The contribution from the independent rates of tracers (Udp) to equation 4-2 also needs to be assessed. We assumed sPSL beads which have a negative zeta potential (ζp), and therefore in a

34,38 salt gradient, undergo diffusiophoresis with the expression for Udp being very similar to equation 4-3. ζw and ζp were measured independently. With all the parameters in the system being known, we substitute v and Udp in equation 4-2 and are now able to compare our modeling results with experimental observed velocities, u, for different tracers (for details regarding modeling predictions and its subsequent validation with experiments, see Appendix C). The data on electrokinetic transport of beads towards the high salt regime compare well with our TDOF model.

As expected, the speeds of the beads decay both spatially and temporally (Fig. 4-1b) with those near to the mouth of the pore (x = 250 µm) having speeds higher than those inside the pore (x =

400 µm). We also found that there is a negligible contribution to speeds coming from density

78 differences, and hence, we reverted back to a simpler horizontal microscope set-up for the rest of our experiments.

4-3-4. Extraction of Trapped Oil Emulsions

Particles or solutes with the same zeta potential can exist in various shapes and sizes. To investigate the contribution of changing sizes to transport in dead-end pores, we turned our attention towards the transport of hexadecane oil emulsions (diameters () from 10 - 80 µm) out of dead-end capillaries. For sPSL beads, sincep > w, diffusiophoresis of the particle dominates the flow field in the capillary at all locations (Fig. C-4 in Appendix C). For oil emulsions, |ζe| < |ζw|, with e = -35 mV the flow dominates over phoretic motion. The small emulsions, being entirely near the wall, are expected to move in the same direction as the diffusioosmotic flow at the wall (vdo). Large emulsions, which extend farther into the capillary, should move in the opposite direction. Thus, the direction of motion of oil emulsions is predicted to be a function of their diameter (Figs. 4-2c and 4-3a).

The experimental observations bear out these predictions. Fig. 4-2a is a schematic of the dead-end capillary system with emulsions inside the pore and sPSL beads outside in the sink. We observed the transport of small oil emulsion droplets (roughly 20 µm diameter hexadecane emulsions stabilized with 2.0%wt Tween-20) out of the dead-end capillary, away from the high salt concentrations; the sPSL beads and the larger emulsions (roughly 80 µm diameter) moved towards higher salt concentrations. In Fig. 4-2b one sees that the fluid flow generates transport and exchange of sPSL beads and oil droplets in the system. The small emulsions that initially occupied the dead-end pore were transported toward the sink, whereas the beads moved in the opposite direction. This results in an exchange of material across the dead-end pore. These images were

79 taken from the top surface of the capillary at all times with the gravity pointing into the figure and thus not playing a role in the horizontal motion of the emulsions. Fig. 4-2c depicts the relative competition between emulsions of different sizes to move in or out of the dead-end pore. The isolated smaller emulsions can be seen to move towards the lower salt regime whereas the bigger emulsions move and push the smaller emulsions in front of them towards the higher salt regime.

Note that the electrolyte gradient and the resultant E-field point in different directions in Figs. 4-

2b and 4-2c.

81 transported towards the dead end. Both transport rates are predicted quantitatively by our model (Fig. 4- 3). Yellow bars indicate the position of these beads and emulsions before and after 30 s (Movie 4-5). The magnitude of the scale bar is 100 m. (c) When the DI water is inside with salt outside, smaller emulsions ( < 10 m) move towards the dead end and larger emulsions ( > 40 m) move away from it (Movie 4-6) demonstrating the reversible nature of transport.

The size dependence of oil emulsions on their direction of motion underscores the effects of pore and particle sizes on the exchange process. While smaller emulsions can be easily extracted

(since they move along the direction of the E-field), for efficient recovery the larger emulsions must be first reduced in size, perhaps through surfactant polymer flooding of oil wells.39 As Figs.

4-3a and 4-3b illustrate, we show through both experiments and modeling that the movement of polydispersed oil emulsions depends on their placement inside the dead-end pore. In order to quantify the rates of oil extraction from our dead-end pores, we used the same electrokinetic model as we did for the tracer particles. Fig. 4-3a shows the positioning of the polydispersed emulsions across the xy plane and the circles in Fig. 4-3b shows their corresponding position along the yz plane. Smaller emulsions are closer to the top surface (the plane connecting {0,100} and

{100,100}) whereas the larger emulsions are a little farther into the bulk. The parabolic nature of the fluid flow drives these emulsions along with it. The smaller emulsions ( < 5 µm) are seen to move out with a speed of 1 µm/s (Fig. 4-3b) (negative sign indicates motion towards the sink, while a positive sign shows movement in the opposite direction, towards the dead-end region).

The relatively larger emulsions ( > 40 µm) are seen to be stationary as predicted from our model.

The really large emulsions ( ≈ 80 µm) (Fig. 4-2c), which extend significantly into the bulk move towards the dead-end, a direction opposite to that observed for the small emulsions.

The time required for material exchange in these pores varies with distance from the mouth of the pore. Fig. 4-3c shows the schematic of an oil emulsion located at a distance d away from

82 the mouth of a dead-end pore of length L, which contains salt. Here, we modeled the time taken for this emulsion to come out of the pore if its diameter is 20 µm. As seen in Fig. 4-3d, the time scales (calculated using equation 4-3 and Fickian diffusion) for extraction of this emulsion increases logarithmically with the log of the distance d, which indicates that this transport process is most effective if the emulsion is situated close to the mouth of the dead-end pore.

a a cc

E E

end

- Dead Dead

d 1000000 b 10000 b - d r = 90 m 100000

10000 1000 1000

r = 10 m t (sec)t

100

t (s)t t (sec) t 100 10

1 0.1 1 d (mm) 10 0.1 1 d (mm)(mm)

Figure 4-3. Transport rate for emulsions of various sizes and time scales out of a dead-end pore. (a,b) The speeds of emulsion droplets out of the dead-end pore were tracked and modeled at a distance of 200 µm away from the mouth of the pore. (scale bar = 100 µm).The smaller emulsions were seen to move towards the sink, both through experiments and modeling, at a speed of just over 1 µm/s whereas the medium-sized emulsions were mostly stationary. Using the diffusiophoretic transport equations, the u for these emulsions was modeled (in b) with the color gradient signifying the direction of motion for these emulsions (negative sign indicates motion towards the sink,while the positive sign shows movement in the opposite direction, towards the dead-end region). In our calculations for b, ζe = -33 mV, ζw = -65 mV, x = 200 µm at t = 300 s. (c,d) The time taken for an emulsion of diameter = 20 µm to exit the dead end pore as a function of its distance from the mouth of the pore (d, mm), as obtained from modeling. Times vary from a few seconds to hours depending on d. Large emulsions are predicted to be stuck in the dead-end pore which is indeed observed experimentally.

83 4-3-5. Flows with Divalent Salts

Most geologic systems contain complex mixtures of ions, including multivalent ions. We further extended our experiments to divalent ions, using saturated calcium carbonate (see Fig. C-

5 in Appendix C) and carbonated water solutions (Fig. C-6 in Appendix C). By using small emulsions with oleic acid as a steric stabilizer, we observed their motion in the water having a

- gradient of dissolved CO2 (i.e., bicarbonate ion, HCO3 ). In such a setup, ζe = -60 mV compared to ζw = -30 mV (at pH ≈ 4). The emulsions are seen to behave like sPSL beads in NaCl gradient as

- they continue to move towards the higher HCO3 concentration regime. Similar behavior is observed for gradient formed by calcium carbonate dissolution. Being able to control local solution conditions with dissolved CO2 provides interesting opportunities, either for sequestration (e.g., toxic or radioactive substances) or removal (e.g., oil) of specific materials.

4-3-6. Rapid Particle Recirculation

There is one more important aspect of TDOFs in our system: Convection dominates over diffusion for the beads, especially at distances less than 500 m from the mouth of the capillary

(Pebeads = Ua/Dbead  1000, where U refers to the velocity scale for the beads, a is the typical dimension of the bead and Dbeads is the diffusion coefficient for the beads in a dilute solution). In

NaCl gradients, in addition to the axial motion of the sPSL beads discussed above, we also observe a transverse drift towards the side walls of the capillary in the dead-end pore setup (Fig. 4-4a,

Movie 4-7). The behavior has similarities to that presented in recent modeling paper by Rubinstein and Zaltzman,40 but in our case we have a spatially and temporally varying E-field in the system arising from the concentration gradients which drive transport. The trajectory of the sPSL beads tracked along the yz-plane (see Fig. 4-4b) for NaCl salt gradient (e.g. 10 mM NaCl in smaller

84 capillary and 1 mM NaCl in the sink) is very different from that observed when KCl salt was used to create the same gradient (i.e. 10 mM KCl in smaller capillary and 1 mM KCl in sink) (Fig. 4-

4c). Beads in KCl gradient undergo little lateral motion. Though the analysis needed to deconvolute the mechanism behind the radial drift from axial motion is beyond the scope of this article, we briefly discuss the physics behind such an observed phenomenon. Since the fluid flow profile is parabolic inside dead-end capillaries, the concentration gradient can exist, mostly near the mouth of the pore, both along the x- and y- axis. This distribution of salt inside the pore generates an E-field also along the y-direction that can make the beads drift towards the side walls.

The beads along the center line move straight due to the symmetry of the E-field. However, the observed lateral motion does not happen in the case of KCl gradients, where chemiphoresis and chemiosmosis are the only operating effects in the system, since K+ and Cl- have virtually identical diffusion coefficients and produce almost no E field.

4-4. Conclusion

We have shown that by employing locally available chemical energy – in the form of spatiotemporal ion gradients – transient diffusioosmotic flows (TDOFs) can be set-up to perform mechanical work in hard-to-reach dead-end pores, resulting in exchange of materials across the pores. Our model accurately predicts these observations. Transient salt gradients are ubiquitous in biological and geological systems. Geological examples include flows originating in disturbed mineral formations41 and geoengineering involving the creation of ion gradients for enhanced oil recovery.42 In biology, TDOFs contribute to the movement of biomolecules to specific targets,43 as well as other forms of intercellular transit.44 In addition, TDOFs are also likely involved in patterns45formed from mineral precipitates. One interesting practical application is the design of a self-regulated drug delivery system where the release rate of drug can be regulated as a function of the physiological change in salt concentration or pH.

86 4-5. Key Results

Transport across dead-end pores, enabled through ionic gradients, is the most important result of this thesis. We saw that these transient flows are spatiotemporal in nature, and are fastest at the beginning of the phenomenon. One key assumption we made in order to quantify this work is that the fluid flows were considered to be fully-developed locally. As we did see in our observations, this is not true since particles further into the pore moved at different velocity than the ones closer to the mouth of the pore. By assuming that the reservoir is infinite, we simplified our analysis. However, a more robust and accurate model would have to be built in order to understand this fluid flow mechanism accurately. Our observations also validate that diffusioosmotic flows are in general not fully developed flows, which makes this field very vibrant and interesting to analyze.

87 4-6. References

1. Lake, L. W. Enhanced Oil Recovery; Prentice Hall, 1989.

2. RezaeiDoust, A.; Puntervold, T.; Strand, S.; Austad, T. Smart Water as Wettability Modifier in

Carbonate and Sandstone: A Discussion of Similarities/Differences in the Chemical Mechanisms.

Energy & Fuels 2009, 23, 4479-4485.

3. Jerauld, G. R.; Brodie, J. A. Impact of Salt Diffusion on Low-Salinity Enhanced Oil Recovery.

In SPE Improved Oil Recovery Symposium. Society of Petroleum Engineers 2014.

4. Suski, B.; Revil, A.; Titov, K.; Konosavsky, P.; Voltz, M.; Dagės, C.; Huttel, O. Monitoring of an Infiltration Experiment Using the Self‐potential Method. Water Resources Research 2006, 42,

W08418.

5. Yoshida, S. Convection Current Generated Prior to Rupture in Saturated Rocks. J. Geophys.

Res.: Solid Earth 2001, 106, 2103-2120.

6. Pride, S. R.; Morgan, F. D. Electrokinetic Dissipation Induced by Seismic Waves. Geophysics

1991, 56, 914-925.

7. Jouniaux, L.; Ishido, T. Electrokinetics in Earth Sciences: a tutorial. Int. J. Geophys. 2012.

8. Syková, E.; Nicholson, C. Diffusion in Brain Extracellular Space. Physiol. Rev. 2008, 88, 1277-

1340.

9. Safford, R. E.; Bassingthwaighte, E. A.; Bassingthwaighte, J. B. Diffusion of Water in Cat

Ventricular Myocardium. J. Gen. Physiol. 1978, 72, 513-538.

10. Bear, J. Dynamics of Fluids in Porous Media; American Elsevier Publishing Company; New

York 1972. pp 44-45

88 11. Fuerstman, M. J.; Deschatelets, P.; Kane, R.; Schwartz, A.; Kenesis, P. J. A.; Deutch, J. M.;

Whitesides, G. M. Solving Mazes Using Microfluidic Networks. Langmuir 2003, 19, 4714-4722.

12. Goodknight, R. C.; Klikoff, W. A.; Fatt, I. Non-steady-state Fluid Flow and Diffusion in

Porous Media Containing Dead-end Pore Volume 1. J. Phys. Chem. 1960, 64, 1162 – 1168.

13. Dagdug, L.; Berezhkovskii, A. M.; Makhnovskii, Y. A.; Zitserman, V. Y. Transient Diffusion in a Tube with Dead ends. J. Chem. Phys. Phys. 2007, 127, 224712.

14. Stone, H. A.; Stroock, A. D.; Ajdari, A. Engineering Flows in Small Devices: Microfluidics toward a Lab-on-chip. Ann. Rev. Fluid Mech. 2004, 36, 381-411.

15. Squires, T. M.; Quake, S. R. Microfluidics: Fluid Physics at the Nanoliter Scale. Rev. Mod.

Phys. 2005, 77, 977-1026.

16. Whitesides, G. M. The Origins and the Future of Microfluidics. Nature 2006, 442, 368-373.

17. Hunter, R. J. Zeta Potential in Colloid Science; New York; Academic, 1981; pp 386.

18. McDermott, J. J.; Kar, A.; Daher, M.; Klara, S.; Wang, G.; Sen, A.; Velegol, D. Self-generated

Diffusioosmotic Flows from Calcium Carbonate Micropumps. Langmuir 2012, 28, 15491-15497.

19. Laser, D. J.; Santiago, J. G. A Review of Micropumps. J. Micromech. Microeng. 2004, 14,

R35–R64.

20. Baaske, P.; Weinert, F. M.; Duhr, S.; Lemke, K. H.; Russell, M. J.; Braun, D. Extreme

Accumulation of Nucleotides in Simulated Hydrothermal Pore Systems. Proc. Nat. Acad. Sc. USA

2007, 104, 9346-9351.

21. Derjaguin, B. V.; Sidorenko, G. P.; Zubashenko, E. A.; Kiseleva, E. V. Kinetic Phenomena in

Boundary Films of Liquids. Kolloidn Zh. 1947, 9, 335-348.

22. Dukhin, S. S.; Derjaguin, B. V.; Matievich, E. Electrokinetic Phenomena. Surface and Colloid

Science. Vol. 7; New York, Toronto; John Willey and Sons 1974.

89 23. Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. Motion of a Particle Generated by

Chemical Gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247-269.

24. Anderson, J. L.; Malone, D. M. Mechanism of Osmotic Flow in Porous Membranes. Biophys.

J. 1974, 14, 957-982.

25. Chiang, T. Y.; Velegol, D. Multi-ion Diffusiophoresis. J. Coll. Int. Sc. 2014, 424, 120-123.

26. Ebel, J. P.; Anderson, J. L.; Prieve, D. C. Diffusiophoresis of Latex Particles in Electrolyte

Gradients. Langmuir 1988, 4, 396-406.

27. Abecassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Boosting Migration of

Large Particles by Solute Contrasts. Nat. Mat. 2008, 7, 785-789.

28. Siria, A.; Poncharal, P.; Biance, A. L.; Fulcrand, R.; Blasé, X.; Purcell, S. T.; Bocquet, L. Giant

Osmotic Energy Conversion Measured in a Single Transmembrane Boron Nitride Nanotube.

Nature 2013, 494, 455-458.

29. Lee, C.; Cottin-Bizonne, C.; Biance, A. L.; Joseph, P.; Bocquet, L.; Ybert, C. Osmotic Flow through Fully Permeable Nanochannels. Phys. Rev. Lett. 2014, 112, 244501.

30. Khair, A. S.; Squires, T. M. The Influence of Hydrodynamic Slip on the Electrophoretic

Mobility of a Spherical Colloidal Particle. Phys. Fluids 2009, 21, 042001.

31. Prieve, D. C.; Gerhart, H. L.; Smith, R. E. Chemiphoresis-A Method for Deposition of Polymer

Coatings without Applied Electric Current. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 32-36.

32. Anderson, J. L. Colloid Transport by Interfacial Forces. Ann. Rev. Fluid Mech. 1989, 21, 61-

99.

33. Florea, D.; Musa, S.; Huyghe, J. M. R.; Wyss, H. M. Long-range Repulsion of Colloids Driven by Ion Exchange and Diffusiophoresis. Proc. Nat. Acad. Sci. USA 2014, 111, 6554-6565.

90 34. Kim, Y.; Shah, A. A.; Solomon, M. J. Spatially and Temporally Reconfigurable Assembly of

Colloidal Crystals. Nat. Comm. 2014, 5.

35. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons; New

York, 2001.

36. Bowen, B. D. Effect of a Finite Half-width on Combined Electroosmosis-Electrophoresis

Measurements in a Rectangular Cell. J. Coll. Int. Sc. 1981, 82, 574-576.

37. Hunter, R. J. Measurement of Electrokinetic Parameters. In Zeta Potential in Colloid Science;

Academic Press, Inc.; London and New York, 1981.

38. Kar, A.; Guha, R.; Dani, N. S.; Velegol, D.; Kumar, M. Particle Deposition on Microporous

Membranes can be Enhanced or Reduced by Salt Gradients. Langmuir 2014, 30, 793-799.

39. Seethepalli, A.; Adibhatia, B.; Mohanty, K. K. Physicochemical Interaction during Surfactant

Flooding of Fractured Carbonate Reservoirs. SPE Journal 2004, 9, 411-418.

40. Rubinstein, I.; Zaltzman, B. Convective Diffusive Mixing in Concentration Polarization: from

Taylor Dispersion to Surface Convection. J. Fluid Mech. 2013, 728, 239-278.

41. Putnis, A. Replacement Process. Geochem. Persp. 2012, 1, 388-402

42. Lager, A.; Webb, K. J.; Collins, I. R.; Richmond, D. M. LoSal Enhanced Oil Recovery:

Evidence of Enhanced Oil Recovery at the Reservoir Scale. In SPE Symposium on Improved Oil

Recovery. Society of Petroleum Engineers. 2008.

43. Yadav, V.; Freedman, J. D.; Grinstaff, M.; Sen, A. Bone-Crack Detection, Targeting, and

Repair Using Ion Gradients. Angew. Chem., Int. Ed. 2013, 125, 1-6.

44. Sui, H.; Han, B. G.; Lee, J. K.; Walian, P.; Jap, B. K. Structural Basis of Water-specific

Transport Through the AQP1 Water Channel. Nature 2001, 414, 872-878.

91 45. Noorduin, W. L.; Grinthal, A.; Mahadevan, L.; Aizenberg, J. Rationally Designed Complex,

Hierarchical Microarchitectures. Science 2013, 340, 832-837.

46. Barz, D. P. J.; Vogel, M.J.; Sheen, P.H. Determination of the Zeta Potential of Porous

Substrates by Droplet Deflection. I. The Influence of Ionic Strength and pH Value of an Aqueous

Electrolyte in Contact with a Borosilicate Surface. Langmuir 2009, 25, 1842-1850.

Chapter 5

Convective Flows in Pseudomorphic Mineral Replacement Reactions

This chapter explores critical questions concerning pseudomorphic mineral replacement reactions (pMRRs) which involves one mineral phase replacing another, preserving the original mineral's size and texture (e.g., bone fossilization). Macroscopically, these transformations are driven by system-wide equilibration through dissolution and precipitation reactions. However, translating these bulk observations of ion migration, which currently is assumed to be diffusion driven, to molecular-scale processes has proven to be difficult making it challenging to assess their role in geochemical systems and exploiting it technologically. Hence the two primary scientific questions we investigate in this work are:

- What are the reaction rates and rate of recovery of trapped resources from minerals

undergoing pMRR?

- What is the relative importance of convective and diffusive transport in pMRRs?

To answer these questions, we develop a new quantitative framework to explain the replacement process of a KBr crystal by KCl (shown in Fig. 1-8) solution through a combination of microscopic, spectroscopic, and modeling techniques. Our observations reveal convective fluid flows, resulting from diffusioosmosis, driving ion exchange and transport in the system. We demonstrate this through the extraction of trapped tracer particles, which act as proxies for oil and gas, from mm-scale KBr crystals.

93 The most significant result of this work was in obtaining extraction quantum dots and polystyrene tracers from the pores of the crystal at rates two orders of magnitude faster than predictions from diffusion. Hence, surface reaction through dissolution and reprecipitation, which has been so-far the accepted mechanism in mineral replacement reactions, would not explain this behavior. So we turned towards quantifying the possibility of self-generated diffusioosmotic flows arising from ionic gradients within the pores to better understand this experimental observation.

The modeling in this chapter has been done in collaboration with Robert Stout and Prof.

Aditya Khair at Carnegie Mellon University. In the model for high salt diffusioosmosis, they have introduced steric ion-ion interaction via Bikerman’s approach which is generally neglected in the typical Smoluchowski’s model for electroosmotic flows in a system.

5-1. The Problem: Diffusion v/s Convective transport

Mineral-water interactions often induce solid-state transformations, which can be exploited to synthesize novel materials1, extract trapped resources (e.g., “leaching”)2,3, and engineer the safe long-term storage of radioactive waste and carbon dioxide4-7. Generally, these interactions are thought to be controlled by two main processes: ion diffusion in solution and surface reactions

(e.g., dissolution and precipitation)8,9. In some cases, the interactions may also be influenced by external temperature and pressure gradients resulting in the transformation to go faster.10-12 Prior works characterizing these interactions have not, however, accounted for an additional transport mechanism – self-generated diffusioosmotic flows – which can spontaneously originate when an ionic gradient builds up across the fluid-mineral interface owing to differences in ion diffusion coefficients.13-16 Such flows can drive convective transport in the system at rates much faster than

94 diffusion. In this chapter, we demonstrate that these diffusioosmotic flows can tremendously enhance transport in dead-end pores formed during mineral-water interactions and illustrate how these flows can be used to accurately model the kinetics of mineral transformation reactions from first principles.

5-2. Sample Preparation and Characterization Techniques

5-2-1. Materials

We prepared our salt solutions using the chemicals obtained from Sigma-Aldrich.

Potassium chloride (KCl) and Potassium Bromide (KBr) were dissolved in DI water (Millipore

Corporation Milli-Q system, with a specific resistance of 1.8 M-cm) to prepare various concentrations of stock solutions. Saturated solutions of KCl and KBr were prepared by adding

420,000 ppm and 678,000 ppm respectively in DI water. Fluorescent surfactant-free sulfate- functionalized polystyrene latex beads (sPSL, a = 4.0 µm ± 2.1%, w/v = 2%, excitation/emission:

580 nm/605 nm) was purchased from Interfacial Dynamics Corporation (Portland, OR). Qdot®

655 ITK carboxyl quantum dots (excitation/emission: 635 nm/655 nm) were purchased from Life

Technologies. These quantum dots (QDs) are 20 nm crystals made from nanometer-scale crystals of a semiconductor material (CdSe), which are shelled with an additional semiconductor layer

(ZnS) to improve their chemical and optical properties. The core-shell structure is functionalized

(in this case, with –COO- group) which gives it the stability in suspensions. Both the beads and

QDs were used to trace the flow velocity under a confocal microscope. KBr (part # 0002-4539) and KCl (part # 0002-4538) crystals of cubical cuttings were obtained from International Crystal

95 Laboratories, NJ, USA. Thick clear polycarbonate sheets (Lexan 12” x 24” x 0.2”) were purchased from Home Depot and cut into a 1” x 2.5” rectangles for making our flow-through reactors.

Circular petri dishes with a 13 mm (diameter) hole at the bottom for cover glass assembly were obtained from Cell E&G (part # PDH00001-200). These petri dishes were used to make the batch reactors. BD Intramedia Polyethylene Tubing with ID = 0.03” and OD = 0.048” were fitted to BD single-use needles (22 gauge with OD = 0.02825”, part # BD305155, obtained from VWR) to inject samples into the flow-through reactor. Harvard 2000 syringe pump, after proper calibration for the diameter of the syringe, was used to inject solution during our flow-through reactor experiments.

5-2-2. Synthesis of KBr Crystal with Inclusions

Mineral replacement reaction can complement or even substitute the current practices in oil and energy recovery using mechanical means. In order to demonstrate this, we made our own

KBr crystals with inclusions of QDs and fluorescent beads within them. These tracers were trapped inside the crystal in a stochastic manner during its formation. We used powdered KBr to create 5-

10 mL of saturated KBr solution in DI water. To this we added 5-8µL of QDs or sPSL beads

(forms a final colloidal suspension with w/v < 0.01% with rapid aggregation time of a week) and the resultant solution was allowed to sit in a glass vial for approximately two days. We found KBr crystals had grown to a size of 1-2 mm3 with tracers trapped inside them. We then used these crystals under the confocal microscope to study the rate of extraction of these inclusions during the mineral replacement process.

5-2-3. Design of Batch and Flow-Through Reactor

A typical batch reactor was created using a petri dish to observe the KBr-KCl-H2O mineral replacement reaction both under the confocal and optical microscope. A circular hole was cut-out from on the petri dish and was covered with a replaceable surface like a square cover glass (VWR, part # 48368-062, 22 mm x 22 mm). Paraffin wax was chosen to seal the cover glass to the petri dish as it creates a leak-proof seal and does not undergo a chemical reaction with any of the components of the KBr-KCl-H2O replacement system. The crystal (normally KBr) was placed on the cover glass attached to the petri dish and 0.5 ml of saturated solution (normally KCl) was dropped on it. The entire system was placed under a transmission or confocal microscope at 4× objective. There was no external flow generated during our experiments in a batch reactor system.

A flow-through reactor was made of 0.5 cm thick polycarbonate sheet (Lexan 12” x 24” sheet obtained from Home Depot) cut into a 1” x 2.5” rectangle. A 1 cm x 2 cm rectangular hole was cut into the center of the material using a Dremel (model # 220-01and tips). On one side of the cut-out, a rectangular plain glass slide (VWR part # 48300-025) was attached using an optical adhesive (NOA 61, obtained from Norland Products) to seal the reactor system securely against high pressure drops generated from the syringe pump. A small KBr crystal (1 x 1 x 0.5 mm) was then placed inside the drilled channel covered by glass slide using tweezers and was held in its place by paraffin wax. We took care in ensuring that the cotton swab used to apply wax over the crystal was thin enough to not create an obstruction for the flow inside the channel. The wax was mounted on the side of the crystal facing the injection port so as to prevent any hydrodynamic lift of the mineral that can come from high flow rates. Two polyethylene tubes were inserted into the channel to form the inlet and the outlet to the reactor. Finally, cover glass was used to enclose the

97 reactor using paraffin wax. The inlet tube was connected to a syringe on a syringe pump which is used to inject saturated solution of KCl into the flow-through reactor for the replacement to occur.

In order to observe the rate of replacement, the distance covered by the replacement front was tracked under the transmission microscope at various flow rates of solution and plotted with respect to time. The same was also done for a batch reactor. In order to observe extraction of QDs and fluorescent beads, the synthesized KBr crystals were used inside the reactors in place of the pristine crystals bought from the supplier. The motion of these tracers were observed near to a face of the crystal in line of the flow.

5-2-4. Visualization and Characterization Techniques

Our systems were characterized using electron, transmission and confocal microscopies.

Brightfield observation of particle motion was made on a Nikon inverted microscope (Eclipse

TE2000-U) fitted with an optical light source and CCD camera (Q-Imaging). Nikon NIS Elements

Imaging Software (V. 4) was used for both particle and replacement rates measurements and tracking. A Leica TCS SP5 laser scanning confocal microscope (LSCM, Leica Microsystems, lasers: Argon, HeNe543, HeNe633, 10x objective, 70.77µm pinhole) was used for imaging and recording motion of fluorescent particles. Observations were made at 4× and 10× magnification for most cases. Image intensity profiles were analyzed using ImageJ software (National Institutes of Health). The electron microscopy images were obtained on a Leo 1530 field emission scanning electron microscope (FESEM) available at the Penn State Nanofabrication Facility and on a

Hitachi S-3000H scanning electron microscope (SEM) at the Penn State Material Characterization

Laboratory. Elemental analysis to determine the composition of the KBr crystal before and after the replacement process was done using energy dispersive spectroscopy (EDS, Oxford

98 Instruments, Palo Alto, CA). The EDS elemental analysis was done in conjunction with SEM to qualitatively and semi-quantitatively determine the chemical composition along the pores of the product phase. X-ray Diffraction (XRD) (PANalytical Empryean, Netherlands) was done on our crystal samples using Cu Kα radiation before and after the replacement process to determine the crystalline structure and identify their phase composition. The release of tracers from a crystal during replacement process was quantified using UV-Vis spectroscopy.

5-2-5. Sample Preparation for SEM and EDS

In a batch reactor, the KBr crystals were allowed to undergo replacement with saturated

KCl for different time intervals and were then washed with benzene (as salts don’t dissolve in apolar solvent) and left to air-dry. In a flow-through reactor, benzene was injected through the syringe pump to halt the replacement process. The cover glass was then removed and the crystal was left to air-dry. For observing the pores, the samples were placed with the pores facing towards the lens under the SEM/FESEM. However, to observe the extent of the replacement process and the dead-end pores formed during the replacement process, the crystals were cleaved into two halves and the newly created side was placed facing towards the lens under the SEM/FESEM.

SEM and FESEM images were taken at an accelerating voltage of 3-5 kV and working distances between 3-7 mm. Both qualitative and semi-quantitative microanalysis of our samples were performed using EDS in the SEM mode. No special sample preparation technique beyond that involved for SEM was required for qualitative analysis through EDS. But some care is taken while collecting X-rays from our samples. If the electron beam from EDS is focused on a hole or deformation in the sample, the X-rays may not be able to escape from the hole and not be detected.

In the Fig. 5-3d and 5-3e, this is represented by the dark regions on the sample which has channels

99 running through the crystal. Since our samples were non-conductive, we had to coat them with carbon tape before carrying out SEM, FESEM and EDS on them.

5-2-6. Sample Preparation for X-Ray Diffraction

Batch and flow-through reactor samples were washed (with benzene) and dried before being taken for X-Ray Diffraction (XRD). The samples we analyzed under the XRD were in the form of small crystals with relatively smooth surfaces. Our Empyrean XRD system is a Bragg-

Brentano diffractometer with Cu radiation being the normal way of operation. We changed the power settings of the instrument to a voltage of 45 kV and current of 40 mA. In our experiments, we used a 10 mm beam mask and 1/2” anti-scatter slit. After the data was recorded, we analyzed the diffraction patterns using the JADE v7.0 software pre-installed on computers connected with the XRD. For representing the XRD data in this chapter, we extracted the individual data sets into

OriginPro software package which lets us do a 2-D plot of the data.

5-2-7. Analyzing/Tracking of Mineral Replacement Data

The inbuilt tracking module in Nikon AR software (connected with the transmission microscope) was used to quantify the replacement front distances and replacement speeds as a function of time. For determining rates at which tracers were extracted from the KBr crystal during replacement, we captured the videos under confocal microscopy and then analyzed it using the

Tracker 4.87 (Open Source Physics) software. The speeds of replacement were found by curve- fitting for the data sets obtained through tracking of the replacement front in the KBr crystal, and then obtaining the slope of the curve. While curve-fitting, we neglected the initial few seconds

100 where the replacement rates were found to be very fast before changing predictably over the passage of time.

5-3. Results for Mineral Replacement Reactions

We became aware of the importance of self-generated diffusioosmotic flows at the mineral- water interface while studying a particular type of interaction: pseudomorphic mineral replacement reactions (pMRRs). These reactions involve one mineral phase replacing another in a dissolution- precipitation process that preserves the parent mineral’s shape and texture.17 Familiar examples of this process include fossilization and petrification.18-20 A key attribute of these reactions is that the product mineral phase is porous, which is thought to be a result of the parent and product minerals having different solubilities and molar volumes.21 The rates at which the pores form during mineral-fluid transformations can also be attributed to the rate of advancement of fluid-mineral interface in the product phase.22-24

5-3-1. The KBr-KCl Pseudomorphic Mineral Replacement Reaction (pMRR)

Our interest in these reactions stems from the fact that the generated porosity could be used to release trapped resources inside rock matrices – such as ores, oil, or natural gas – under conditions in which net rock dissolution is impractical. To study the process, we examined the replacement of a KBr crystal by saturated KCl solution according to the reaction:

- - KBr(s) + Cl (aq)  KCl(s) + Br (aq) where (s) denotes a solid phase and (aq) denotes an aqueous phase. This reaction has been studied extensively in the past25,26, and we selected it due to its simplicity, easy access to large mm-scale

101 pure specimens, and the high solubility of each phase. We initially studied the replacement of KBr by KCl in a closed, batch reactor cell using an optical light microscope. In these experiments, as expected, we visually observed rapid replacement27,28 which is illustrated by the crystal edge exhibiting a darker color due to the parent crystal (KBr) and product phase (a solid solution of

K(Br,Cl)) having different refractive indices (Figs. 5-1a and 5-1b show time lapse images of the crystal at t = 0 sec and t = 60 secs, respectively). Note that the replacement process was observed to be incorrigible in nature when a KCl crystal was placed in a saturated KBr solution, owing to the difference in solubility of these crystals in their respective solutions.

Despite the overall crystal shape being preserved during replacement, the surface topography changed considerably. During the replacement process, nanometer to micrometer scale pores formed on the crystal surface that penetrated several hundred microns beneath the crystal matrix, advancing the replacement front (shown schematically in Fig. 5-1c). Using field-emission scanning electron microscopy (FESEM), we examined the surface and the cross sectional structure of the replaced mineral (Figs. 5-1d and 5-1e), respectively; the latter was accessed by fracturing a mineral specimen. In these images, it can be seen that the pores formed during replacement are dead-end in nature, consistent with previous observations for the same KBr-KCl replacement reaction.29 Porosity distribution across the product phase is seen to be uniform in nature, with the structures becoming increasingly dendritic over time. The growth rates of these pores, measured through tracking the replacement front, was found to be nonuniform which we discuss in the next sections. The observed replacement was confirmed by characterizing the mineral’s unit cell dimensions before and after the reaction using X-ray diffraction (XRD) (Figs. 5-1g and 5-1h). A

KBr crystal was seen to undergo phase change, as expected, during the replacement process. Fig.

5-1g shows the peak shifts observed when a KBr crystal gets replaced by KCl with the solid

102 solution of K(Br,Cl) having lattice parameters which lie in between the two pure structural forms.

When the solid solutions of K(Br,Cl) were analyzed under the XRD at various intervals of time

(Fig. 5-1h), we observed small shifts in the 2 value and large drops in intensity signifying gradual phase changes and ordering of inter-layer structure.

Figure 5-1. Pseudomorphic mineral replacement reaction of KBr crystal in saturated KCl solution. (a, b) Time lapse images of a KBr crystal undergoing replacement in a batch reactor of saturated KCl solution. The darker region around the edges of the crystal, similar in morphology to the parent mineral, exhibits the replacement due to precipitation from the solution.(c) The schematic of the replacement process shows pores developed on the crystal during the reaction which are spatially non-uniform and separated from each other. (d) Surface structure of the crystal after 5 mins under the SEM reveals pores which are roughly 10 – 20 m in width, and (e) cross-sectional view of the crystal shows that these pores penetrate roughly 100 m into the crystal lattice. These pores are dead-end at the dissolution front. (f) XRD analysis of the product specimen after 45 mins of replacement reveals the crystal structure which is found to lie

103 in between the pure KBr and the pure KCl lattice orientations. (g) Evolution of crystallographic parameters in the product mineral reveals that as the KBr crystal approaches complete replacement, the disorder in the lattice parameters decrease which is seen through decrease in intensity counts for the crystal. Scale is 100 m.

5-3-2. Convective Extraction of Quantum Dots

To gain insights into the fluid transport mechanism occurring within the generated dead- end pores, we fabricated KBr crystals that contained trapped fluorescent tracer particles (20 nm diameter blue carboxyl quantum dots, QDs). We then tracked the mobility of these tracers during the replacement of a KBr crystal upon exposure to a saturated solution of KCl (5.6 M) in a batch- reactor. Since these tracers have diffusion coefficients of approximately 10-11 m2/s (QDs), extraction by diffusion would occur on the time scale of hours (i.e., for a 250 m long pore, the calculated extracted times from diffusive transport, t  l2/D, are 100 minutes for QDs and 10,000 minutes sPSL beads). Tracking the release of these particles into solution during replacement, by monitoring the florescence of the particle and solution, allowed us to differentiate between diffusive migration and another transport mechanism. For the blue QDs, we observed a decrease in the intensity of the blue color within the crystal (Fig. 5-2a – 5-2c) and the concurrent appearance of QDs in the aqueous phase, as tracked using UV-Vis spectrophotometry. Surprisingly, the rate of release of QDs from the crystal was found to be two orders of magnitude faster than predictions from diffusion time scales. The QDs that were initially observed to be extracted near to the edge of the crystal followed by the ones distributed further into the matrix. Such a gigantic enhancement in transport rates could not be accounted for by “pure diffusion”, and hence we looked at the various transport mechanisms that could have resulted in such a fast release of QDs from the crystal lattice.

104 Accessing trapped resources across dead-end pores are impossible through pressure driven mechanisms30-32 and while conventional electrokinetics can cause flows in channels33-35 initiating it in naturally occurring dynamic porous system is practically unfeasible. However, recently our research group has shown that ionic gradients across dead-end pores can drive diffusioosmotic flows (a form of electroosmotic flow) facilitating a quantitative exchange of materials.36 When ions diffuse at different rates, an in situ electric field (E-field) is spontaneously generated in order to maintain electroneutrality in the system. This E-field can act across the electrical double layer

(or Debye layer) of charged surfaces (which are typically in the order of few nanometers for both dispersed colloidal particles and stationary pore walls) driving transport and fluid flow in the system, analogous to electrokinetic phenomenon37-39.

To determine if diffusioosmotic flows were indeed generated across the dead-end pores during mineral replacement process, we carried out energy dispersive spectroscopy (EDS) observations on our SEM samples (Fig. 5-1d and 5-1e). EDS reveals that ionic gradients exist across the pores of the product phase post-replacement and these gradients entail further dissolution deeper into the crystal matrix. EDS of the cross-sectional structure of a replaced mineral obtained after fracturing it (Fig. 5-2d and 5-2e) shows the distribution of ions across the product phase for both bromide and the chloride ions, respectively. The color mapping for both these observations (represented through the change in intensity over an arbitrary distance normal to the replacement front, Fig. 5-2f) reveals a finite concentration gradient across the 100 m dead- end pore that subsequently decreases over time.

105

Figure 5-2. Extraction of QDs from a KBr crystal during pMRR in a batch reactor. (a,c) Time lapse confocal microscope images of a KBr crystal containing QDs (blue dots) undergoing pMRR shows that as the reaction proceeds, the intensity of the QDs (i.e. intensity of blue dots) inside the crystal decreases. However, during this process the KBr crystal is not seen to undergo any visible change in shape or size though it undergoes replacement forming pores through its entire volume. (d) EDS scans for the SEM images of these crystals after fracturing it shows the elemental distribution of bromide ions, and (e) chloride ions within the product phase of the crystal. (f) Line scan through the elemental distribution surface map obtained from EDS reveals that a finite ionic gradient persists for approximately 100 ms across the pores of the mineral. Scale is 100 μm.

5-3-3. Experiments in a Flow-Through Reactor

Though the extraction of QDs was initially observed to occur at rates much faster than predictions from diffusion, we observed a decline in this activity when the pMRR was allowed to go to completion. Surprisingly, when we switched to 4 m red fluorescent sulfate polystyrene latex sPSL beads as tracers inside crystal, we did not observe any extraction. Estimation from the diffusion coefficients for these beads (10-13 m2/s) suggest the extraction to take 10,000 minutes.

However, our beads never got extracted. To quantify this observation further, we plotted the rate of change in total normalized intensity of QDs inside the crystal which was found to decay initially and then stay steady after 10 minutes of replacement process (Fig. 5-3a). Upon examining the

106 product crystal under SEM after 10 minutes of replacement, we found that the pores on the surface had actually sealed off halting the extraction and slowing down the replacement process (inset in

Fig. 5-3b). This supports our observation for extraction of QDs. Such precipitation occurs due to the local saturation around the crystal and are normally known to be induced at the same location as that of the dissolution, thus making dissolution and reprecipitation processes spatially inseparable. However, on fracturing the crystal and imaging the newly formed surface under the

SEM, we found that these pores had not sealed off from inside. This was intriguing as the conventionally accepted mechanism for mineral replacement would not have predicted such spatially separated dissolution and reprecipitation fronts. Additionally, as diffusion processes could not account for the transport rates of QDs observed in our system, we also needed to quantify the contribution of a possible convective flow within the pores.

In order to investigate the role of transport processes within the pores, we switched to a flow-through reactor system (shown in Fig. 5-3c). EDS analysis of the crystals corroborate the presence of ionic gradients across the pores of the product phase which is seen through the inset in Fig. 5-3c. By changing the flow rates of the saturated KCl solution through the cell, we were able to enhance the external mass transfer rates across the boundary layer of the crystal which disrupted local saturation preventing precipitation and sealing off of the pores. This was verified under SEM (shown in Fig. 5-3d) where the pores were seen to be almost straight linear channels with a constant width and penetrating deep within the crystal. Imaging the surface of the crystal also yielded pore openings that were not sealed and were rather symmetrically distributed due to the flow in the system (inset to Fig. 5-3d). As expected, the pores in the product phase were indeed dead-end in nature. With a better mass transfer rates across the fluid-mineral interface and precipitation being halted at high flow rates (Q = 2 ml/min) of the solution, we observed extraction

107 rates of QDs (trapped in KBr crystals) being uniform over the entire duration of the experiment.

This was confirmed through the plot in Fig. 5-3a for the flow-through reactor which is distinctly different from that obtained in case of a batch reactor.

Figure 5-3. Flow-through reactors used to enhance mass transfer and extraction of QDs. (a) Rate of change of total normalized intensity of QDs trapped in KBr crystals undergoing replacement. For a batch reactor system, the rate of change is seen to decrease initially and then remain steady for the entire duration of the experiment. In a flow-through reactor system, the rate of change is observed to decrease consistently until all the QDs are extracted from the crystal. (b) SEM images of the crystals in a batch reactor system indicates precipitation on the surface resulting in pores being sealed off after 10 mins into the experiment. Both the inset and the central image confirm that these pores are closed on outside but open within the crystal, and are roughly 180 – 200 μm in width. (c) Flow-through reactor made of polycarbonate sheet being used to study pMRR under a more dynamic set of conditions. Inset to (c) reveals the ionic gradients observed across the pores of the crystal which extend for at least 250 μms in to the crystal lattice. This was obtained through EDS analysis as explained earlier. (d) SEM images of the crystals that had undergone replacement for 20 mins in a flow-through reactor (at Q = 2 ml/min) indicates dead-end pores which are not sealed off on the outside. Scale is 100 μm.

108 5-3-4. Rate-Limiting Step

On switching to a flow-through reactor cell, we also observed that 4 μm sPSL beads trapped inside the KBr crystal could now be extracted through the pores in the product mineral. Fig. 5-4a shows the extraction of these beads which was complete in roughly 3 minutes from the start of the experiment. The yellow circles highlight the initial position of these particles inside the crystal, which when exposed to a saturated KCl solution (Q = 2 ml/min) travel out of the mineral in the direction indicated by the yellow colored arrows. This rapid release of the tracers, which is two orders of magnitude faster than their diffusion time scales, suggests another form of transport mechanism to be prevalent inside the pores of the crystal. The extraction of both the QDs and the sPSL beads was observed when an ionic gradient exists across the pores the crystal. We were able to control this ionic gradient by alternately injecting either a KBr or a KCl solution through the reactor. While the extraction of QDs was monotonic in case of a saturated KCl solution flowing through the cell; it was halted immediately upon switching to a saturated KBr solution through the reactor (see Fig. 5-4b). The transport through the pores, hence, could be chemically controlled in pMRR by changing the salt solution in the system.

The other rationale behind using a flow-through reactor was: If replacement was surface reaction-limited (i.e., detachment was the rate-limiting step), the replacement rate would be independent of the flow rate. If, however, replacement was transport-limited, replacement rates would increase at higher flow rates. In these experiments, replacement rates were initially independent of fluid flow rate over the first 150 seconds, then replacement rates were faster when flow rates were higher. This suggests that transport limitations in pMRR, which have generally not been considered before, plays a critical role in the rate of replacement and the pore structure formation and evolution. By quantifying the slopes of the curve in Fig. 5-4c, we were able to

109 account for the transport rates of the fluid (which corresponds to the rate of replacement as the ions are driven by the fluid in the system) inside the pores. Fluid speeds inside pores increased linearly as the flow rates of saturated KCl solution got faster in the system (Fig. 5-4d).

110 was obtained by calculating the slope of the curves in (c). We considered the slope over the region where the curves are linear indicating precipitation from the solution not affecting the replacement process.

These experiments reveal two key aspects of pMRRs which can also be applicable to a host of other reactions and mineral transformations: i) Dissolution and reprecipitation processes in pMRR are spatially separated, and ii) convective transport through the pores of the mineral facilitate internal mass transfer to dominate over surface reaction and diffusion – the mechanisms which are generally considered to be rate limiting steps in pMRRs. Since the pores formed in our crystals were dead-end in nature and the transport of tracers were clearly convective, we turned our attention towards modeling the rates of diffusioosmotic flows within these pores.

5-3-5. Electrokinetic Model of pMRR

The modeling in this chapter has been done in collaboration with Robert Stout and Prof.

Transport across mineral-fluid interface can be categorized into three specific subdomains – the bulk, the transient boundary layer, and flows inside dead-end. First we solve for the diffusioosmotic velocity, udp which arises when there are ion gradients present in the system, the diffusion coefficients of these ions vary from one another and the walls of the pore are charged.

However, due to the large (molar) ion concentrations occurring in the mineral replacement process, one may suspect that the standard electrokinetic model of point-sized non-interacting ions, based on dilute solution theory, is of questionable validity. To test this, we modeled the effect of steric

111 hindrance in the Debye layer via Bikerman’s model40, where the ideal solution electro-chemical potential for ion 푖 is augmented to incorporate finite ion size effects. This modified electro-

∞ ∞ ∞ chemical potential, in the bulk solution, is 휇푖 = 푧푖푒휙 + 푘퐵푇 ln 푛푖 − 푘퐵푇 ln(1 − 휈), where 푧푖 is the charge number of species 푖, 푒 is the fundamental charge, 푘퐵 is Boltzmann’s constant, 푇 is

∞ 푁 3 ∞ temperature, 푛푖 is the bulk ion density of species 푖, and 휈 = ∑푖=1 푎푖 푛푖 , is the bulk volume fraction of ions with size 푎푖. Combination of this form of the electro-chemical potential with

Poisson’s equation yields the following modified Poisson-Boltzmann equation41 governing the equilibrium electrostatic potential in the solution,

푁 2 푧푖푒휙 푑 휙 푒 ∞ − 휀 = − ( ) ∑ 푧 푛 푒 푘퐵푇 (1) 푑푦2 1 − 휈 + 퐵 푖 푖 푖=1

푧 푒휙 − 푖 푁 3 ∞ 푘 푇 where 퐵 = ∑푖=1 푎푖 푛푖 푒 퐵 . The solution of this equation yields the equilibrium ion density

푧 푒휙 − 푖 0 ∞ 푘 푇 profiles normal to the pore surface, 푛푖 = 푒푛푖 푒 퐵 /(1 − 휈 + 퐵). The ion density profiles also vary along the pore surface due to the imposed salt gradient; hence the above equation is solved at a number of points along the pore.

To find an expression for the induced electric field arising from the imposed salt gradient

∞ ∞ ∞ across the pore, we assert the condition that the fluxes, 푗푖 = −(퐷푖⁄푘퐵푇)푛푖 ∇휇푖 , of all charges

푁 ∞ must sum to zero, ∑푖=1 푧푖푗푖 = 0, to ensure zero global current. Using the modified electro- chemical potential, the induced electric field is found to be

∑푁 ∞ ( ∞) ( ) ∑푁 ∞ ∞ ∞ 푘퐵푇 푖=1 푧푖퐷푖푛푖 ∇ ln 푛푖 − ∇ ln 1 − 휈 푖=1 푧푖퐷푖푛푖 푬 = −∇휙 = ( ) 푁 2 ∞ (2) 푒 ∑푖=1 푧푖 퐷푖푛푖

Notice that if 휈 = 0, we recover the classical result for electric field given by Prive et al where they used the ion migration equation and the condition of electroneutrality for a binary

112

42 ∞ system of electrolyte. This is used, along with the gradient in electro-chemical potential ∇휇푖 =

∞ ∞ −푧푖푒푬 + 푘퐵푇∇ ln(푛푖 ) − 푘퐵푇∇ ln(1 − 휈) to calculate the slip velocity along the pore wall via a generalization of the slip velocity formula given by43

푁 1 ∞ 풗 = − ∑ ∇휇∞ ∫ (푛0 − 푛∞)푦푑푦 (3) || 휂 푖 푖 푖 푖=1 0

Note that the above formula presumes that the Debye length is small compared to pore width, which is reasonable at the large concentrations under consideration.

Interestingly, we find that the slip velocity derived at the pore wall surface (Fig. 5-5) from the modified Poisson-Nernst-Planck (MPNP) equation44 matches quite well with the traditional

PNP equations solved by O’Brien-White in 197845. However, our model under predicts the observed speeds by few micrometers per second as the experimental observed speeds were roughly

0.8 μm/s. The possible reasons behind this are: i) the electrokinetic model does not implicitly account for grain size, pore size, or pore throat size which the modified Revil’s grain size- dependent HS model46 suggests, ii) the accurate -potentials of both the pore walls and the QDs is relatively unknown, and iii) while a spatiotemporal ionic gradient is considered in our model, it still does not account for a reactive pore wall which could cause additional flows in the system.

113

5-4. Conclusion

In our study of pseudomorphic mineral replacement reactions, we showed that convective flows generated through ion gradients inside the pores of the mineral (a solid solution of K(Br,Cl)) are diffusioosmotic in nature. Through a combination of microscopy, spectroscopy and semi- analytical methods, we showed that these fluid flows can lead to extraction of trapped resources at rates which are orders of magnitude higher than diffusion. Such diffusioosmotic fluid flows provide a new perspective towards fluid-solid interactions which are important in earth science, materials science, and chemistry. These studies also provide fresh impetus towards developing new models for electrostatic forces in order to determine the structure of Debye layer at high salt concentrations, and also exploring the various physical limits of micro- and nanoscale fluid dynamics. Our study highlights the importance of internal mass transfer for transport across fluid- mineral interfaces which are facilitated by electrokinetic flows and not diffusion, in situations

114 where transport is the rate-limiting process. This chapter may enable researchers in exploring various “chemical controls” that could enhance or diminish reactivity across fluid-mineral interfaces for various tailored applications. We expect these findings to impact mining processes and improve hydraulic fracking efficiencies with an intent towards using autonomous chemical processes like pMRR in extracting natural gas from shale formations.

115 5-5. References

1. Reboul, J. et al. Mesoscopic architectures of porous coordination polymers fabricated by

pseudomorphic replication. Nat. Mat. 2012, 8, 717-723.

2. Hellmann, Roland, et al. Unifying natural and laboratory chemical weathering with interfacial

dissolution–reprecipitation: a study based on the nanometer-scale chemistry of fluid–silicate

interfaces. Chemical Geology 2012, 294, 203-216.

3. Boateng, D. A.; Phillips, C. R. Interpretation of the leaching kinetics of pentlandite in a complex

system by the shrinking core model. Ind. Eng. Chem. Proc. Des. Dev. 1984, 23, 557-561.

4. Putnis, A. Why Mineral Interfaces Matter. Science 2014, 343, 1441-1442.

5. Putnis, C. V.; Ruiz-Agudo, E. The mineral-water interface: where minerals react with the

environment. Elements 2013, 9, 177–182.

6. Matter, J. M.; Kelemen, P. B. Permanent storage of carbon dioxide in geological reservoirs by

mineral carbonation. Nat. Geo. 2009, 2, 837-841.

7. Lu, A. H.; Hao, G. P. Porous materials for carbon dioxide capture. Ann. Reports Sec."

A"(Inorganic Chemistry) 2013, 109, 484-503.

8. Putnis, A.; Putnis, C. V. The mechanism of reequilibration of solids in the presence of a fluid

phase. J Solid State Chem. 2007, 180, 1783-1786.

9. Putnis, A. Mineral replacement reactions. Rev. Miner. Geochemistry 2009, 70, 87-124.

10. Rendon-Angeles, J. C.; Yanagisawa, K.; Ishizawa, N.; Oishi, S. Topotaxial conversion of

chlorapatite and hydroxyapatite to fluorapatite by hydrothermal ion exchange. Chem. Mat. 2000,

12, 2143-2150.

116 11. Chopin, C. Ultrahigh-pressure metamorphism: tracing continental crust into the mantle. Earth

Plan. Sc. Lett. 2003, 212, 1-14.

12. Putnis, A.; Austrheim, H. Fluid‐induced processes: metasomatism and metamorphism.

Geofluids 2010, 10, 254-269.

13. Anderson, J. L. Colloid transport by interfacial forces. Ann. Rev. Fluid Mech. 1989, 21, 61-99.

14. Abecassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Boosting migration of large particles by solute contrasts. Nat. Mat. 2008, 7, 785-789.

15. McDermott, J. J.; Kar, A.; Daher, M.; Klara, S.; Wang, G.; Sen, A.; Velegol, D. Self-generated diffusioosmotic flows from calcium carbonate micropumps. Langmuir 2012, 28, 15491-15497.

16. Ebel, J. P.; Anderson, J. L.; Prieve, D. C. Diffusiophoresis of latex particles in electrolyte gradients. Langmuir 1988, 4, 396-406.

17. Putnis, A. Mineral replacement reactions: From macroscopic observations to microscopic mechanisms. Min. Mag. 2002, 66, 689-708.

18. Oliver, N. H.; Bons, P. D. Mechanisms of fluid flow and fluid–rock interaction in fossil metamorphic hydrothermal systems inferred from vein–wallrock patterns, geometry and microstructure. Geofluids 2001, 1, 137-162.

19. Boateng, D. A.; Phillips, C. R. Interpretation of the leaching kinetics of pentlandite in a complex system by the shrinking core model. Ind. Eng. Chem. Proc. Des. Dev. 1984, 23, 557-561.

20. Scurfield, G.; Segnit, E. R. Petrifaction of wood by silica minerals. Sed. Geology 1984, 39,

149-167.

117 21. Pollok, K.; Putnis, C. V.; Putnis, A. Mineral replacement reactions in solid solution-aqueous solution systems: Volume changes, reactions paths and end-points using the example of model salt systems. Am. J Sc. 2011, 311, 211–236.

22. Lasaga, A. C. Kinetic theory in the earth sciences. Princeton University Press. 1998

23. Steefel, C. I.; Lasaga, A. C. A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Amer. J Sc. 1994, 294, 529-592.

24. Brantley, S. L. Kinetics of mineral dissolution, in Kinetics of Water-Rock Interaction, edited by S. Brantley, J. Kubicki, and A. F. White 2008, pp. 151–210, Springer, New York.

25. Putnis, C. V.; Mezger, K. A mechanism of mineral replacement: isotope tracing in the model system KCl-KBr-H2O. Geochimica et Cosmo. Acta. 2004, 68,2839-2848.

26. Putnis, C. V. Direct observations of pseudomorphism: compositional and textural evolution at a fluid-solid interface. Amer. Min. 2005, 90, 1909–1912.

27. Siebecker, M.; Li, W.; Khalid, S.; Sparks, D. Real-time QEXAFS spectroscopy measures rapid precipitate formation at the mineral–water interface. Nat. Comm. 2014, 5.

28. Hellmann, R. et al. Nanometre-scale evidence for interfacial dissolution–reprecipitation control of silicate glass corrosion. Nat. Mat. 2015.

29. Raufaste, C.; Jamtveit, B.; John, T.; Meakin, P.; Dysthe, D. K. The mechanism of porosity formation during solvent-mediated phase transformations. Proc. Royal Soc. A: Math., Phys. Eng.

Sc. 2010, rspa20100469.

30. Bear, J. Dynamics of Fluids in Porous Media. American Elsevier Publishing Company; New

York 1972. pp 44-45.

118 31. Fuerstman, M. J.; Deschatelets, P.; Kane, R.; Schwartz, A.; Kenesis, P. J. A.; Deutch, J. M.;

Whitesides, G. M. Solving Mazes Using Microfluidic Networks. Langmuir 2003, 19, 4714-4722.

32. Goodknight, R. C.; Klikoff, W. A.; Fatt, I. Non-steady-state Fluid Flow and Diffusion in

Porous Media Containing Dead-end Pore Volume 1. J. Phys. Chem. 1960, 64, 1162 – 1168.

33. Stone, H. A.; Stroock, A. D.; Ajdari, A. Engineering Flows in Small Devices: Microfluidics toward a Lab-on-chip. Ann. Rev. Fluid Mech. 2004, 36, 381-411.

34. Squires, T. M.; Quake, S. R. Microfluidics: Fluid Physics at the Nanoliter Scale. Rev. Mod.

Phys. 2005, 77, 977-1026.

35. Whitesides, G. M. The Origins and the Future of Microfluidics. Nature 2006, 442, 368-373.

36. Kar, A.; Chiang, T. Y.; Ortiz-Rivera, I.; Sen, A.; Velegol, D. Enhanced Transport Into and Out of Dead-End Pores. ACS Nano 2015.

37. Derjaguin, B. V.; Sidorenko, G. P.; Zubashenko, E. A.; Kiseleva, E. V. Kinetic Phenomena in

Boundary Films of Liquids. Kolloidn Zh. 1947, 9, 335-348.

38. Dukhin, S. S.; Derjaguin, B. V.; Matievich, E. Electrokinetic Phenomena. Surface and Colloid

Science. Vol. 7, New York, Toronto; John Willey and Sons 1974.

39. Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. Motion of a Particle Generated by

Chemical Gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247-269.

40. Bikerman, J. J. Philos. Mag. 1942, 33, 384

41. Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal dispersions. Cambridge University

Press 1992.

42. Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247-269.

119 43. Khair, A. S.; Squires, T. M. Ion steric effects on electrophoresis of a colloidal particle. J. Fluid

Mech. 2009, 640, 343-356.

44. Kilic, M. S.; Bazant, M. Z.; Ajdari, A. Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations. Phys. Rev. E 2007, 75, 021503.

45. O'Brien, R. W., & White, L. R. Electrophoretic mobility of a spherical colloidal particle. J

Chem. Soc., Faraday Trans. 2: Mol. Chem. Phys. 1978, 74, 1607-1626.

46. Revil, A.; Schwaeger, H.; Cathles, L. M.; Manhardt, P. D. Streaming potential in porous media:

2. Theory and application to geothermal systems. J Geophys. Res.: Solid Earth (1978–2012) 1999,

104, 20033-20048.

120 Chapter 6

Conclusion & Future Work

6-1. Summary of the Thesis

Electrokinetic flows near charged surfaces have been extremely powerful in diverse fields such as colloid science, micro-and nanofluidics, and electrochemistry. However the spontaneous origin of these flows occurring in natural and artificial systems, undergoing disruptions, is lesser understood. A common example is the LoSal process1 where it has been observed that flooding oil reserves like Berea-sandstone cores with water which has approximately 200 ppm of salt content i.e. 1/100th of the reservoir brine composition, makes the yield of oil recovery go up by as much as 6-8 % of the total output. There are many mechanisms likely to affect such increase in oil extraction yields, such as sweep-efficiency improvements, interfacial-tension reduction, multicomponent ion exchange, and electrical double layer (EDL) expansion. Among all these,

EDL expansion at low salinity has been found to be the driving mechanism for improved oil recovery.2 However, current models fail to account for the mechanism of transport for these emulsions from deep crevices, which raises a very specific question: how does the EDL expansion ensure release of trapped oil emulsions which are mostly stuck inside tight and dead-end pores where pressure driven flows cannot exist?

Through our studies on transient ionic gradients occurring either from mineral dissolution or from imposed salinity variations across dead-end pores, we were able to show that while salinity differences can clearly result in EDL expansion, their presence across pores generates convective motion of fluid and tracers which leads to extraction of emulsions. With this early motivation in

121 our study, we applied the same concept to a lot of newer fields where diffusiophoresis hadn’t been tested before, such as membrane systems and mineral-water interactions. The thumb rule in all these studies were: if an ionic gradient exists in a system with the ions diffusing at different rates, we could accurately predict speeds of charged particles and fluid flow through our traditional electrokinetic equations. However, it was surprising to also notice that diffusiophoresis can occur in high salt concentration gradients with the classic equations yielding a reasonably accurate prediction for observed speeds of tracers in the system. This study with pseudomorphic mineral replacement reactions opens up a host of new options for analyzing geochemical systems, radioactive waste remediation, and leakage of harmful chemicals into aquifers. This study also gave us an insight into predicted rate-limiting processes and mass transfer phenomena which we discuss later in this chapter. Below, I provide a detailed account of the conclusions we were able to draw for the various scientific questions discussed in this thesis.

Conclusion drawn from micropumps

We demonstrate flows that are self-generated by ionic gradients caused from dissolving mineral particles. The mechanism is self-diffusiophoresis, the first such study we know for mineral systems. A calcium carbonate microparticle, found extensively in geologic formations, upon dissolution sets-up ionic gradients which give rise to spontaneous electric fields. In the presence of charged surfaces like particles or walls, this electric field drives electrokinetic flows. Flow profiles changed on altering particle or surface zeta potentials, as well as adding additional salt, which supports our hypothesis that the flows are self-diffusiophoretic. The rates of particle motion that we observed could be as high as 50 μm/s close to the dissolving mineral surface.

122 Conclusion drawn from membrane studies

We demonstrated diffusiophoresis as an important mechanism of particle deposition on hollow fiber microporous membranes. Previously, the primary mechanism that has been considered is only a filtration mechanism. We conduct experiments in a system devoid of any convective flow or pressure gradient, and subject to only a salt gradient that causes the diffusiophoretic particle transport. The membrane creates the gradient by releasing salt to the surrounding solution and thereby, generates a spontaneous electric field, attracting particles by the diffusiophoretic effect. Different salts (NaCl, KCl, LiCl) demonstrated this effect, as expected, with the relative extent of particle deposition shown to be an active function of the i) difference in diffusion coefficients of the ions, ii) zeta potential of particles, and iii) ionic-gradient applied across the walls of the membrane. Modeling results also support our experimental data of tracer particle velocities according to the theory of diffusiophoresis. Finally, we were able to develop an approach to prevent the particle deposition by introducing CaCO3 microparticles in the system.

These particles induce the formation of an exclusion zone around the membrane by creating an opposing electric field and reducing the zeta potential on tracers.

Conclusion drawn from transport in dead-end pores

In this work, we demonstrated experiments and supporting calculations on the electrokinetic flow, via transient diffusioosmosis (TDOF), in a dead end pore geometry. The pore system consists of a small dead-end cylindrical channel of square cross section immersed into a slightly larger dead-end pore. The small pore contains an electrolyte solution (typically NaCl or KCl, some divalent salts are also used) while the larger pore is free of salt. The resulting (transient) salt gradient results in a spontaneous (and transient) electric field directed from the small to large pore,

123 which drives a diffusioosmotic fluid flow in the same direction. Mass conservation requires a pressure-driven back flow towards the dead end of the smaller pore. Thus, species that are close to the wall are transported to the large pore, while species near the center of the small pore, or in the large pore, can be sent to the dead end of the small pore. This is demonstrated with colloidal particles of different sizes and also hexadecane oil emulsions. Further, our electrokinetic model, which has no adjustable parameters, allows quantitative predictions that agree with the experimental observations. We found that these flows could extend for about a mm into the dead- end pore. Thus TDOF can yield an exchange of material across pores, which is expected to be of significance in biological and geological systems.

Conclusion drawn from mineral replacement reactions

We demonstrated diffusioosmosis as an essential transport mechanism through which mineral-water transformations take place in nature. Ion gradients that frequently occur during pseudomorphic mineral replacement reactions, a class of mineral-water interaction, enable dissolution/reprecipitation to be coupled with the convective flows generated along the pores in the mineral system. By controlling the precipitation rates, we observed that the convective flows inside the pores were able to extract trapped resources from the crystal matrix out into the sink.

These fluid flows were found to be diffusioosmotic in nature which enable internal mass transfer across the fluid-mineral interface to dominate over surface-reaction. Our electrokinetic observations could also be modelled accurately by considering finite ion-ion pair interaction through Bikerman’s corrections which in fact resembled closely with the studies done using the classic O’Brien and White equations.

124

6-2. New! - Internal Mass Transfer enabled by Diffusioosmotic Flows

In any mineral-water interaction, which are mostly heterogeneous reactions, mass transfer and surface reaction with the surrounding fluid plays a critical role in the overall transformation.

At any given condition, e.g. changes in pH or the rate of mixing of the background fluid, transport and interface reactions must occur together, and for these steps, the slowest reaction must be rate- limiting. In order to decipher the dominant mode in a particular reaction, experimentally, the fluid interacting with the mineral is stirred with the rate of reaction being studied during this process. If the rate of reaction changes with the stirring rate, odds are high that the reaction process is transport-limited. And if the rates do not change with stirring or changes in pH, then the opposite is true, i.e. the process is surface reaction limited.

One such example is the dissolution of calcite in water. Fig. 6-1 shows the study done on rate of calcite dissolution in water at various pH values. In region 1, where dissolution is fast with changes in pH, the process is transport limited. In region 2, where the rate of dissolution is unaltered by the changes in pH, the reaction is surface reaction controlled. Traditionally, it is considered that in region 2, diffusion across the boundary layer is fast compared to the rate of reaction which makes the process surface-reaction limited. Hence, diffusion is regarded as the internal mass transfer mechanism. Mathematically, it can be represented by the Fick’s first law:

Ji D i c i (6-1)

125

However, our study with calcite micropumps shows that at pH  5-8, diffusion of ions can create diffusioosmotic flows emanating radially out from the calcite surface thus resulting in fluid circulation around the microparticle. This enhances the internal mass transfer within the crystal which is expected to affect surface-reaction of the calcite particle. This idea of “internal mass transfer through diffusioosmotic flows” has not been captured in mineral-fluid interactions before.

This phenomenon could also explain the time scales of transformations of many mineral phases which are reportedly very fast in nature compared to their predictions of geological time scales of evolution from pure diffusion process. Mathematically, we can represent this through the Nernst-

eff Planck equation, where Ji represents the actual flux of ions enabling internal mass transfer in the

eff eff 2DD system and Di is the effective diffusion coefficient of ions (for a z:z salt, D ) i DD

126 ze Jeff D eff ci D eff c E (6-2) i i ikT i i

While general transport-limiting processes refer to external mass-transfer, our studies have shown that internal mass transfer plays a critical role in the evolution of a mineral phase. Some of the major characteristics of both the external and internal mass transfer processes are:

Table 6-1. External mass transfer processes v/s Internal mass transfer processes

Property External Mass Transfer Internal Mass Transfer

Observed Phenomenon Results in dissolution/ reaction Results in mineralogical phase changes

Cause Advection, Mixing Internal electrokinetic (e.k) flows

Role of Diffusion Negligible Diffusion drives e.k flows Through external means like Through chemical means like pH Manipulation pumps and valves changes, salt concentration Depends on Péclet number Depends upon ionic gradient in the Rate of mass transfer and Reynolds number system.

6-3. New! - Concentration Boundary Layer Diffusiophoresis

We have classified fluid flows into broadly three sub-domains based on the mechanism through which they originate in the system – Pressure driven (p), electrokinetic driven () and concentration gradient driven (c). As shown in Fig. 6-2a, pressure driven flows in tubes are known through Hagen-Poiseuille’s parabolic flow. Electrokinetic driven flows are known through electroosmosis in a channel which is generated upon application of an external electric field in the system through inserting electrodes. Concentration gradient driven flows, however new, have been

127 known to generate chemiosmotic flows. Concentration gradients are also known to drive

Marangoni flows due to a difference in interfacial tension across the fluid and the object.

Traditionally, these three subdomains are considered to be independent of each other.

However, recent studies have shown that these fluid flow driving mechanisms are interrelated.

While pressure driven flows are known to generate electrical potentials across a tube through the mechanism of streaming potential4, electrokinetic driven flows in a closed capillary cell generate pressure driven back flows (which gives them the parabolic profile) in order to ensure fluid continuity.5 Concentration gradients across semi-permeable membranes leads to a pressure imbalance generating osmotic flows in the system.6 This is the reason why grapes burst in a hypotonic solution and shrink in a hypertonic solution. Recently, electric fields across lipid bilayers have also been shown to exhibit concentration gradients which can be detected through labeled probes under epifluorescence microscopy.7 In this thesis, we discuss the other two aspects, diffusioosmosis and boundary layer diffusiophoresis, which highlight the ways through which microscale fluid flows can be manipulated. While diffusioosmosis is not a novel concept, boundary layer diffusiophoresis has not been explored before in literature. My focus here is to establish qualitatively the theory behind this mechanism and illustrate few examples where this mechanism may be critical to the observed phenomenon.

128

Figure 6-2. Interrelation between various fluid flow mechanisms and the role of boundary layer diffusiophoresis. (a) At the microscale, different mechanisms for driving fluid flows such as pressure gradient (p), gradient in electric potential () and concentration gradient (c) are coupled with each other through the participation of ions and charged surfaces in solution. This thesis highlights the contributions from diffusioosmosis and boundary layer diffusiophoresis as additional fluid flow and transport mechanisms. (b) The geometry of the concentration boundary layer (CBL) model which extends from the dissolving calcite surface out into the bulk with a thickness of c. The arrows denote the fluxes 2+ - - of Ca , HCO3 and OH from the mineral surface. The difference in diffusion coefficients of these ions generates a steady-state or transient electric field across the CBL leading to BLDP of the dispersed tracers.

Boundary layer theory is a well-studied aspect of transport phenomena and defined as the layer of fluid in the immediate vicinity of a surface where viscous forces are significant. The fluid in the background, flowing past a surface, is halted at the entrance with the resistance to motion gradually being dissipated into the main body via viscosity. This results in the development of a velocity boundary layer which is represented by the thickness  signifying the distance from the

129 plate at which the velocity profile is fully developed. Mathematically, /x 5 / Rex where x represents the length of the plate, and Rex is the Reynolds number of the fluid in the direction of fluid flow. Alternately, when a fluid at certain concentration of salt is used to sweep another fluid on a stationary surface at a different concentration, it results in a concentration boundary layer

(CBL). Additionally, a reactive surface like calcite or any other mineral can result in in a CBL which may be spatiotemporal or transient in nature. The thickness of the CBL (c) in a laminar flow of fluid is given by

1/2 1/3 cx/x Re Sc (6-3)

1/3 Or, c Sc (6-4) where Sc is the Schmidt number representing the viscous diffusion rate over molecular diffusion rate. As an example, the thickness of the concentration boundary layer over a 1 cm long plate (x ~

-2 10 m) with Rex ~ 10 and Sc ~ 1000 (typical value for water), is c ~ 300 μm. Thus, this sets up an ionic gradient across the boundary layer which decays rapidly into the bulk. For a confined volume of fluid (where a source of higher concentration of ions and a sink of lower concentration of ions exist, a situation which is common in microfluidics or capillary experiments), the time scales for

2 which these ionic gradients exist, t, is only a few minutes (t ~ c /D ~90 seconds). However, in a system where there is a constant fresh feed of salt solution, the ionic gradient can be maintained for a much larger period of time.

Ionic gradients across the concentration boundary layer can be spatiotemporal in nature depending upon the volume of fluid flowing over the plate and the time scales of observation. Such gradients of ions across the boundary layer can act a priori as feed to the diffusiophoresis of dispersed charged particles. To the best of my knowledge, the idea of diffusiophoresis across

130 concentration boundary layers has not been explored in literature. I call this phenomenon as

“Boundary Layer Diffusiophoresis” or BLDP as the concept can also be extended to include thermal diffusiophoresis when the surface and fluid are at different temperatures with respect to each other. To get an estimate of the diffusiophoretic speeds, an ionic gradient of 1 M across c (~

300 μm) with the - potential of the particle being of the order of kBT/e (~ 25 mV) will generate particle speeds on the order of few micrometers per second.

How can BLDP originate? BLDP can originate under certain set of conditions:

1. Flow over a stagnant plate

If a channel is inundated initially with a salt solution of either higher or lower concentration

compared to the solution fed at a later stage.

2. Flow over a reacting surface

Heterogeneous reactions are expected to demonstrate this effect. Reactions on a Janus particle

and reaction described in chapter 5 are two such examples.

BLDP is expected to play a significant role in reverse osmosis where concentration polarization across the membrane surface provides a continuous feed for the diffusiophoretic attraction of charged tracers in the feed water. We expect that clogging caused by BLDP would be the highest near the entrance for the feed water and steadily decrease along the membrane surface. This is due to the flux of ions being the highest near the thin CBL region.

Here, I briefly explain two examples where BLDP may play a vital role in particle motion in the system.

1. Janus particle swimming in a convective stream: A Janus particle, made of half-coated polystyrene bead with platinum, can move in a dilute solution of H2O2 by decomposing it

131 asymmetrically across its two ends. This generates a local concentration gradient across the particle which makes the fluid to slip on its surface. The resultant motion of the particle is always directed away from the active catalyst site, which in our case is platinum.8 Typically, these motors are analyzed in a quiescent flow (Fig. 6-3a) where their motion is confined to an x-y plane parallel to the wall.

When a background shear flow of low Péclet number (Pe, where Pe = rate of advection/rate of diffusion), say Pe = 0.5, is applied perpendicular to the plane of symmetry of the Janus particle, a boundary layer is formed across its surface. The thickness of this boundary layer will vary since the fluid does not sweep the surface of the Janus particle at the same rate. This could result in a polarization of the CBL as shown in Fig. 6-3b. Such a polarized boundary of solute across the reactive face of the Janus particle can create a drift in the z-direction, thus yielding a net velocity

9 of Uxyz. A recent paper by Frankel and Khair (2014) analyzes this problem numerically. We expect this to have significance in cargo transport abilities in vivo for similar Janus motors and pumps.

132

Figure 6-3. Unexpected cross-wise motion of particles under a convective flow at moderate Péclet number (Pe  0.5). (a) A self-diffusiophoretic Janus motor undergoes motion upon catalytic decomposition of H2O2 across its active surface (which can be platinum with the inactive site being polystyrene). (b) Upon application of a shear flow, a CBL would be immediately set up across the Janus particle with its thickness being inversely proportional to the rate at which fluid sweeps its surface. The CBL is expected to be polarized under a shear flow resulting in a cross-wise drift of the particle. (c) CBL formed across the walls of a dead-end pore can induce cross-wise motion of tracers as seen in Fig. 4-4.

2. Cross-wise motion in dead-end pores: In chapter 4, we analyzed the motion of tracers in a dead- end pore set-up where a salt gradient across the pore can generate TDOFs that leads to exchange of materials across the pore. Towards the end of that chapter, we also showed experimental results for the tracers behaving in a rather strange manner as they enter the dead-end pore. Along with the axial motion that was caused by the ionic gradient in the system, the sPSL beads were seen to move in a cross-wise fashion towards the wall of the dead-end pore. This effect was seen to be more pronounced in cases where a NaCl gradient was used than in a KCl gradient. It was also noticed that sPSL beads entering the pore bear to the side-walls of the dead-end capillary exhibited larger and faster drifts than the ones entering more towards the center axis of the dead-end

133 capillary. Our model could not capture this subtle behavior of the particles, which we think may have been caused by the presence of CBL in the system.

Since the reservoir and the sink in a dead-end capillary experiment are at two different concentrations, the transient diffusioosmotic flow can build up a temporal CBL along the walls of the smaller dead-end capillary. The concentration gradients along the CBL decays spatiotemporally along the length of the dead-end pore, with it being the highest at the mouth of the pore. As expected, we see tracers near the mouth move rapidly towards the wall than the particles which are away from the wall. Since concentration gradients of KCl generate solely a chemiosmotic and chemiphoretic motion, the tracers were seen to move in rectilinear paths except the ones very close to the wall which also moved in a cross-wise fashion. This observation is critical to understanding particle deposition along the walls of a micro- and nanochannel undergoing sudden fluctuation in terms of concentration of the salt in the system.

6-4. Simultaneous Propulsion and Pumping of Micromotors

Micropumps and self-powered micromotors have potential applications in chemical analysis10, extraction of oil from dead-end pores, repair of cracks in materials11, pumping fluids in microchannels12 and prevention of membrane fouling. The overarching goal is to intelligently maneuver and guide motion and assemblies at micro- and nanoscale in order to perform various tasks efficiently.

The micromotors, e.g. gold-platinum bimetallic nanorods (l = 2 μm, a = 200 nm), operate through chemical decomposition of hydrogen peroxide solution which generates concentration

134 gradients along its surface. These gradients can drive motion of the motors through mechanisms such as electrophoresis and diffusiophoresis. Stationary motors can generate fluid flows in the system through electroosmosis and diffusioosmosis. The motion of these motors in solution is stochastic in nature. They can spin, tumble, translate linearly, take turns indiscriminately, and normally expend their chemical energy rapidly. This has proved to be a bottleneck in widespread application of these motors, for example in directed cargo-delivery duties. However, there lies a possibility in overcoming this though the use chemical micropumps in conjunction with micromotors in solution. Since the fluid flows are always directed radially out from calcite micropumps studied earlier in the thesis, the Au/Pt catalytic motors can harness this external fluid flow and navigate through a maze to a particular destination. Through their own self-propulsion mechanism which complements the fluid flow from pumps, we can possibly set-up an intelligent and robust microscale “cargo delivery factory”.

However, calcite microparticles are observed to dissolve rapidly in hydrogen peroxide medium with Au/Pt nanorods (see Fig. 6-4a). This is because of the following reaction

2 CaCO3(s ) H ( aq ) Ca ( aq ) HCO 3( aq )

HCO3(aq ) H ( aq ) H 2 CO 3( aq )

2 CaCO3()s H 2 CO 3() aq Ca () aq2 HCO 3() aq 2 CaCO3()s H 2() O aq Ca () aq HCO 3() aq OH () aq

As more protons are produced at the platinum end of the microrods and bicarbonate being a strong conjugate base of a weak acid H2CO3, the reactions are favorable to progress towards consumption of calcite in the system. As the micropumps dissolve fast, it leads to density gradient flows which dominates over diffusioosmosis before the micropumps, eventually, cease to exist. As seen in Fig.

6-4a, the micropump circled in green gradually disappears resulting in reequilibration of the

135 micromotors in the system. Hence, we synthesized barite (BaSO4) micropumps which do not get consumed instantly as the bisulfate ions produced by a similar dissolution mechanism are weak

2+ conjugate bases of a strong acid H2SO4. More importantly, the Ba ion has a lower diffusion

- coefficient than HSO4 ions which leads to electric fields in the system being directed radially out from the microparticle.

Fig. 6-4b shows the pumping action caused by a barite pump in DI water with 3 % H2O2 solution. Our barium sulfate microparticles were synthesized by combining equimolar amounts of

BaCl2 and (NH4)2SO4 in the presence of .25 M H2O2 solution at a pH of 12 obtained from the addition of NaOH.13 The pumping of sPSL tracer particles was observed with fluorescent microscopy. Pumping rates were analyzed under various concentrations of H2O2 from 0% up to

5% and it was noticed that average speeds of tracers go up to as high as 10 μm/s. Note that the diffusiophoretic speeds attained in this case are lower than that obtained with CaCO3 micropumps and it has to do with the ions governing the E field generated in the surrounding solution. While in case of calcite, the difference between hydroxyl and calcium ions was large (leading to a large

 = (DCa2+ - DOH-)/( DCa2+ + DOH-)), in the case of barite micropumps (with bisulfate and barium as the two participating ions) this difference is small leading to a small  value. Hence the E field generated in case of calcite is higher than in case of barite.

The next step in the project is to test the barite micropumps with micromotors and study their directionality in motion. We wish to quantify the optimum spacing between two barite micropumps which leads to exclusion zones that do not overlap with each other. These exclusion zones are normally generated due to the fluid flow emanating radially outwards from the micropump carrying the dispersed tracers radially out into the bulk. By confining the micromotors into a narrow band between two micropumps, we can self-propel them perpendicular to the

136 direction of fluid flows, and make them navigate through a maze of micropumps to a desired location (Fig. 6-4c).

137

6-5. References

1. Morrow, N.; Buckley, J. Improved oil recovery by low-salinity waterflooding. J Petro. Tech.

2011, 63, 106-112.

2. Nasralla, R. A.; Nasr-El-Din, H. A. Double-Layer Expansion: Is It A Primary Mechanism of

Improved Oil Recovery by Low-Salinity Waterflooding?. SPE Res Eva. Eng., 2014. preprint.

3. Brantley, S. L. Kinetics of mineral dissolution, in Kinetics of Water-Rock Interaction 2008, edited by S. Brantley, J. Kubicki, and A. F. White, pp. 151–210, Springer, New York.

4. Gross, D.; Williams, W. S. Streaming potential and the electromechanical response of physiologically-moist bone. J Biomechanics 1982, 15, 277-295.

5. Bowen, B. D. Effect of a Finite Half-width on Combined Electroosmosis-Electrophoresis

Measurements in a Rectangular Cell. J. Coll. Int. Sc. 1981, 82, 574-576.

6. Cath, T. Y.; Childress, A. E.; Elimelech, M. Forward osmosis: principles, applications, and recent developments. J Mem. Sc. 2006, 281, 70-87.

7. Groves, J. T.; Boxer, S. G. Electric field-induced concentration gradients in planar supported bilayers. Biophys. Journal 1995, 69, 1972-1975.

8. Baraban, L.; Tasinkevych, M.; Popescu, M. N.; Sanchez, S.; Dietrich, S.; Schmidt, O. G. ().

Transport of cargo by catalytic Janus micro-motors. Soft Matter 2011, 8, 48-52.

9. Frankel, A. E.; Khair, A. S. Dynamics of a self-diffusiophoretic particle in shear flow. Phy. Rev.

E 2014, 90, 013030.

10. Wu, J.; Balasubramanian, S.; Kagan, D.; Manesh, K. M.; Campuzano, S.; Wang, J. Motion- based DNA detection using catalytic nanomotors. Nat. Comm. 2010, 1, 36.

138 11. Yadav, V.; Freedman, J. D.; Grinstaff, M.; Sen, A. Bone‐Crack Detection, Targeting, and

Repair Using Ion Gradients. Angew. Chem. 2013, 125, 11203-11207.

12. Sengupta, S. et al. DNA Polymerase as a Molecular Motor and Pump. ACS Nano 2014, 8,

2410-2418.

13. Zhang, X. H.; Yan, F. W.; Guo, C. Y.; Li, F. B.; Huang, Z. J.; Yuan, G. Q. Hydrogen peroxide triggered morphological evolution of barium sulfate crystals under basic conditions. Cryst. Eng.

Comm. 2012, 14, 5267-5273.

139 Appendix A

Ionic Gradients in Micropumps

A-1. Concentration and Diffusiophoretic Velocity Profile

A-1-1. Concentration Profile

To fully understand and analyze the velocity profile of fluid and tracer particles moved through diffusioosmotic and diffusiophoretic pumping of a dissolving mineral microsphere, we must first understand the concentration gradient of the ions in the system. An appropriate model of the calcium carbonate microsphere system is that of a sphere dissolving into an infinite bath.

We make the assumptions that the microsphere has radius a with a non-moving solid-liquid interface, that there is a constant surface ionic concentration Cs equal to the saturation concentration of calcium carbonate at r = a, the overall diffusion coefficient of the ions is a constant, D, and that the sphere is dissolving into an infinite bath with concentration Cb.

Fick’s Second Law describes this situation (unsteady-state diffusion):

C DC2 (A-1) t

with boundary conditions:

C(r  a,t)  Cs (A-2) C(r  ,t)  Cb

And initial condition:

(A-3) C(r,t  0)  Cb

140

The solution for this concentration profile is:

a  r  a  C(r,t)  Cs  Cb  erfc   Cb (A-4) r  4Dt 

As time progresses, the error function complement goes to 1 and we reach the expected steady- state concentration profile:

a C(r)  C  C   C (A-5) s b r b

A-1-2. Time to Pseudo-Steady State

It is convenient to use the steady-state concentration profile for analyzing our diffusiophoretic velocities, but to do so we must be sure that we have observed the system after it has reached steady state. We typically observe tracer movement up to 80 μm away from the micropump. In this case, for our system with r = 3.0×10-06 m, D = 1.70×10-9 m2/s (weighted

-4 harmonic average of the three primary ions), Cs = 1.11*10 M (as determined above) and Cb = 0, we should reach 95% of the steady state concentration value at a distance of 80 μm in a time of t

= 111 s. Since our experiments are typically performed over the course of 10-20 minutes, with a

5 minute preparation time, we expect that the observed area of our system should be at pseudo- steady state throughout the course of experimentation.

141 A-1-3. COMSOL Solution for Concentration Profile

Using the Fick’s 2nd law of diffusion and the non-dimensionalized boundary conditions, we simulate the concentration profile for ions using COMSOL Multiphysics 4.3 (Fig. A-1a). As expected, we found that the concentration gradients radially decay away from the microparticle surface (Fig. A-1b).

Figure A-1. Concentration profile plot for CaCO3 dissolution in an infinite bath. (a) Scaled concentration plot shows that about 500 μm away from the microparticle, the concentration goes to zero. (b) Concentration gradients decay radially away from the microparticle, as expected. This results in tracers speeds being the highest near to the pump while gradually decaying as they travel into the bulk.

A-1-4. Diffusiophoretic Velocity of a Tracer Particle

The equation for diffusiophoresis of a tracer particle in a concentration profile near a charged surface is given as:

C(r)  DC  DA  kbT   ( p   w ) U (r)       C(r)  DC  DA  e   (A-6) 2   C(r)  2  k T   2  e   2  e p     b  ln1 tanh  w   ln1 tanh   C(r)    e   4k T   4k T         b    b 

142 where Dc and DA are the diffusion coefficients of the cation and anion, respectively, ζp and ζw are the zeta potentials of the particle and wall, respectively, kbT is the thermal energy, e is the electron charge, ε is the permittivity of the medium, and η is the viscosity of the medium.

For our steady-state concentration profile,

    C(r) a C  C   b s  (A-7) C(r) r 2  a(C  C )   C  s b   b r 

with the special case of no bath concentration:

C(r) 1  - (A-8) C(r) r

One interesting observation that can be made from these equations is that the surface concentration has little effect on the overall velocity, especially when it is much higher than the bath concentration.

From this equation, we would expect the velocity to be roughly inverse to the radial distance. However, this does not take into account the changing zeta potentials of both the particle and the wall as a function of calcium carbonate ion concentration. We explored this by attempting to fit these curves to the data shown in Fig. 2-4.

In Fig. 2-4c, we have attempted to fit both the above 1/r function in the case of no bath concentration as well as the full 1/r2 dependency for a finite bath concentration. The following two fitting curves resulted:

143 91.7 U (r)  c1 r   (A-9) 24896  1    U c2 (r)  2 r  -10 (271.46)  10    r 

We observe that due to an infinitesimally small bath concentration, the three-parameter fit collapses onto the one-parameter fit, as shown in Fig. 2-4c.

To fit 2-4d, which contained two pumps facing each other, a liner superposition of separate

1/r dependencies for each particle was used. The following fit resulted:

34.03 34.03 U d (r)   (A-10) r  25.1 r  25.1

In both 2-4c and 2-4d, we observe that these fits undercut a significant portion of the data

(with correlation coefficients R2 between 0.6 and 0.7). This is due to an additional radial term in the full diffusiophoresis equation: that of the zeta potentials of the tracer particles and of the glass surface, which have CaCO3 concentration dependence and therefore also a radial dependence. We do not have zeta potential measurements for the full range of CaCO3 concentrations; however, observation of the difference between the data in Fig. 2-4 and the fits reported here can be used to gain insight into the shapes of those curves.

144 A-2. Impact of Zeta Potential Variation

We can also observe a change in direction and magnitude of the velocities of tracers near to the pump surface given the zeta potential measurements shown in the chapter through the addition of KCl, which mediates the zeta potential change with CaCO3 concentration:

Table A-1. Speeds of sPSL tracers in different solution conditions

Observed Speed Condition ζp (mV) ζw (mV) (μm/s)

CaCO3 -30 -35 35.9 no other salt

CaCO3 -91 -54 -1.03 10 mM KCl

Observed speeds were estimated using frame-by-frame particle tracking as outlined in the methods section.

145 Appendix B

Transport Model in Hollow Fiber Membranes

B-1. Negligible Osmotic Effects

By using different salts – in our case, NaCl, KCl, and LiCl – we were able to create systems with the same osmotic pressure on each side of the membrane. Fig. B-1a shows confocal microscopy images of particles attached to the membrane surface at the isoosmotic molar solutions of KCl and NaCl on either side of the membrane. When the NaCl solution is inside the HFM, and

KCl and tracer particles outside, a net migration was observed from the bulk solution towards the outer membrane wall. This is expected from the theory of diffusiophoresis. An important follow up test is to use LiCl with particles instead of KCl with particles. Now the theory indicates that the motion should be away from the outside of the HFM membrane, into the bulk. This is what we observe in Fig. B-1b.

Figure B-1. Particle migration under equal osmotic concentration across the membrane surface (a) Identical osmotic concentrations of NaCl and KCl is setup as described in Fig. 3-1 with NaCl inside the HFM and KCl outside containing 4.0 µm fluorescent sPSL beads. The beads aggregate on the membrane surface because of the transient salt gradient induced diffusiophoretic transport (b) When KCl was

146 replaced by LiCl of the same osmotic concentration as NaCl inside the HFM, an exclusion region was formed along the walls of the HFM. Particles in this case didn’t stick to the membrane surface.

B-2. Model for Salt Gradients across HFM

We used COMSOL 4.3 to model our salt gradients through the microporous walls of the

HFM. In doing so, we assumed the following system parameters:

Table B-1. System parameters for HFM

Parameters Values Definition

R1 0.1 mm Inner radius of HFM

R2 0.14 mm Outer radius of HFM

R3 0.45 mm Radius of the capillary

L 21 mm Length of HFM

Scale 10 Axial coordinate scale factor

H_max 0.1×R1 Maximum mesh length size

D 1×10-9 m2/s Diffusion constant in liquid phase

-10 2 Dm 1×10 m /s Diffusion constant in membrane

C0 0.01 mol/lit Inside concentration of dialysate

147 Table B-2. Equations to evaluate concentration profile across HFM

System of Inside the HFM On the HFM Outside the HFM equations Fick’s 2nd CCC2 1 CCC2 1 CCC2 1 D() D () D() Law t r2 r r tm r2 r r t r2 r r C CCCC |0; DD||DD|| Boundary r r 0 rrr R11 m r R mrr r R22 r R Conditions CCCC C DD|| DD|| |0 rrr R11 m r R mrr r R22 r R r rR3 Initial C (0, r) = C0 C (0, r) = 0 C (0, r) = 0 Conditions

Note that there is no convection term in the above set of equations as we donot impose any flow in the system.

Figure B-1. Using the parameters in Table B-1 and the equations in Table B-2, we solved for the concentration distribution across HFM which produces a salt gradient causing diffusiophoresis. (a) and (b) are the concentration profile of solute at two different time intervals, i.e. t = 0.1 s and t = 10 s, respectively.

148 The effective diffusion coefficients through the HFM wall, using the pore diffusion model, are shown in the table below

Salt Diffusivities (m2/s) through HFM LiCl 1.89 × 10-10 NaCl 2.76 × 10-10 KCl 3.73 × 10-10

149 Appendix C

Electrokinetic Model for Flows in Dead-End Pores

C-1. Horizontal Dead-end Capillary Set-up

A system of two capillaries (sink and reservoir) is used to form a simple yet robust set-up of transient ion gradients that can generate transport of charged species in the system (Fig. C-1).

Figure C-1. Dead-end capillary set-up with a spatiotemporal salt gradient. A system of two capillaries (sink and reservoir) is used to form a simple yet robust set-up of transient ion gradients that can generate transport of charged species in the system. (a) The larger capillary, filled with DI water or 1 mM salt (which can be either NaCl or KCl), usually forms the sink in our experiments. The capillary was then waxed at one end and placed on a rectangular microscope glass slide. (b) A smaller capillary, generally filled with 10 mM salt (with the salt being the same as that in the sink), forms the reservoir and is inserted into the sink with the top end waxed. This forms a closed system of reservoir and sink with the only opening for studying flows being at the mouth of the smaller capillary that is placed inside the sink.

C-2. Vertical Dead-end Capillary Set-up

As shown in Fig. C-2, an inverted Nikon TE-2000 U microscope tilted on its back was used to study transport in dead-end pores. Such a vertical set up of capillaries accounts for any density

150 driven flows that may arise in the system. By placing the denser solution at the bottom (sink) and the lighter solution at the top (reservoir), we prevented any density gradient to build up in the system. By flipping the concentrations of the salt in the sink and the reservoir, we hypothesized that we should be able to set-up density gradient flows that have a velocity profile similar to the one shown by Hogg & Leschziner (1988)1.

C-2-1. Impact of Density Driven Flows

We observed a parabolic flow profile of tracers due to the salt gradient imposed with the velocity at the center being highest and the velocity at the walls being lowest. Time lapse images

(Fig. C-2) of a dead-end capillary experiment with equal densities of NaCl and KCl (in the reservoir and the sink, respectively) shows that particles move towards the high concentration regime of NaCl. From these transport profiles, we conclude that density gradients have a negligible contribution towards the speeds of the tracers in our dead-end capillary system.

The specific gravities of 10 mM NaCl (1.0004) and 10 mM KCl (1.00053) are almost comparable to that of water (0.9984) at 20ºC. Our model and experiments for diffusiophoretic transport rates of both sPSL and amidine-functionalized PSL (aPSL) beads under these salt gradients exhibit close agreement with the model that eliminates the possibility of a density driven flow in the system.

To further test for diffusiophoresis of beads in comparison to flow due to density gradients, we compared the speeds of the tracers in different salt solutions. In the case of KCl, the speeds were found to be an order of magnitude lower than that observed in the case of NaCl (Fig. C-2).

151

Figure C-2. Vertical set-up involving optical microscopy to study flows and transport in dead-end pores. (a) The dead-end capillary set-up of reservoir and sink was placed on a TE 2000 U microscope which was rotated to a 90º position about its hinge. Such an arrangement accounted for any density flows that might occur in the salt-DI water system, and was also useful in compensating for the settling speeds of tracers in the solution. (b) Axial decay in velocities of sPSL beads due to the spatiotemporal salt gradient induced across a dead-end pore. The speed of sPSL beads (u) are seen to be significantly higher in case of NaCl gradient than that observed in KCl gradient. The velocities decay rapidly over space and time due to the transient nature of flows in the system. Our model (discussed in the chapter 4) successfully accounts for the nature of such variations in speeds. (c) Time-lapse images showing migration of sPSL beads diffusiophoretically from a KCl solution to NaCl solution, both having the same density. The experiment was carried out in a vertically-aligned microscope (as shown in a). NaCl filled the smaller dead-end capillary at the top, whereas KCl occupied the larger capillary at the bottom with 3 m non-fluorescent sPSL beads suspended in it. The beads were observed to move into the NaCl regime (thereby populating the viewing area for these dead-end capillaries) with speeds almost same (RMS deviation in model and experiments < 5%) as predicted in Fig. 4-1. Diffusiophoresis predicts the observed behavior. This indicates that density gradients play a negligible role in the motion of tracers.

152 C-2-2. Transport Profile of Amidine-functionalized PSL Beads

Amidine-functionalized polystyrene beads (aPSL, diameter = 1.5 µm), which carry a positive charge in 10 mM NaCl solution (Fig. C-3), are seen to exhibit a different transport profile as compared to that of sPSL beads in a 10 mM NaCl gradient. In the case of aPSL beads, the diffusiophoretic transport of the beads is comparable to the diffusioosmotic flow along the wall with both velocities directed towards the sink. However, away from the wall, the movement of aPSL beads, which were initially in the sink, is dominated by the fluid flow in the system (for short distances) and are seen to travel towards the dead end pore along the center. Deeper into the dead- end pore, the flow velocity and the particle velocity cancel each other due to increasing in zeta potential of the aPSL beads on moving from DI water in the sink to that of 10 mM NaCl (Fig. C-

3). This results in a stationary dispersion of beads in the bulk.

Figure C-3. Zeta potential of beads in various salt solutions and the transient spatiotemporal nature of the salt gradient. (a) At various concentrations of NaCl and KCl, pH = 5.8, the charges on the beads were evaluated using the ZetaSizer. The values for ζbeads were then used in the model for calculating the respective diffusiophoretic velocities of the beads. (b) Concentration profiles of NaCl and KCl for varying times at different distances from the mouth of the dead-end capillary. Note that the gradient is independent of the initial concentration of salt in the system.

153 C-3. Transport Controlled by the Variation in Zeta Potentials

The charge on colloidal surfaces (zeta potential, ζtracers, where tracers refers to both beads and oil emulsions), in different solutions, was measured with a ZetaSizer Nano ZS90 (Malvern,

MA, model ZEN3690). The charge on capillary surfaces was obtained from Jaafar et al.2 who used a streaming potential measuring device for determining the charge on the glass surface. The zeta potential on borosilicate glass surface at pH = 5.8 was found to be -55 mV in 10 mM NaCl and -

60 mV in 10 mM KCl, respectively. Fig. C-3a gives the zeta potential of beads (sulfate polystyrene latex, sPSL, and amidine-functionalized polystyrene latex, aPSL) under similar conditions of pH and salt concentration. The zeta potential for oil emulsions (hexadecane stabilized with 2%w/v

Tween-20) in our system was found to be -35 mV in 10 mM NaCl and -37 mV in 10 mM KCl.

The zeta potential for amine-functionalized PSL beads was found to be -22 mV in 10 mM NaCl and -20 mV in 10 mM KCl. As equation 4-3 suggests, the tracer speed varies with the relative magnitude of the zeta potentials of the particle and the wall surface, i.e. if the difference is positive, the particle moves along the direction of E-field and vice versa (Fig. C-4).

154

Figure C-4. Transport profiles originating from transient diffusioosmotic flows (TDOFs) in a dead-end system. (a) When ζtracers - ζwall > 0, the diffusiophoretic motion of the tracer dominates over the fluid flow direction (from equation 4-2), that is, the net observed speed is towards the high salt regime. (b) When ζtracers - ζwall < 0, diffusioosmotic fluid flow dominates over the diffusiophoretic transport of tracers and thus the tracers along the wall move out towards the sink (along with the fluid flow), whereas those in the center move in towards the dead-end region (also along the fluid flow). (c) TDOF generated in a dead-end capillary, giving a parabolic flow profile for green fluorescent sPSL beads (diameter = 200 m) due to an imposed salt gradient (NaCl) inside the dead-end pore (acting as a reservoir) and DI water in the outer sink.

155 C-4. Other Multi-valent Ionic Gradients

Carbonated water solution was prepared by bubbling CO2 into DI water for one hour and emulsions stabilized by oleic acid were added to it. Similar to monovalent salt solutions, we also observed transport and exchange of material in dead-end pores through the use of saturated calcium carbonate salt solution.

C-4-1. Ion gradient from calcium carbonate dissolution

Similar to chapter 2 on CaCO3 micropumps that create diffusioosmotic fluid flows, a saturated solution of CaCO3 can also produce ions to drive transport. When a solution of saturated calcium carbonate was filled inside the sink with the dead-end pore containing 100 mM NaCl and

2+ - - oil emulsions (see Fig. C-5), Ca , OH and HCO3 ions were produced at the salt-water interface.

The leading ion, OH-, and the lagging ion, Ca2+, set-up an E-field in the system that generates fluid flow and particle motion similar to that described for NaCl solutions. Fig. C-5 shows time lapse images of oil emulsions being extracted from a dead-end pore upon application of the gradient derived from CaCO3 dissolution. Due to dynamic changes of zeta potentials on the surfaces of emulsions and walls (similar to the effect shown by McDermott et al. (2012)), the wall acts as a pump for the emulsions to move towards the higher CaCO3 regime.

156

FigureFigure C-5. Extraction 11  Extraction of oil droplets of oil droplets from a deadfrom- enda dead pore-end due pore to CaCO. Time3 lapsegradient. image Times show-lapse an oilimages showingplug oil being plug beingextracted displaced through from diffusioosmotic dead-end pores flows through induced diffusioosmotic by external salt flows gradients induced set by-up external in salt gradientsthe confined acting system. across The the saltsystem. outside The in salt the outside reservoir in the is 0.5 reservoir mM CaCO3 is 0.5 mM with CaCO 3.0 µm3 with sPSL 3.0 µm sPSL particlesparticles in in it. it. The The inner inner capillary capillary has has 100 100 mM mM NaCl NaCl with with oil oil emulsions emulsions of of varying varying shapes sizes..

C-4-2. Ion gradient from dissolved carbon dioxide

+ - Similar to the effect of ion gradients from calcium carbonate, a gradient H and HCO3 ions derived from dissolved carbon dioxide can also drive TDOFs in dead-end pores. We saw small emulsions, stabilized with oleic acid, being extracted from a dead-end pore due to such gradients

(Fig. C-6)

Figure 12  Time lapse images of small emulsions being extracted out from a dead-end pore + - Figurecontaining C-6. Transient carbonated carbonate water waterinto a gradient sink containings. Time lapseDI water. images As ofthe small H and emulsions HCO3 are being the extractedions out fromproduced a dead due-end to thepore gradient, containing E field carbonated is set-up water spontaneously into a sink directed containing in towards DI water. the Asdead the-end H+ and - HCOregion.3 are the Under ions producedthese conditions, due to the the gradient, smaller Eemulsions field is set, have-up spontaneously a charge lower directed than that inwards for glass towards the dead-end region. The smaller emulsions, which have a charge lower than that for glass wall (ζe = -60 wall (ζe = -60 mV > ζwall= -38 mV) and are thus diffusiophoretically pulled out towards the sink mV >and ζwall where= -38 mV),they get diffusiophoretically extracted from inside moved the out dead into-end the pore. sink and extracted from inside the dead-end pore.

157 C-5. Electrokinetic Model to Quantify Observed Speeds

The major contribution to this section came from Dr. Tso-Yi Chiang. She developed a model to quantify the observed particle speeds in our experiments with dead-end pores. The essential idea behind her electrolyte diffusiophoresis idea was to maintain zero electric current at all times inside the pore in presence of a salt gradient. She ensured this by solving for the flux of ions using the Nernst-Planck equation which considered the migration from electrical potential in and no convection in the system. By obtaining the E field in the system and then solving for the concentration distribution across the EDL with the Poisson’s Boltzmann equation, the pressure build-up across the dead-end pore, and the Stokes equation; she was able to calculate the velocity of fluid and particles inside our dead-end pores. Our modeling was done using Wolfram

Mathematica 8.0 software (www.wolfram.com/mathematica).

C-5-1. Debye Layer inside Dead-end Pores

When surfaces are immersed in an electrolyte solution, due to ion absorption or dissociation of charged groups on the surface, they acquire a charge that is mostly uniform in nature. These charges attract counter-ions from the solution towards them, thus forming an electrical double layer (EDL) which screens other background ions from reaching the surface. The thickness of the double layer, Debye length (κ-1)3, is given by

kT 1 C-1   22 2Z e c where, ε is the fluid permittivity, k is the Boltzmann constant, T is temperature, Z is the valence of the ion, e is the elementary charge and c∞ is the concentration of the electrolyte solution. In our

158 case, for a 10 mM NaCl solution, κ-1 = 3 nm. Hence, we assume infinitesimally thin Debye layers for our model.

C-5-2. Expression for Fluid and Particle Speed

When a steady uniform salt gradient is applied across a charged surface, a particle or a wall, flows in the system arise from two mechanisms – tangential salt gradients inducing excess pressure in the EDL, and the difference in ionic diffusivities setting up an electric field (E) (self- generated) in the system. The steady E-field (given by equation 4-1) is a function of nn and difference in ionic mobilities Di. The former induces chemiosmotic flow whereas the later causes electroosmotic flow. The net diffusioosmotic flow velocity is represented by vdo shown as

 kTDD 2 k22 Tze  n  2 w C-2 vdo  w 22ln 1  tanh   Ze D D Z e4 kT n

Flows arising across the surface of a charged particle which is suspended in liquid moves the particle in the direction opposite to the flow. This phenomenon of particle motion resulting from applied salt gradients is called diffusiophoresis. The particle speed, Udp, is given as

22 ze  kTDD 2 k T2 p  n Udp p 22ln 1  tanh  C-3  Ze D D Z e4 kT n

159 C-5-3. Spatiotemporal Concentration Gradient

Assuming the length of the capillary is much longer than the width of it (1–D diffusion), using Fick’s second law,

n(,)(,) x t2 n x t  D* C-4 tx2

* where D =2D+D-/(D+ + D-). With boundary conditions n(L,t) = n0, n(0,t) = 0 and initial condition n(x,0) = n0, the complete concentration profile can be given by

x n(,) x t n0 erfc C-5 2 Dt*

Solving numerically for nn0 (see Fig. C-3b), we observe a temporal behavior of the concentration gradient for both NaCl and KCl. These salt gradients can persist for hours depending on the type of salt used and the length of the capillary.

C-5-4. Transient Diffusioosmotic Flow (TDOF)

To generate the complete flow profile in the dead-end capillary due to spatiotemporal salt gradients, we need to account for the pressure drop developed across the dead-end section of the inner capillary. This pressure drop is generated from the flow set-up across the mouth of the inner capillary. In order to maintain fluid continuity, the pressure drop causes a return flow along the walls of the channel and gives a parabolic diffusioosmotic flow profile inside the dead-end capillary system (see Fig. C-4). In order to obtain the complete fluid flow profile (v) inside the capillary, we modify Bowen’s equation for diffusioosmotic flow (vdo) profiles in a square capillary and solve it numerically (given by equation C-6).

160

2232 cosh(y 2 a ) 1 cosh(3 y 2 a ) a133 cos( z 2 a )  cos(3 z 2 a )  z 3v cosh(  2) 3 cosh(3  2) v(,) y z v do  C-6 do 2a2 192 1 155 tanh( 2) tanh(3 2)  3

where, y and z are axes defined in Fig. 4-1a. The net speed of tracers is thus given by

u(,,,)(,,,)(,,,)xyzt v xyzt Udp xyzt C-7

C-6. Theory behind Exchange of Tracers

If ζtracers>ζwall(e.g. sPSL beads and glass wall in NaCl gradient), the diffusiophoretic motion of the tracers dominates over the diffusioosmotic fluid flow. Fig. C-4 demonstrates the transport profile of the tracers due to imposed salt gradients.

In the case of ζtracers<ζwall (e.g. amine functionalized PSL beads and glass wall in NaCl gradient), the diffusioosmotic flow dominates over the diffusiophoretic motion. Our experiments agree well with the model predictions for speeds of these tracers computed using equation 4-3.

161 C-7. References

1. Hogg, S.; Leschziner, M. A. Second-moment-closer Calculation of Strongly Swirling Confined

Flow with Large Density Gradients. Int. J. Heat and Fluid Flow 1988, 10, 16-27.

2. Jaafar, M. Z.; Vinogradov, J.; Jackson, M. D. Measurement of Streaming Potential Coupling

Coefficient in Sandstones with High Salinity NaCl Brine. Geo. Res. Let. 2009, 36, L21306.

3. Hunter, R. J. Foundations of Colloid Science; Oxford University 1, 1989; pp 46-51.

162

Appendix D

Video Analysis in Pseudomorphic Mineral Replacement Reaction

D-1. MATLAB Code for Normalized Intensity Calculation

To find the normalized intensity of the blue light (emitted from QDs) from the movies in chapter 5 (not provided as hyperlinks at this point as it is not yet published), I wrote a MATLAB code which could extract the intensity variation as a function of time. This helped me relate the rate of QDs extraction to the time taken for pores to close in our batch reactor. The data from this code, when used for a flow-through reactor case, appropriately yielded Fig. 5-3a showing the decay in intensity of blue light to be uniform over time.

MATLAB CODE:

vidObj = VideoReader('flowcell1.avi'); %Read the movie file

nFrames = vidObj.NumberOfFrames; vidHeight = vidObj.Height; vidWidth = vidObj.Width;

%% figure; img = read(vidObj,1); h = imagesc(img); hold on; answer = inputdlg({'Enter location of the line on X axis, 1-Left 512- Right',... 'Enter the end points of line in Y coordinates separated by a space, 1- Top 512-Bottom'}); lineX = str2double(answer(1)); %Draw the line about which intensity is to be measured lineY = str2num(answer{2});

163 blueComp = zeros(lineY(2)-lineY(1)+1,nFrames); % Intialize matrix for holding blue component values plot([lineX lineX],[lineY(1) lineY(2)],'r','LineWidth',2); % Plot the red line representing the desired line blueComp(:,1) = img(lineY(1):lineY(2),lineX,3); % Get the blue component along the line for k = 2 : nFrames img = read(vidObj,k); set(h,'CData',img); blueComp(:,k) = img(lineY(1):lineY(2),lineX,3); drawnow; end

%% figure; sumBlue = sum(blueComp); normalizedBlue = sumBlue/max(sumBlue); normalizedBlueTruncated = sumBlue(72:end)/max(sumBlue(72:end)); %Initialize the 72nd fram as the starting point plot(normalizedBlue); figure; plot(normalizedBlueTruncated);

164 Appendix E

Vendors

E-1. Colloidal Particles

Vendor Product and Information Life Technologies Polystyrene latex beads (sPSL, aPSL), 3175 Staley Road fluorescent beads (sPSL, amine PSL). 15 ml Grand Island, NY 14072 bottles. Cost  $320 USA quantum dots. Various sizes. wt% ~ 2-8%. 5 Phone: 800.955.6288 ml bottles. Cost  $320 Dyes like Lucigenin, Rhodamine (prices). Cost  $50 Bangs Laboratories Inc. Silica particles of various sizes. wt% ~ 4%. 9025 Technology Drive 15 ml bottles. Cost  $250 Fishers, Indiana 46038-2886 USA

E-2. Chemicals

Vendor Product and Information Sigma Aldrich Salts like KCl, KBr, NaCl, LiCl etc. 1001 West Saint Paul Avenue Some particles like sPSL but the particles Milwaukee, Wisconsin 53233 sizes were less reliable compared to that 800-558-9160 supplied from Life Tech. Tween-20. 2% of Tween-20 stabilizes oil-in- water emulsion.

165 E-3. Equipment

Vendor Product and Information Nikon Brightfield inverted microscopes, Nikon NIS 1001 West Saint Paul Avenue Elements Imaging Software (V.4) Milwaukee, Wisconsin 53233 800-558-9160 Leica Microsystems Inc. LCSM TCS5 Confocal microscope 1700 Leider Lane Buffalo Grove, IL 60089 United States Office Phone: +1 800 248 0123 Fax: +1 847-236-3009 Malvern Instruments Ltd Zetasizer Nano ZS90 (ZEN3690). DTS 1061 Enigma Business Park cuvette. Grovewood Road Malvern WR14 1XZ United Kingdom

E-4. Materials

Vendor Product and Information Vitrocom Rectangular square glass capillaries. Product 1001 West Saint Paul Avenue #s: 8100, 8320, 8290. Cost  $35 Milwaukee, Wisconsin 53233 800-558-9160 Spectrum Labs Hollow fiber modules. Molecular weight cut- 18617 S Broadwick St off of 13kDa. Rancho Dominguez, CA 90220 International Crystal Laboratories, Crystals of KBr and KCl. NJ USA Amazon.com Rock pieces of various minerals like gypsum and calcite.

166 E-5. Experimental Supplies

Vendor Product and Information VWR Pipettes, glassware, centrifuge tubes, clear 2039 Center Square Rd. glass slides, square cover slips Bridgeport, NJ 08014 Orders: (800) 932-5000 Phone: (856) 467-2600 Fax: (866) 329-2897 Fischer Scientific BD Intramedia tubings. 21 gauge syringes. 300 Industry Drive, Pittsburgh, PA 15275. Millipore Corporation Milli-Q system MilliQ water purification system 290 Concord Road Billerica Massachusetts 01821 USA, Telephone: +1 (781) 533-6000 Home Depot, clear polycarbonate sheets (Lexan 12” x 24” x State College, PA 16803 0.2”) Omega Engineering Handheld conductivity/pH meter P.O. Box 4047 PHH-10-KIT ($450) Stamford, Connecticut 06907-0047 1-800-826-6342

VITA

ABHISHEK KAR

Education & Job

The Pennsylvania State University, State College, Pennsylvania 2010 - 2015 PhD. In Chemical Engineering, expected in May 2015 Institute of Minerals and Materials Technology, Bhubaneswar, India 2009 – 2010 Quick Hire Scientist, PGRPE Program, CSIR National Institute of Technology, Durgapur, West Bengal, India 2005 – 2009 B.Tech. in Chemical Engineering Research Experience

Doctoral Research The Pennsylvania State University 2012 – 2015 Thesis Advisor: Distinguished Prof. Darrell Velegol Research topics included flows in dead-end pores, diffusiophoretic remediation of fouling on membranes, and fluid flows in pseudomorphic mineral replacement reactions Masters Research The Pennsylvania State University 2010 – 2012 Thesis Advisor: Distinguished Prof. Darrell Velegol Research topics included study of chemical micropumps, and zeta potentials through capillary electrophoresis Undergraduate Research National Institute of Technology, Durgapur, India 2008 – 2009 Thesis Advisor: Prof. Parimal Pal Research topic: Study on Chemical and Biological treatment of coke-oven wastewater Professional Experience

Research Mentor for 10 undergraduate students at Penn State on various projects. Teaching Assistant for 4 courses in Chemical Engineering at Penn State Leader of the team that won the Penn State DOW SISCA event. 2013 Member of the Chemical Safety Club, Penn State 2013 - 2014 Publications & Patents

McDermott, Kar, Majd, Klara, Wang, Sen & Velegol. Langmuir 2012 Kar, Guha, Dani, Velegol & Kumar. Langmuir 2014 Kar, Chiang, Rivera, Sen & Velegol. ACS Nano 2015 Kar, McEldrew, Mays, Strout, Khair, Velegol & Gorski. in preparation 2015 Kar, Guha, Velegol. in preparation 2015 Velegol, Kar, Guha, Kumar. US Patent (filed) 2015