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Mechanical & Aerospace Engineering Theses & Dissertations Mechanical & Aerospace Engineering

Spring 2011

Manipulating Particles for Micro- and Nano-Fluidics Via Floating Electrodes and Diffusiophoresis

Sinan Eren Yalcin Old Dominion University

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Recommended Citation Yalcin, Sinan E.. "Manipulating Particles for Micro- and Nano-Fluidics Via Floating Electrodes and Diffusiophoresis" (2011). Doctor of Philosophy (PhD), Dissertation, Mechanical & Aerospace Engineering, Old Dominion University, DOI: 10.25777/9qzm-hz36 https://digitalcommons.odu.edu/mae_etds/93

This Dissertation is brought to you for free and open access by the Mechanical & Aerospace Engineering at ODU Digital Commons. It has been accepted for inclusion in Mechanical & Aerospace Engineering Theses & Dissertations by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. MANIPULATING PARTICLES FOR MICRO- AND NANO-

FLUIDICS VIA FLOATING ELECTRODES AND

DIFFUSIOPHORESIS

by

Sinan Eren Yalcin B.S. May 2003, Istanbul Technical University M.S. May 2006, Istanbul Technical University

A Dissertation Submitted to the Faculty of Old Dominion University in Partial Fulfillment of the Requirement for the Degree of

DOCTOR OF PHILOSOPHY

AEROSPACE ENGINEERING

OLD DOMINION UNIVERSITY May 2011

Approved by

Okta•Jctayy Baysal (Director)

Shizhi Qian (Member)

Julie Zhili Hao (Member)

Yan Peng (Member) ABSTRACT MANIPULATING PARTICLES FOR MICRO- AND NANO-FLUIDICS VIA FLOATING ELECTRODES AND DIFFUSIOPHORESIS

Sinan Eren Yalcin Old Dominion University, 2011 Director: Dr. Oktay Baysal

The ability to accurately control micro- and nano-particles in a liquid is fundamentally useful for many applications in biology, medicine, pharmacology, tissue engineering, and microelectronics. Therefore, first particle manipulations are experimentally studied using electrodes attached to the bottom of a straight microchannel under an imposed DC or AC . In contrast to a dielectric microchannel possessing a nearly-uniform , a floating electrode is polarized under the imposed electric field.

The purpose is to create a non-uniform distribution of the induced surface charge, with a zero-net-surface charge along the floating electrode's surface. Such a field, in turn, generates an induced-charge electro-osmotic (ICEO) flow near the metal strip. The demonstrations by using single and multiple floating electrodes at the bottom of a straight microchannel, with induced DC electric field, include particle enrichment, movement, trapping, reversal of motion, separation, and particle focusing. A flexible strategy for the on-demand control of the particle enrichment and positioning is also proposed and demonstrated by using a locally-controlled floating metal electrode. Then, under an externally imposed AC electric field, the particle deposition onto a floating electrode, which is placed in a closed circular cavity, has been experimentally investigated. In the second part of the study, another particle manipulation method was computationally investigated. The diffusiophoretic and electrodiffiisiophoretic motion of a charged spherical particle in a nanopore is subjected to an axial electrolyte gradient. The charged particle experiences because of the imposed electric field and the diffusiophoresis is caused solely by the imposed concentration gradient. Depending on the magnitude and direction of the imposed concentration gradient, the particle's electrophoretic motion can be accelerated, decelerated, and even reversed in a nanopore by the superimposed diffusiophoresis.

Based on the results demonstrated in the present study, it is entirely conceivable to extend the development to design devices for the following objectives:

o to enrich the concentration of, say, DNA or RNA, and to increase their

at a desired location.

o to act as a filtration device, wherin the filtration can be achieved without

blocking the microfluidic channel and without any porous material,

o to act as a microfluidic valve, where the particles can be locally trapped in any

desired location and the direction can be switched as desired,

o to create nanocomposite material formation or even a thin nanocomposite film

formation on the floating electrode,

o to create a continuous concentration-gradient-generator nanofluidic device that

may be obtained for translocation process. This may achieve

nanometer-scale spatial accuracy sample sequencing by simultaneously

controlling the electric field and concentration gradient. V

Dedicated to my mother, my father, and my sister. VI

ACKNOWLEDGMENTS

The Ph.D process was the greatest experience I have ever had in my life. I am so thankful to many people who helped me and supported me during my Ph.D.

Firstly, I would like to express my gratitude and appreciation to my advisor

Prof. Oktay Baysal for allowing me to study under his supervision, his constant support, and his encouragement during my Ph.D. education. It was a great pleasure and opportunity for me to be his student, and I will always be thankful for the worthwhile education and experience I learned under his supervision.

I would like to convey my special thanks to Prof. Oktay Baysal and Prof.

Shizhi Qian for involving me "Electrokinetic Particle Manipulation" studies. With this project, I learned how to conduct both experimental and numerical research together which is a key requirement to be a good scientist. In addition, the regular meetings and discussions with Prof. Baysal and Prof. Qian were the most precious moments for me. That's why, I also especially would like to thank to both of my advisors for giving me their precious time.

I would like to thank to Prof. Shizhi Qian for his constant support and encouragement both here and while in South Korea. The regular meetings and discussions with Prof. Baysal and Prof. Qian were most precious moments for me.

I have special thanks to Prof. Ashutosh Sharma for his continuous support, encouragement, and discussions while I was in South Korea. I had the chance to meet and study with him when I was exchange student in South Korea for a year. Taking into account that he is one of the most distinguished professors in his research area, it was a privilege to work with him. vii

I also wish to express my gratitude to my committee members, Prof. Julie

Zhili Hao and Prof. Yan Peng for their contributions, their feedback, and their valuable advice.

Finally, I am extensively indebted to my parents Husniye Yalcin and Omer

Atilla Yalcin for supporting me all the time and giving me the chance to study a Ph.D in engineering in the USA. I could never have finished my Ph.D. without their support. I also would like thank to my sister Sibel Ebru Yalcin, for her support, motivation and daily talks when we were both pursuing our Ph.Ds. viii

TABLE OF CONTENTS

LIST OF FIGURES xi

Chapter

I. INTRODUCTION 1 1.1 Motivation for the Research 9 1.2 Organization of the Dissertation 10 1.3 Objectives of the Research 11 1.4 Contribution of the Research 12

II. RESEARCH METHODOLOGY 14 2.1 Experimental Methodology 14 2.1.1 Microfluidic Channel Fabrication 14 2.1.2 Data Analysis 16 2.2 Computational Methodology 16 2.2.1 Introduction 16 2.2.2 Mathematical Model for the Fluid Motion 18 2.2.3 Mathematical Model for the Ionic Mass Transport 20 2.2.4 Dimensionless Form of the Mathematical Model 22 m. PARTICLE MANIPULATION IN MICROFLUIDIC DEVICES VIA FLOATING ELECTRODES 25 3.1 Manipulating Particles in Microfluidics via Floating Electrodes 26 3.1.1 Introduction 26 3.1.2 Experiment 27 3.1.3 Results and Discussion 28 3.1.3.1 Particle Manipulations by a Single Floating Electrode 30 3.1.3.1.1 Particle Trapping 30 3.1.3.1.2 Reversal of Particle Motion 32 3.1.3.1.3 Particle Separation 35 3.1.3.2 Double Floating Electrodes 36 3.1.3.2.1 Trapping and Depletion 36 3.1.3.2.2 Particle Focusing 38 IX

3.2 On-Demand Particle Enrichment in a Microfluidic Channel by a Locally Controlled Floating Electrode 39 3.2.1 Introduction 39 3.2.2 Experiment 41 3.2.3 Mathematical Model 43 3.2.4 Results and Discussion 45 3.2.4.1 On-Demand Control of Particle Enrichment 48 3.2.4.2 On-demand Control of the Position of Enriched Particles 52 3.3 Particle Deposition onto the Floating Electrode under AC Electric Field 56 3.3.1 Introduction 56 3.3.2 Experiments 57 3.3.3 Results and Discussion 58 3.3.3.1 Without Floating Electrode 58 3.3.3.2 With Floating Electrode 61

IV. ELECTRODIFFUSIOPHORETIC MOTION OF A CHARGED SPHERICAL PARTICLE IN A NANOPORE 72 4.1 Diffusiophoretic Motion of a Charged Spherical Particle in a Nanopore 72 4.1.1 Introduction 72 4.1.2 Mathematical Model 74 4.1.3 Results and Discussion 74

4.1.3.1 Effect of/cap, Ratio of Particle Size to EDL Thickness 76

4.1.3.2 Effect of ap, the Particle Surface Charge Density 81

4.1.3.3 Effect of a/ap, Ratio of Pore Size to Particle Size 84 4.2 Electrodiffusiophoretic Motion of a Charged Spherical Particle in a Nanopore 89 4.2.1 Introduction 89 4.2.2 Mathematical Model 90 4.2.3 Results and Discussion 91

V. CONCLUSIONS AND RECOMMENDATIONS Ill 5.1 Concluding Remarks Ill 5.2 Recommendations for Future Research 113 X

REFERENCES 115

VITA 132 XI

LIST OF FIGURES

Figure Page

2.1 Schematic top view of a straight microchannel with one (a) and two (b) floating electrodes on the bottom wall of the channel, and a picture of a microchannel with one floating electrode positioned in the center of the microchannel (c) 16

2.2 Schematic of a nanopore of length L and radius a connecting two identical reservoirs on either side. A concentration gradient of electrolyte solution is applied across the two reservoirs. A charged spherical particle of radius ap bearing uniform surface charge density, ap, is positioned at the center of the nanopore 18

3.1 Schematic top view of a straight microchannel with one (a) and two (b) floating electrodes on the bottom wall of the channel, and a picture of a microchannel with one floating electrode positioned in the center of the microchannel (c). L=l cm, d=100 |j.m, the depth of the channel is 8 fxm, LE= 500 |j.m, and a= 300 urn 28

3.2 Fluorescent intensity distribution in ImM KCl electrolyte under 30 V/cm (a), 50 V/cm (b), 70 V/cm (c), 90 V/cm (d) 31 3.3 Schematic illustration of the fluid flow near the floating electrode (the dark region in the middle of the bottom channel wall). The imposed electric field is directed toward left. The dielectric channel wall is negatively charged, and the induced charge on the anodic (cathodic) side of the floating electrode is negative (positive). Clockwise (counterclockwise) vortices are induced near the anodic (cathodic) side of the floating electrode. The net electroosmotic flow is directed to left 32 3.4 Concentration and motion of the 500 nm particles in 1 mM KCl solution after 6 sec (a), 8 sec (b), 10 sec (c), 12 sec (d), 14 sec(e), 16 sec (f), and 18 sec (g) under 50 V/cm. The left side of the dashed line represents the floating electrode 33

3.5 Fluorescent intensity distribution at 50 V/cm in O.lmM (a) and 10 mM (b) KCl solution 34

3.6 Trajectories of 500 nm (a) and 4 urn (b) particles in 1 mM KCl at 10 V/cm. The region between two dashed lines represents the floating electrode. The arrows in (a) and (b) represent the directions of the xn

corresponding particle motions 35 3.7 500 nm particles distribution between two floating electrodes after 30 sec (a), 1 min (b), 7 min (c), and 10 min (d) at 30V/cm in ImM KC1 solution. The dark regions on both ends represent the two floating electrodes 37

3.8 Fluorescent intensity distribution between two floating electrodes after 30 sec (a), 1 min (b), and 10 min (c) at 30 V/cm in ImM KC1 solution 37 3.9 Snapshot (a) and fluorescent intensity distribution (b) along a cross- section shown in (a) at 50V/cm in ImM KC1 solution. The dark regions on both ends represent the two floating electrodes 39 3.10 Schematic top view of a straight microchannel with one floating electrode and two control electrodes patterned on the channel bottom wall (a), and a picture of the microfluidic channel (b). L=l cm, d=100 nm, the depth of the channel is 8 (im, LE= 500 |j.m, LCE= 300 (j.m, and a=50nm 42

3.11 Schematic of microfluidic channel with locally controlled floating electrodes 44 3.12 Flow field and streamlines in the region of the three floating electrodes when the external electric field is 10 V/cm (a) and 30 V/cm (b) 46

3.13 Fluorescent intensity distribution in ImM KC1 electrolyte when Eext=10 V/cm and Ec„nt«-3.33V/cm (a), -6.66V/cm (b), -lOV/cm (c), and -13.33V/cm (d). The time interval between Econt and Eext is 0 49 3.14 Sequential images of the enriched particles in the upstream of the right control electrode after 10 s (a), 20 s (b), 30 s (c), 40 s (d), 50 s (e), 60 s (f), and 70 s (g) under Eext=10 V/cm and Ecne-lOV/cm. The left side of the dashed line represents the right control electrode 51

3.15 Flow field and streamlines in the region of the control and floating electrodes when Eext=10 V/cm, Econt=-6.66V/cm (a), -lOV/cm (b), and -13.33V/cm (c) 51

3.16 The fluorescent intensity in 1 mM KC1 when Eext= 30 V/cm and ECont«31.67 V/cm after 1 min (a), 3 min (b), 5 min (c), and 8 min (d). Both Eext and Econt are directed from the anodic reservoir toward the cathodic reservoir, and the time interval between Econt and Eext is 15 seconds 53

3.17 The sequential images of the enriched particles after 20 s (a), 40 s (b), 1 min (c), 2 min (d), 3 min (e), 4 min (f), 5 min (g), 6 min (h), 7 min (i), and 8 min (j). The left side of the dashed line represents the right control electrode. The condition is the same as that in Figure 3.16 53 xiii

3.18 Flow field and streamlines in the region of the control and floating electrodes whenEext=10 V/cm and Econt=31.67V/cm 54

3.19 The fluorescent intensity in 1 mM KCl when Eext= 30 V/cm and Econt«31.67 V/cm after 1 min (a), 3 min (b), 5 min (c), and 8 min (d). Both Eext and Eont are directed from the anodic reservoir toward the cathodic reservoir, and the time interval between Eo^ and Eext is 5 seconds 55

3.20 The sequential images of the concentrated particles after 1 min (a), 2 min (b), 3 min (c), 4 min (d), 5 min (e), 6 min (f), 7 min (g), and 8 min (h). The condition is the same as that in Figure 3.19 55 3.21 Schematic top view experimental setup of one floating electrode and two control electrodes patterned on the glass slide with circular PDMS cavity on top of electrodes. LcE= 300 urn, LFE= 500 |a.m, R=3mm, and a= 50 \\m 58 3.22 Particle motion between driving electrodes when no floating electrode is used at 100Hz (a), 100kHz (b), 1MHz (c), and 10MHz (d) 59 3.23 Real part of the Clasius-Mossotti factor of 500 nm dielectric particles 60 3.24 Addition of ICEO flow pattern at low frequencies (a), high frequencies (b) 62 3.25 Snapshot images of deposited particles onto the floating electrode after washing the electrodes under 2 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f) 64

3.26 Fluorescent intensity distribution of deposited particles onto the floating electrode under 2 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f) 65

3.27 Fluorescent intensity distribution of the deposited particles onto the floating electrode after 20 min, under 2 Vpp 100Hz (a), 100kHz (b), 1MHz (c), 10MHz (d); and 5Vpp 100Hz (e), 100kHz (f), 1MHz (g), and 10MHz(h) 67

3.28 SEM images of the deposited particles onto the floating electrode under 0.5 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f) 68 3.29 SEM images of the deposited particles onto the floating electrode after 20 min. under 2 Vpp 100Hz (a), 100kHz (b), 1MHz (c), 10MHz (d); and 5Vpp 100Hz (e), 100kHz (f), 1MHz (g), and 10MHz (h) 69 1 Schematic of a nanopore of length L and radius a connecting two identical reservoirs on either side. A concentration gradient of electrolyte solution is applied across the two reservoirs. A charged spherical particle of radius ap bearing uniform surface charge density, ap, is positioned at the center of the nanopore 73

2 Dimensionless particle velocity as a function of kap for KCl solution with a « -27.3 (solid line with open triangles), -13.7 (dashed line with open squares), 13.7 (dashed line with solid squares), and 27.3 (solid line with solid triangles). a/ap=2, and a=1000 77

3 Dimensionless particle velocity as a function of kap for NaCl solution with <7p« -27.3 (solid line with open triangles), -13.7 (dashed line with open squares), 13.7 (dashed line with solid squares), and 27.3 (solid line with solid triangles). a/ap=2, and a=1000 79

4 Dimensionless particle velocity as a function of ap for KCl solution with

fcap=0.1 (solid line with squares), 1 (dashed line with triangles), and 3 (dash-dotted line with circles). a/ap=2, and a=1000 82

5 Dimensionless particle velocity as a function of o^for NaCl solution

with &ap=0.1 (solid line with squares), 1 (dashed line with triangles), and 3 (dash-dotted line with circles). a/ap=2, and a=1000 83

6 Dimensionless particle velocity as a function of a/ap for KCl solution with kap=0.l (lines with squares), 1 (lines with triangles), and 3 (lines with circles) when ap=-213 (solid lines with open symbols) and 27.3 (dashed lines with solid symbols). a=1000 85

7 Dimensionless particle velocity as a function of a/ap for NaCl solution with kap=0.l (lines with squares), 1 (lines with triangles), and 3 (lines with circles) when ap=-213 (solid lines with open symbols) and 27.3 (dashed lines with solid symbols).

8 Schematics of a nanopore of length L and radius a connecting two identical reservoirs on either side. The surface charge density along the wall of the nanopore is aw. A charged spherical particle of radius ap bearing uniform surface charge density ap is positioned at the center of the nanopore. A concentration gradient of electrolyte solution and an electric field are applied across the two reservoirs 90 9 Particle's electrophoretic velocity in the absence of the concentration gradient (i.e., a = 1) as a function of the type of electrolytes when /cap = 1 (lines with open symbols) and /cap = 3 (lines with solid symbols 93 XV

4.10 Spatial distribution of the dimensionless concentration of the cations around the particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 1 in KC1 solution 97 4.11 Spatial distribution of the dimensionless concentration of the anions around the particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 1 in KC1 solution 97 4.12 Electrodiffusiophoretic velocity as a function of the concentration ratio, a, in KC1 solution when xap = 1 (a) and 3 (b). The solid lines with circles, dashed lines with triangles, and dash-dotted lines with squares represent, respectively, the results of (5 = 0, 1, and -1 98

4.13 Particle velocity deviation ^ as a function of the concentration ratio, a, in KC1 solution when /cap = 1 (a) and 3 (b). The solid lines with circles, dashed lines with triangles, and dash-dotted lines with squares represent, respectively, the results of/? = 0, 1, and -1 104

4.14 Spatial distribution of the dimensionless concentration of the cations around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). Kap= 1 and a = 0.001 in KC1 solution 106 4.15 Spatial distribution of the dimensionless concentration of the anions around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). rcap= 1 and a = 0.001 in KC1 solution 106 4.16 Spatial distribution of the concentration difference, c\* - C2*, around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 0.001 in KC1 solution 109 1

CHAPTER I

INTRODUCTION

The study of microfluidics includes behavior, precise control, and manipulation of the fluids that are geometrically constrained to a small, typically, in sub-millimeter scale.

A lab-on-a-chip (LOC) is a device that integrates one or several laboratory functions on a single chip of only millimeters to a few square centimeters in size. LOCs deal with the handling of extremely small fluid volumes down to less than pico liters.

LOC devices are also referred to as "Micro Total Analysis Systems" (uTAS).

Microfluidics is a broader term that also describes mechanical flow control devices, such as, pumps and valves, or sensors like flowmeters and viscometers. LOC generally refers to the scaling of single or multiple lab processes down to chip-format, whereas uTAS is about the integration of the total sequence of lab processes to perform a chemical analysis. The benefits from LOC devices include low fluid volume consumption allowing for compactness of the system, faster analysis, response times, and massive parallelization due to compactness, lower fabrication costs, and safe environment of analysis due to compactness of the system [1-9].

The ability to accurately control and manipulate micro and nano-scale particles in liquid is fundamental for many applications in biology, medicine, pharmacology, tissue engineering, and microelectronics [8-14]. The commonly used manipulation methods are magnetic, optical, hydrodynamic, and electrokinetic methods [9, 13, 15]. An electrokinetic particle manipulation methods, such as electroosmosis, electrophoresis and dielectrophoresis, provide one of the most important non-mechanical particle manipulation techniques in microfluidic devices.

The are present due to the electric double layer (EDL), which forms as a result of the interaction of ionized solution with static charges on 2 dielectric surfaces [16]. The basic idea behind electrokinetic phenomena may be described as follows: a rearrangement of ions in an aqueous liquid solution occurs when a liquid contacts with a charged solid surface, where an EDL with a diffuse cloud of oppositely charged counter ions is built up to balance the surface charge. An externally applied electric field exerts a body force on the charged diffuse ions layer, driving the ions and the bulk liquid into a motion relative to the solid-liquid interface.

The motion of ionized liquid relative to the stationary charged surface under an imposed electric field is called electroosmosis (EO). The motion of the charged particles relative to the stationary liquid under an imposed electric field is called electrophoresis (EP). Typically, electroosmosis, electrophoresis, and dielectrophoresis

(if the electric field is spatially nonuniform) coexist in electrokinetic particle manipulation. They have broad applications in analytical chemistry, cell sorting, disease diagnostics, biosensors, and drug development due to its applicability, adaptability and easy integration into LOC devices [15, 17-22].

Typical electrokinetic phenomena involves surfaces with fixed, constant charge, or , thus the velocity of the resultant fluid flow is linearly proportional to the applied electric field [16, 23]. Electrokinetic phenomena including electroosmosis, electrophoresis, and dielectrophoresis, play an important role in facilitating both fluid transport and particle manipulation in micro- or nano-fluidic

LOC devices [15, 17-22, 24-43]. When a DC electric field is applied in tangent to a charged stationary dielectric surface in contact with an electrolyte solution, the interaction between the imposed electric field and the net charge within the EDL formed in the vicinity of the charged surface induces an electroosmotic flow (EOF).

EOF does not require any moving parts and is amenable for integration into a microfluidic device. If the surface is conducting, it is polarized under an electric 3 field, generating induced charge which forms induced double layer and consequently induced-charge electro-osmosis (ICEO) [23, 44-46].

There are a number of shortcomings for linear electrokinetic phenomena. For example, electrophoresis cannot separate particles by size or shape for particles with fixed, uniform zeta potential in free solution. A strong electric field must be applied to the whole system to achieve the necessary field strengths, generating Joule heating and having little direct control over local fields and flows within microchannels. In contrast to a dielectric microchannel possessing a nearly uniform surface charge (or zeta potential), a metal strip (floating electrode) can be polarized under an imposed electric field, resulting in a non-uniform distribution of the induced surface charge with a zero net surface charge along the floating electrode's surface. This results in an accordingly ICEO flow near the metal strip. The ICEO flow can be regulated by controlling the strength of the imposed electric field, and affects both the hydrodynamic field as well as the particle's motion.

The fundamental difference between the traditional and induced-charge electrokinetic (ICEK) flows is the origin of the diffuse-layer charge. In traditional electrokinetics, charges on the solid-electrolyte interface rise in equilibrium, due to the adsorption or dissolution of specific ions or groups. In ICEK, on the other hand, the DL is induced by the applied field. Induced double-layers (IDLs) occur quite generally around polarizable surfaces [47]. A very important characteristic of ICEO is that it generates a steady flow even in an AC electric field. Since the electric field induces the double layer charge, the sign of the charge varies in phase with the direction of the electric field. This results in a nonzero net force (which depends on the product of the two), which drives a steady flow [48]. In the presence of an electric field, a charged particle immersed in an electrolyte solution experiences an 4 electrophoretic motion driven by the electrostatic force through the interaction between the electric field imposed and the particle's surface charge. A particle also experiences dielectrophoresis when the electric field is spatially nonuniform.

Nonlinear electrokinetic phenomena at polarizable surfaces share a fundamental feature: all involve a nonlinear flow component in which double-layer charge induced by the applied field is driven by that same field. Induced-charge electrokinetic phenomena hold a variety of potential advantages for LOC devices, such as, strong flows through small spaces, steady flows from AC fields, avoiding electrochemistry by low , and zeta potential control. Specific realizations of

ICEO include AC electro-osmosis at microelectrodes, AC pumping by asymmetric electrode arrays, DC electrokinetic jets around dielectric structures, DC and AC flows around polarizable colloidal particles, DC and AC particle motions around polarizable electrodes [23]. Nonlinear electrokinetic flows around polarizable (metallic or dielectric) objects have been studied in recent decades. The phenomena fall into two major categories: electrokinetic phenomena of the second-kind and induced-charge electrokinetics (ICEK). Second-kind electrokinetic effects do not arise from the double layer, being instead driven by space charge in the bulk solution. They typically occur around ion-selective porous granules subject to applied fields large enough to generate strong currents of certain ions through the liquid/solid interface.

This leads to large concentration variations and space charge in the bulk electrolyte on one side, which interacts with the applied field to cause motion [49-52].

In contrast to a microchannel with dielectric walls possessing a nearly uniform surface charge, or zeta potential, floating electrodes attached to the bottom wall of a microchannel can be polarized under an external electric field, generating a spatially non-uniform surface charge on its surface. An ideally polarizable floating electrode is 5 negatively charged near the anodic side (close to the anode) and is positively charged near the cathodic side (close to the cathode), and the net induced charge is zero over the entire surface of the metal strip. In addition, the magnitude of the induced surface charge is proportional to the strength of the imposed electric field [23, 44-48, 53, 54].

The interaction between the mobile ions in the EDL of the floating electrode and the imposed electric field generates an induced-charge electro-osmotic (ICEO) flow having two opposite eddies near the oppositely charged floating electrode. The ICEO around the floating electrode affects the overall hydrodynamic field as well as the particle electrokinetic motion through the interplay between the hydrodynamics and . The most relevant ICEO literature thus far concerns exploiting and exploring its applications in microfluidic devices, such as pumping, mixing, and generating concentration gradient primarily under AC electric field [44, 55-62].

These are the first studies that employ the ICEO flow induced by the floating electrodes attached to the channel bottom wall. In DC electric fields, they achieve versatile and facile particle manipulations, including trapping, enrichment, focusing, separation and control of the direction of particle motion, and at AC electric field to achieve particle deposition onto the floating electrode.

Applying induced-charge electroosmosis for mixing enhancement with microelectrode arrays and streaming flow pumping with asymmetric conducting bodies using AC electric field, were first theoretically predicted [23, 46, 56]. So far, the applications of ICEO have been purely based on fabrications of complex microelectrode arrays. These have not included flow controlling effect other than pumping. More recently, concentration enrichment via bipolar electrodes in microfluidic channels has been extensively studied [63-66]. The mechanism of the 6 sample concentration and separation by a single floating electrode in a microchannel is the bipolar electrochemical reaction [67-68] rather than the ICEO has been found.

A different driving mechanism that obviates the imposition of the electric field is the diffusioosmosis induced by an application of solute concentration gradients across a channel [69-84]. In recent years, there has been a growing interest in developing nanofluidic devices handling particles comparable in size to DNA, proteins, and other biological molecules for biological and chemical analyses [85-98].

In these devices, it is necessary to manipulate fluids or with high precision and efficiency. The pressure-driven flow, widely used in many large-scale applications, would not be a good driving mechanism because a huge pressure gradient is usually required to achieve a reasonable flow rate in a nanochannel.

Analogous to the electroosmosis, the diffusioosmosis originates from the electrostatic interactions between an electrolyte and a solid surface in contact. If a charged particle is positioned in a nanopore, connecting two fluid reservoirs containing a dilute electrolyte solution with different concentrations, counterions are accumulated adjacent to the particle surface due to the electrostatic interactions between the ionic species present in the electrolyte solution and the surface charge on the nanoparticle. This forms an electrical double layer (EDL) of thickness typically on the order of 10 nm. Due to the presence of the imposed concentration gradient, electrolyte ions diffuse in the nanopore, accompanied by a net diffusive flux of charge when the diffusive mobilities of anions and cations are unequal. As a result, an electric field, Edjffusivity, is induced, so that the diffusion of high-mobility (low- mobility) ions is decelerated (accelerated). The generated electric field, Ediirusivity, through its action on the counterions accumulated in the EDL, creates a body force that, in turn, induces an electroosmotic flow. In addition, a secondary electric field is 7 induced by the induced dipole moment, a consequence of the double layer polarization or DLP [99, 100]. Note that the DLP considered here is the consequence of the imposed concentration gradient without accounting for the polarization or relaxation of the EDL by the induced electric field, particle motion, and fluid convection. Due to the imposed concentration gradient, the concentrations of both counterions and co-ions on the high concentration side of the particle are higher than those on the low-concentration side, and the thickness of the EDL on the high- concentration side is thinner than that on the low concentration side. As a consequence, the center of charge inside the EDL, dominated by the counterions, shifts away from the particle's center. Together with the charge of the particle and the charge of the EDL, a dipole moment is induced, resulting in an electric field which reaches beyond the limits of the EDL arising at its positive pole and terminating at the negative pole [99, 100]. The concentration polarization inside the EDL by the imposed concentration gradient is called Type I DLP, and its resulting electric field by the induced dipole moment is named EI.DLP, the direction of which is opposite to (the same as) that of the applied concentration gradient when the particle is negatively

(positively) charged. Near the outer boundary of the antisymmetric EDL, co-ions dominate, and its concentration on the high-concentration side is higher than that on the low concentration side, and such concentration polarization is called the Type II

DLP.

Similar to the induced dipole moment and electric field inside the EDL by the

Type I DLP, a dipole moment and its accompanied electric field, EH-DLP, are induced by the Type II DLP. The direction of the induced electric field, EH-DLP, is opposite to that established by the unbalanced counterions inside the EDL, EI.DLP- Therefore, depending on the operating conditions, the interactions between the net charge in the 8

EDL and the induced overall electric fields, established by the difference of ionic diffusivities (Ediffusivity) and the DLP (EI-DLP and EH-DLP), generate electroosmotic flow [69-84]. In addition, an osmotic pressure gradient is generated within the EDL due to the chemiosmotic effect, thereby inducing a fluid flow from the higher to lower electrolyte concentration regions [76, 77, 80].

The driving forces generated in this way can thus move charged particles

[101-121]. The first driving force is chemiphoresis due to the induced osmotic pressure gradient, which always propels the particle toward higher salt concentration, regardless of the sign of charge on the particle. The second driving force exerted upon the particle arises from the interactions between its charge and the induced electric fields originated from the difference in ionic diffusivities and the DLP, which is usually called electrophoresis. Typically, .the electrophoretic effect is dominant over the chemiphoretic effect in most practical applications. The induced electric field, EI.DLP, by the Type I DLP propels the particle toward higher salt concentration, while the electric field, EH-DLP, generated by the Type II DLP drags the particle toward lower salt concentration, regardless of the sense of the charge on the particle.

Although the electrophoretic effect by the induced electric field, Ediffusivity, typically dominates over the secondary electrophoretic effect by the DLP-induced electric field in an infinite medium, the present study shows that the electrophoresis arising from the DLP-induced electric field can be dominant when the EDL thickness, the particle, and the pore diameter are of the same order of magnitude.

When the thickness of an EDL is comparable to the nanopore diameter, the

EDL surrounding the particle will reach the nanopore wall and will be compressed by the impervious nanopore wall, inducing a nonuniform ionic concentration distribution around the particle [114, 116, 117, 121]. The DLP due to the EDL compression by 9 the nanopore wall plays an important role in diffusiophoresis in a nanochannel. In contrast to the electrophoretic motion of charged particles driven by an externally imposed electric field, the diffusiophoretic motion of the charged particle in a nanopore is mainly driven by the induced electric field established by the DLP.

1.1 Motivation for the Research

Particle manipulation in micro and nano-fluidics has wide potential applications in biological, chemical, and colloidal science, such as, cell sorting, disease treatment, particle focusing, micro-nanowire formation, drug delivery, self propulsion, composite material formation, and thin film formation. The commonly used manipulation methods are magnetic, optical, hydrodynamic, and electrokinetic methods [9, 13, 15]. As mentioned before, electrokinetic particle manipulation method provides one of the most important non-mechanical particle manipulation techniques in micro- and nano-fluidic devices. The electrokinetic particle manipulation of samples is very popular since it is easy to fabricate electrodes in LOC devices. In the present study, the motivation is to change or disturb the electric field distribution inside the micro- and nano-fluidic device and obtain flexible, versatile, and new particle manipulation methods.

To date, most of the studies on electrokinetic manipulation of dielectric particles in microfluidics have been limited to microchannels with dielectric walls possessing a nearly uniform surface charge. Thus, no vortices form inside channel.

Instead, however, if some parts of the channel walls are conductive (floating electrode is attached), the surface charge of the floating electrode is non-uniform, and induced- charge electroosmotic (ICEO) flow occurs, and micro vortices can be generated.

Thus, it is easy to change flow field and particle motion without any complicated 10 electrode geometries. The most relevant ICEO literature thus far concerns exploiting and exploring its applications in microfluidic devices, such as, pumping, mixing, and generating concentration gradient primarily under AC electric field [44, 55-62]. Via passive and active control of the floating electrode under DC electric field, a non­ uniform electric field inside the microfluidic channel can be generated to achieve various particle manipulations. Another motivation for the present research is the deposition of particles onto a non-uniformly charged floating electrode. In conventional electrophoretic deposition, suspended particles are forced to move toward an electrode by applying an electric field to the , then the particles are collected at one of the electrodes and form a coherent deposit is formed on it. By creating the non-uniform surface charge distribution of the floating electrode under

AC electric field, polarity of the floating electrode switches withrespect to time and different types of particles can be deposited onto the floating electrode and nanocomposite materials can be formed.

A different electrokinetic method, that is, diffusiophoretic- electrodiffusiophoretic particle manipulation method, is a challenging idea of manipulating particle motion inside the channel. In a traditional electrophoretic motion, particles move towards the same direction under externally imposed electric field. By imposing the concentration gradient, a particle's electrophoretic motion can be controlled, therefore, that particle's electrophoretic motion can be enhanced, slowed down or even reversed.

1.2 Organization of the Dissertation

In this dissertation, the work on nonlinear induced-charge electrokinetic phenomena in microchannels and the corresponding LOC applications will be discussed. Then, 11 the diffusiophoretic motion in LOC devices will be shown. Consequently, the organization of the dissertation is as follows.

In Chapter I, the literature on the nonlinear electrokinetic phenomena and diffusiophoresis is reviewed. In Chapter n, our experimental and numerical research methodology used in the present study is discussed. In Chapter III, the particle manipulation in microfluidic devices via floating electrodes under DC electric field and then particle deposition onto a floating electrode under AC electric field is discussed. In this Chapter, the unique particle concentration enrichment, separation, particle focusing via single and double floating electrodes is discussed. Also, the control of the position of the enriched particles in microfluidic channels under DC electric field is explained. Chapter III concludes with the particle deposition onto the floating electrode under AC electric field. In Chapter IV, the diffusiophoretic, then the electrodiffusiophoretic motion of particle inside the channel are discussed.

Initially the diffusiophoretic motion of particle is discussed and then effect of diffusiophoresis on electrophoretic motion of particle is discussed. Conclusions and future recommendations are presented in Chapter V.

1.3 Objectives of the Research

The primary objective of the present research is to investigate and then demonstrate particle manipulations in micro- nano-fluidic channels using electrokinetics. The premise is that such manipulations can then be used to achieve numerous favorable applications. To achieve this goal, the following steps are taken.

• Study the effectiveness of ICEK method to general electrokinetic method

• Investigate the particle motion in microfluidic channels using single and

double floating electrodes inside the middle of the microfluidic channel 12

• Create local control of floating electrode via inserting additional two micron-

sized control electrodes on both sides of the floating electrode

• Create on-demand particle enrichment control via locally controlled floating

electrode

• Create on-demand control of the position of enriched particles via locally

controlled floating electrode

• Create particle deposition onto the floating electrode

• Study diffusiophoretic particle motion inside the nanofluidic channel

• Study electrodiffusiophoretic particle motion inside nanofluidic channel

1.4 Contributions of the Research

The overall contribution of the present research is the strategies for and successful demonstrations of electrokinetic methods in micro- and nano-fluidic devices for particle manipulations. These particle manipulations include trapping, enrichment, reversal of motion, separation, particle focusing, enriched particles' position control via floating electrodes in microfluidic devices under DC electric field, and particle deposition onto the floating electrode under AC electric field. A novel particle manipulation method demonstrated is bysuccessfully using floating electrodes.

Another important contribution of the present research is the effective use of electrokinetic particle transportation methods called diffusiophoresis and electrodiffusiophoresis. The self diffusiophoretic motion of a particle is designed under a concentration difference. The effect of diffusiophoretic motion on electrophoretic motion of the particle is sucessfully demonstrated. The results of the present research are published in the following journal articles: 13

• Yalcin S.E., Sharma A., Qian S., Joo S.W., Baysal O., "On-demand particle enrichment in a microfluidic channel by a locally controlled floating electrode", Sensors and Actuators B, Chemical, 2010, 153(1), pp.277-283.

• Yalcin S.E.m, Sharma A., Qian S., Joo S.W., Baysal O., "Manipulating particles in microfluidics by floating electrodes", Electrophoresis, 2010, 33(22), pp.3711- 3718.

• Yalcin S.E., Lee S.Y., Joo S.W., Baysal O.. and Qian S., "Electrodiffusiophoretic motion of a charged spherical particle in a nanopore", The Journal of Physical Chemistry B, 2010, 114 (11), pp 4082-4093.

• Lee S.Y., Yalcin S.E., Joo S.W., Sharma A., Baysal O., and Qian S.,"The effect of axial concentration gradient on electrophoretic motion of a charged spherical particle in a nanopore", Microgravity Science and Technology, 2010, DOI 10.1007/S12217-010-9195-8.

• Lee S.Y., Yalcin S.E., Joo S.W., Baysal O., and Qian S., "Diffusiophoretic motion of a charged spherical particle in a nanopore", The Journal of Physical Chemistry C, 2010, 114(19), pp.6437-6446 14

CHAPTER II

RESEARCH METHODOLOGY

This chapter describes the mehtods for the experiments and the computations used in this research. Two important parts for the experiments are the fabrication and the data analysis technique. They will be presented in the next subsection. Given in the last subsection is the computational methodology.

2.1 Experimental Methodology

2.1.1 Microfluidic Channel Fabrication

The PDMS/glass microfluidic channel with /without floating electrodes were fabricated using the standard soft-lithographic technique [122]. Briefly, positive photoresist, SPR220-7 (MicroChem, MA), was first spin-coated on a clean glass slide yielding a uniform thickness of 9 urn, followed by a three-step soft bake (70 °C for 30 sec, 115 °C for 90 sec, and 70 °C for 30 sec) to evaporate the solvent and densify the resist film. Next, the photoresist film was exposed to UV light (MIDAS Mask

Aligner) under a 3500-dpi mask with the desired straight microchannel geometry, followed by a 35 minute relaxation and then three-step post-exposure hard bake (70

°C for 30 sec, 115 °C for 90 sec, and 70 °C for 30 sec). The photoresist was then developed for 1 minute in MF-24A (MicroChem, MA) developer solution forming the mold of the designed microchannel for PDMS casting. The microchannel mold was positioned in a petri dish and covered with the PDMS mixture (Sylgardl84 Silicone

ElastomerKit, DowCorning Corporation, Freeland, MI) of prepolymer and curing agent with a ratio of 10:1 by weight. The liquid PDMS was then cured in a vacuum at

65 °C for 4 h. Once cured, the PDMS with the straight microchannel portion was cut 15 out and two holes of 5 mm in diameter were punched in the predesigned regions to serve as the fluid reservoirs.

The fabrication of the floating electrodes was similar to that of the microchannel mold. Positive photoresist, AZ 1512 (Yeungnam Scientific

Instruments, Korea), was first spin-coated onto a clean glass slide, followed by a soft bake at 100 °C for 50 seconds. The photoresist film was then exposed to UV light under a 3500 dpi photo mask with the desired electrode geometry, followed by post exposure bake at 100 °C for 50 seconds. After the hard bake, a negative master was obtained by developing the photoresist for 1 minute with the commercial AZ 500 MEF

(Yeungnam Scientific Instruments, Korea) developer solution. Subsequently, the patterned glass slide was sputtered (Emitech, K675X, UK) with 25 nm chromium and then 25 nm gold. Then the coated glass slide was sonicated in acetone to remove the photoresist and obtain the floating electrodes patterned on the glass slide.

Finally, the microchannel side of the PDMS slab and the glass slide with the patterned floating electrodes were treated by 30-second oxygen plasma (Femto

Science, Korea). Immediately following the oxygen plasma treatment, the two treated surfaces were bonded to form the microchannel with floating electrodes on the bottom of the channel. Figure 2.1 shows an example set up of the top view of a microchannel with one (Figure2.1a) and two (Figure 2.1b) floating electrodes, and a picture of the fabricated%nicrochannel (Figure 2.1c) used in the study. ' 16

L, L,

TIT

(c) 4.4*11 i •.,!•£*'•:

Figure 2.1. Schematic top view of a straight microchannel with one (a) and two (b) floating electrodes on the bottom wall of the channel, and a picture of a microchannel with one floating electrode positioned in the center of the microchannel (c).

2.1.2 Data Analysis

The experimental data were recorded via I-Solution software and analyzed via Matlab software. Initially all images were opened via Matlab software and every images were subtracted from the initial image at t=0. Then the normalized images were digitalized via Matlab software. The average fluorescent intensities were taken over the entire width of the channel and then fluorescent intensity distribution (IF) was drawn along the axial distance.

2.2 Computational Methodology

2.2.1 Introduction

A nanopore with radius a and length L is considered connecting two reservoirs filled with an electrolyte solution with different bulk concentrations, CL and CR, as shown in 17

Figure 2.2. A charged spherical nanoparticle of radius ap and uniform surface charge density

Due to the axi-symmetry, the domain of the electrolyte is represented by the region bounded by the outer boundary ABCDEFGH, the line of symmetry HI, the particle surface UK, and the symmetry line KA. The dashed line segments, AB, BC, FG, and

GH, represent the conceptual boundary of the reservoirs. The lengths LR and radius b of the reservoirs are sufficiently large to ensure that the electrochemical properties at the locations of AB, BC, FG, and GH are not influenced by the charged nanoparticle.

It is assumed that the walls of the two reservoirs (line segments CD and EF) are electrically neutral surfaces. Without losing generality, it is assumed that CR > CL, SO that a positive concentration gradient is imposed along the z-direction, where z measures the axial distance from left to right in the inertial cylindrical coordinate system (r, z) shown in Figure 2.2. No external pressure gradient and electric field are imposed along the nanopore.

A continuum mathematical model, consisting of the ionic mass conservation equations for the concentrations of the ionic species, the Poisson equation for the in the electrolyte solution, and the Navier-Stokes equations for the flow field, has recently been used to study the electrophoretic motion of nanoparticles through a nanopore [32-35] with results in satisfactory agreement with those obtained experimentally and from the molecular dynamics (MD) simulations pertaining to the translocation of DNA molecules in nanopores. Huang et al. [123] investigated the liquid flow through a nanopore with 2.2 nm diameter and 6 nm long to confirm that the results through the continuum approach and the MD simulations are in good agreement. In the present study, the continuum approach is adopted in describing the diffusiophoresis system. 18

G t

D Nanopore E b J <"& , a K S'.J $ 1 r ^

L

1 Ressrvcir Messrs cir

U, LR

Figure 2.2. Schematic of a nanopore of length L and radius a connecting two identical reservoirs on either side. A concentration gradient of electrolyte solution is applied across the two reservoirs. A charged spherical particle of radius ap bearing uniform surface charge density, op, is positioned at the center of the nanopore.

2.2.2 Mathematical Model for the Fluid Motion

The flow of an incompressible electrolyte solution generated by an induced electrostatic force and pressure gradient is described by the conservations of mass

V»u = 0 (1) and momentum

2 -Vp + //V u - F (z,c, + z2c2) V V = 0 (2) where the modified Stokes equations are used due to the extremely small Reynolds number in the electrokinetic flow in the nanopore. The electrolyte is considered to be binary. The velocity vector u = uer + vez is composed of radial and axial components (u,v), where er and e2 are, respectively, unit vectors in the r- and z- directions. In the above p is the pressure, V is the electric potential in the electrolyte solution, a and C2 are, respectively, the molar concentrations of the positive and 19 negative ions in the electrolyte solution, zi and z? are, respectively, the valences of the positive and negative ions, F is the Faraday constant, and fi is the viscosity of the electrolyte solution. The momentum "Equation 2" shows the balance between the induced pressure gradient, viscous dissipation, and the electrostatic force through the interaction between the induced electric field and the net charge density in the electrolyte solution.

On the solid walls of the nanopore and the reservoirs (line segments CD, DE, and EF in Figure 2.2), no-slip boundary conditions are imposed: u - v - 0. On planes

AB and GH of the reservoirs, since they are far away from the nanopore and there is no externally applied pressure gradient across the two reservoirs, normal flow with pressure p=0 is applied. Symmetric boundary condition is used along the lines of symmetry, HI and KA. Slip boundary conditions are used on the segments BC and

FG since they are far away from the entrances of the nanopore. Finally, along the surface of the particle (arc segment UK in Figure 2.2) translating with a diffusiophoretic velocity up, the thickness of the adjacent Stern layer is neglected, and impose the no-slip condition

u(r, z) = upez, on UK (3) where up is the particle velocity vector with the magnitude of wp in the r-direction.

The particle's diffusiophoretic velocity up is determined by requiring the total force in the z direction (FT) acting on the particle to vanish

FT=FE+FD=0 (4) where

E FE = tfs (T .n). ezdS (5) and 20

D FD=tts (T .n).ezdS (6) are, respectively, the electrostatic and hydrodynamic forces acting on the particle.

Here S is the particle surface, T£ =^EE—*r(E-E)land TD =-/?I + //(Vu + Vu7') are, the Maxwell stress tensor and the hydrodynamic stress tensor, respectively, e is the of the electrolyte solution, E = -VF is the electric field, and I is the identity tensor.

2.2.3 Mathematical Model for the Ionic Mass Transport

A general multi-ion mass transport model includes the ionic mass conservation equation for the concentration of each ionic species and the Poisson equation for the electric potential in the electrolyte solution. The flux density of each aqueous species due to convection, diffusion, and migration is given by the Nernst-Planck equation

N, = u ck - DkVck - zk^ FckVV (k=\ and 2) (7) where Dk is the diffusion coefficient of the A* ionic species, T is the absolute temperature of the electrolyte solution, and R is the universal gas constant. Under steady state, the concentration of each species is governed by the Nernst-Planck equation

V«Nt=0 (A=land2) (8)

The electric potential, V, in the electrolyte solution is governed by the Poisson equation

2 -eV V = F(zlCl+z2c2) (9) 21

On the plane AB, which is sufficiently far away from the nanopore, the concentrations of the positive and negative ions are the same as the bulk concentration of the electrolyte solution present in the left fluid reservoir:

cl=c2=CL onAB (10)

Similarly

c^c2=CR onGH (11)

On the fixed walls of the reservoirs and the wall of the nanopore (line segments CD, DE, and EF in Figure 1), which are impervious to ions, the net ionic fluxes normal to the rigid walls are zero (e.g., n»Nl = n«N2 = 0). Along the surface of the nanoparticle (arc segment UK in Figure 1), which is impervious to ions and translating with a velocity up (eq 3), the net ionic flux normal to the particle surface satisfies [124]:

n«N, = n.N2=0 on CD, DE, EF and UK (12) where n is the unit vector normal to the corresponding surface.

The boundary conditions on the segments BC and FG are defined with the assumption that these surfaces are in the bulk electrolyte reservoirs. Accordingly, zero normal flux is used for the ionic mass conservation equations:

n^N^n.N^O on BC and FG (13)

Along the segments HI and KA, symmetric boundary conditions are used for the ionic mass conservation equations:

n«N,=n»N2=0 on HI and KA (14)

Symmetric boundary condition for the electric potential in the electrolyte solution is used on the planes HI and KA:

n.VF = 0 on HI and KA (15) 22

Along the plane AB, the boundary condition for the electric potential is

V = 0 onAB (16) where the potential,

fs F(z1N1 + z2N2)-ndS = 0 (17) where S is the surface area of the plane AB.

For electrodiffusiophoresis case

V = 0 onGH (18)

Since the surfaces of BC and FG are far away from the nanopore and are in the bulk electrolyte reservoirs, no-charge boundary condition for the potential is used:

n.VF = 0 onBCandFG (19)

Since the walls of the reservoirs and the nanopore (planes CD, DE and EF) do not carry fixed charge, set

n«VF = 0 onCD,DEandEF (20)

Along the particle surface, a uniform surface charge is applied:

n»(-sVV) = (Tp on UK (21)

2.2.4 Dimensionless Form of the Mathematical Model

The macroscopic electrolyte concentration measured at the particle's center is used in the absence of the particle and nanopore wall, C0 = (CL + CR )/2, as the ion concentration scale, RTIF as the potential scale, the nanoparticle's radius ap as the 23

2 2 2 length scale, U0 = eR T /(juapF J as the velocity scale, and juUo/ap as the pressure scale. The dimensionless governing equations of the above multi-ion model are:

V«u*=0 (22)

_Vy + VV --(Kapf (ziC; +¥;)VF' = 0 (23)

V-N =0 (24)

-VV =-(*•«, ^z.c'+z^*) (25)

In the above, variables with superscript * are dimensionless.

1 2 K~ = AD = yjeRT/2F C0 is the dimensional EDL thickness. The dimensionless flux

density normalized by U0C0 is

N* = u'c" -AVc'-zA c'VK' (26) I I II I I I '

2 2 2 and A, =DjD0 with D0-eR T /(^iF ). The dimensionless current density

normalized with FU0C0 is

J* = z,N* + z2N* (27)

The dimensionless particle velocity wp* is determined by the zero net force,

F;+F;=O (28)

with

dV dV' 1 dV) (dV ds (29) s-J —i r«, + — 8z' dr' n. 5r dz 2 and

.5M* 3M* . . . _ du*. i-^ + ^X+i-P +2-H-K tffc* (30) *-r cz or oz 24

w* and u] are, respectively, the r- and z- components of the dimensionless velocity u*. nr and nz are, respectively, the r- and z- components of the unit vector n which is normally directed into the particle's center of mass.

For the set of the dimensionless Nernst-Planck equations (24), the boundary conditions c[ = c* = 2/(1 + a) at the plane AB with a - CR/CL , c[ =c'2= 2a/(l + a) at the plane GH, and n • N* = n • N* = 0 at other boundaries.

For the dimensionless Poisson equation (25), the boundary conditions V* = ' at the plane AB, V* = Oat the plane GH, n»(-VK*) = Oon the planes BC, CD, DE,

EF, and FG, n • (-V V*) = ap on the segment UK, and insulation at other boundaries.

ap\s the dimensionless surface charge density of the particle normalized by

sRT/(apF). 25

CHAPTER III

PARTICLE MANIPULATION IN MICROFLUIDIC DEVICES VIA

FLOATING ELECTRODES

This chapter describes the various particle manipulations, including enrichment,

movement, trapping, separation, and focusing, by using single and multiple floating

electrodes. Then, a flexible strategy for the on-demand control of the particle

enrichment and positioning in a microfluidic channel have been experimentally

demonstrated by using two micron-sized control electrodes on both sides of the

floating electrode attached to the bottom wall of a straight microchannel under an

imposed DC electric field. In contrast to a dielectric microchannel possessing a

nearly uniform surface charge (or zeta potential), the metal strip (floating electrode) is

polarized under the imposed electric field results in a non-uniform distribution of the

induced surface charge with a zero net surface charge along the floating electrode's

surface, and accordingly induced-charge electro-osmotic (ICEO) flow near the metal

strip. The ICEO flow can be regulated by controlling the strength of the imposed

electric field, and affects both the hydrodynamic field as well as the particle's motion.

By using a single floating electrode, charged particles could be locally concentrated in

a section of the channel or in an end-reservoir; and move toward either the anode or

the cathode by controlling the strength of the imposed electric field. By using double

floating electrodes, negatively charged particles could be concentrated between the

floating electrodes, subsequently squeezed to a stream flowing in the center region of the microchannel toward the cathodic reservoir, which can be used to focus particles.

By controlling the electric field on the floating electrode by an additional locally imposed electric field, on-demand control of the particle enrichment and its position inside a microfluidic channel has been demonstrated. 26

After particle deposition onto the floating electrode in a closed circular cavity has been experimentally demonstrated under an externally imposed AC electric field by two micron-sized electrodes. When no floating electrode is used, the particles are not deposited to dielectric glass surface, but instead by using a floating electrode between AC electrodes, negatively charged particles could be deposited onto the floating electrode and remains on the electrode surface after washing the floating electrode. By using different AC frequencies and different time interval, more or less particles can be deposited more uniformly onto the floating electrode.

3.1 Manipulating Particles in Microfluidics via Floating Electrodes

3.1.1 Introduction

In contrast to a microchannel with dielectric walls possessing a nearly uniform surface charge or zeta potential, floating electrodes attached to the bottom wall of a microchannel are polarized under an external electric field. This results in a spatially non-uniform surface charge on floating electrode's surface. The ideally polarizable floating electrode is negatively charged near the anodic side (close to anode) and is positively charged near the cathodic side (close to cathode), and the net induced charge is zero over the entire surface of the metal strip. In addition, the magnitude of the induced surface charge is proportional to the strength of the imposed electric field

[23, 44-48, 53, 54]. The interaction between the mobile ions in the EDL of the floating electrode and the imposed electric field generates an ICEO flow having two opposite eddies near the oppositely charged floating electrode. The ICEO around the floating electrode affects the overall hydrodynamic field as well as the particle electrokinetic motion through the interplay between the hydrodynamics and electrostatics. The most relevant ICEO literature thus far concerns exploiting and 27 exploring its applications in microfluidic devices, such as pumping, mixing, and generating concentration gradient primarily under AC electric field [44, 55-62]. This is the first study to employ the ICEO flow induced by the floating electrodes attached to the channel bottom wall at DC electric fields to achieve versatile and facile particle manipulations, including trapping, enrichment, focusing, separation and control of the direction of particle motion. Note that this work is different from the one by Crooks's group [63-66], in which the mechanism of sample concentration and separation by a single floating electrode in a microchannel is the bipolar electrochemical reaction [67-

68] instead of ICEO.

3.1.2 Experiment

Microfluidic channel and electrode fabrication methodology have been explained in

Section 2.1, thus it is not explained here again. Figure 3.1 schematically shows the top view of a microchannel with one (Figure 3.1a) and two (Figure 3.1b) floating electrodes, and a picture of the fabricated microchannel (Figure 3.1c) consisting of a

1-cm long straight channel with a rectangular cross-section of 100 |4.m in width and 8 urn in depth. The floating electrodes are positioned in the central region on the channel bottom wall. The length of each floating electrode is LE = 500 urn, and the distance between the adjacent floating electrodes is a = 300 urn.

Spherical polystyrene particles (Invitrogen, Eugene, OR) of 4 urn in diameter and fluorescenceparticle s (Invitrogen, Eugene, OR) of 500 nm in diameter were used in the experiments. The particles were suspended in different concentrations of KC1 solutions. Sodium Dodecyl Sulfate, (SDS), (Fisher Scientific, Fair Lawn, NJ) was added at a volume ratio of 0.5% to the particle solutions for reducing the particle adhesions to channel walls. 28

L, L

| ,1 1 rzrI l

(c)

Figure 3.1. Schematic top view of a straight microchannel with one (a) and two (b) floating electrodes on the bottom wall of the channel, and a picture of a microchannel with one floating electrode positioned in the center of the microchannel (c). L=l cm, d=100 urn, the depth of the channel is 8 um, LE= 500 urn, and a= 300 urn.

The DC electric field was generated by applying a DC drop between two platinum electrodes of 1.25 mm in diameter that were placed into the two fluid reservoirs, filled with the particle solution. The imposed electric field was supplied by a DC power supply (PNCYS, EP5001). Pressure-driven flow was carefully eliminated before each experiment by balancing the liquid heights in the two reservoirs. The particle concentration and motion were visualized and recorded using an inverted optical microscope (Nikon Eclipse Ti, Nikon Instruments, Japan) equipped with a CCD camera (Pixelink, P1-E421CU).

3.1.3 Results and Discussion

The electrokinetic particle transport experiments were first conducted in the microchannel without floating electrodes. The zeta potentials of the microchannel 29 dielectric walls, including both PDMS and glass, are negatively charged. The 4-um polystyrene particles and 500 nm fluorescence particles are also negatively charged.

The experiments in the microchannel without the metal strips show that both particles electrokinetically migrate toward the cathode in different concentrations of KC1 solutions at various strengths of the imposed electric field. Since the zeta potential of the bottom channel wall made of glass is much higher than that of the particles, the electroosmotic flow directed to the cathode dominates over the electrophoretic motion, thus dragging the negatively charged particles toward the cathode. As the imposed electric field increases, the particle electrokinetic velocity, which is a net outcome of the fluid electroosmosis and particle electrophoresis, increases. However, the apparent electrokinetic mobility, the ratio of the electrokinetic velocity to the imposed electric field, does not depend on the applied electric field, which has also been confirmed by the previous experimental works [42-43] done by others. Since the focus is on the effect of the floating electrodes on the particle electrokinetic motion, the detailed results in the microchannel without the floating electrodes are not shown here in this study.

Subsequently, electrokinetic motions of the two types of particles in a microchannel with one and two floating electrodes were experimentally investigated at different KC1 solutions and at various electric fields imposed. Since the induced surface charge on the floating electrode is proportional to the electric field strength, the ICEO flow is not sufficiently strong to deflect the particle motion driven by the dominant electroosmotic flow when the imposed electric field is relatively weak.

Therefore, at a low driving electric field, the particle motion in a microchannel with floating electrodes is very similar to that in a microchannel without floating electrodes under all other conditions being the same. However, as discussed below, various 30 particle manipulations including trapping, reversal of particle motion, depletion, separation, enrichment, and focusing by the ICEO flow on floating electrodes have been experimentally observed when the imposed electric field is relatively high.

3.1.3.1 Particle Manipulations by a Single Floating Electrode

3.1.3.1.1 Particle Trapping

Figure 3.2 depicts the spatial distribution of the cross-sectional averaged fluorescent intensity (IF) of 500 nm fluorescent particles near the anodic side of the floating electrode in 1 mM KC1 when the imposed electric field is 30 V/cm (a), 50 V/cm (b),

70 V/cm (c), and 90 V/cm (d). The IF is the deviation of the cross-sectional averaged fluorescent intensity at time t from that at l=Q when the electric field was imposed.

The origin of the axial distance is the anodic edge of the floating electrode as shown in Figure 3.1. The net fluid motion is directed from right to left.

In marked contrast from the case without the floating electrode in which the

500 nm fluorescent particles continuously migrate from the anodic reservoir toward the cathodic reservoir by the dominant electroosmotic flow, the fluorescent particles are now trapped in the upstream region next to the anodic edge of the floating electrode when the electric field of 30 V/cm is imposed in 1 mM KC1, as shown in

Figure 3.2a. As the time increases, more particles are trapped by the floating electrode leading to the increase in the particle concentration (reflected in the IF) as shown in Figure 3.2a. The trapped particles are continuously supplied from the anodic reservoir by the dominant electroosmotic flow in the upstream of the floating electrode. In the downstream of the channel between the cathodic reservoir and the floating electrode, the initial fluorescent particles before the electric field is imposed, 31 move toward the cathodic reservoir by the net electroosmotic flow directed toward the cathodic reservoir.

80 •;, («) IF 60 \^%\ 40 0s 20 \ V^\W/? * ,'f 20s V l'/»40s* '' :iv n 0 250 500 750 1000 1250 1500 1750 0 250 500 750 1000 1250 1500 1750 60 A s (

20 2s

0 250 500 750 1000 1250 1500 1750 0 250 500 750 1000 1250 1500 1750

Figure 3.2. Fluorescent intensity distribution in ImM KCl electrolyte under 30 V/cm (a), 50 V/cm (b), 70 V/cm (c), 90 V/cm (d).

After all of the particles migrated into the cathodic reservoir, there were no observed fluorescent particles in the downstream, suggesting that the trapped particles do not leak to the downstream and can be continuously held there. The induced charge of the anodic (cathodic) side of the floating electrode is negative (positive), this results in a non-uniform ICEO flow consisting of two opposite eddies. The direction of the ICEO flow in the vicinity of the cathodic side of the floating electrode is opposite to that of the electroosmotic flow over the glass substrate, while the direction of the ICEO flow at the anodic side is the same as that of the electroosmotic 32 flow. Due to mass conservation, a clockwise (counterclockwise) circular motion is induced in the anodic (cathodic) region of the floating electrode. Figure 3.3 schematically shows the fluid flow in the region of the floating electrode. The mechanism of the particle trapping is the clockwise ICEO flow formed in the anodic region of the floating electrode.

3 .ex. sa. Q ,Q —-fez Je?. Q, .Q Q ,Q -

E fo\2 ^Ipllllil

Figure 3.3. Schematic illustration of the fluid flow near the floating electrode (the dark region in the middle of the bottom channel wall). The imposed electric field is directed toward left. The dielectric channel wall is negatively charged, and the induced charge on the anodic (cathodic) side of the floating electrode is negative (positive). Clockwise (counterclockwise) vortices are induced near the anodic (cathodic) side of the floating electrode. The net electroosmotic flow is directed to left.

3.1.3.1.2 Reversal of Particle Motion

When the imposed electric field exceeds a critical value, the particles, initially trapped next to the anodic edge of the floating electrode, now move toward the anodic reservoir, as shown in Figures 3.2b-3.2d for the electric fields of 50 V/cm (Figure

3.2b), 70 V/cm (Figure 3.2c), and 90 V/cm (Figure 3.2d). Figure 3.4 depicts the sequential images of the concentrated 500 nm particles at 50 V/cm, showing the movement of the concentrated particles as a front toward the anodic reservoir.

Similar results are obtained for the 4 urn in diameter particles. As the imposed 33 electric field increases, the motion of the concentrated particles moving toward the anodic reservoir increases. Note that the particle motion is opposite to that in a microchannel without floating electrode in which the particles move from the anodic reservoir toward the cathodic reservoir by the dominant electroosmotic flow.

Therefore, the particle motion can be reversed by the floating electrode by increasing the electric field strength. Again, the negatively charged particles in the downstream of the channel between the floating electrode and the cathodic reservoir migrate toward the cathodic reservoir by the net electroosmotic flow of the dielectric channel walls, suggesting that there is a net fluid flow from the anodic reservoir toward the cathodic reservoir. The induced surface charge and the corresponding ICEO flow increase by increasing the imposed electric field. Therefore, higher electric field induces stronger local flow vortices in the region of the floating electrode. The strong clockwise vortices in the anodic side of the floating electrode, schematically shown in

Figure 3.3, propel the concentrated particles toward the anode reservoir.

Figure 3.4. Concentration and motion of the 500 nm particles in 1 mM KC1 solution after 6 sec (a), 8 sec (b), 10 sec (c), 12 sec (d), 14 sec(e), 16 sec (f), and 18 sec (g) under 50 V/cm. The left side of the dashed line represents the floating electrode. 34

Figure 3.5 depicts the evolution of the spatial distribution of the fluorescent intensity at the electric field of 50 V/cm in 0.1 mM (a) and 10 mM (b) KC1 solutions.

Again, the concentrated particles move toward the anodic reservoir because of the strong vortices of the ICEO flow. The zeta potentials of the microchannel dielectric walls, including both PDMS and glass, increase and accordingly the electroosmotic flow increases as the bulk electrolyte concentration decreases [125]. As the electrolyte concentration increases, the electroosmotic flow moving toward the cathodic reservoir decreases, leading to faster motion of the concentrated particles toward the anodic reservoir, as shown in Figure 3.5.

60

IF 40

20

0 0 250 500 750 1000 1250 1500 1750

120 IF 90

60

30 0 0 250 500 750 1000 1250 1500 1750 Axial Distance (fim)

Figure 3.5. Fluorescent intensity distribution at 50 V/cm in 0.1 mM (a) and 10 mM (b) KC1 solution. 35

3.1.3.1.3 Particle Separation

Both 500 nm and 4 u.m negatively charged particles migrate toward the cathodic reservoir in a microchannel without floating electrodes due to the dominant electroosmotic flow. One can separate them in a microchannel with a single floating electrode at an appropriate imposed electric field. For example, at 10 V/cm, the 500 nm fluorescent particles in a mixture of both particles suspended in 1 mM KC1 solution move to the cathode, while the 4 urn particles move towards the anode. After

30 minutes, most of the 500 nm particles are in the cathodic reservoir, while the 4 urn particles are in the anodic reservoirs. The microchannel and the reservoirs were first filled with 1 mM KC1 solution without particles, and subsequently introduced a drop of the particle mixture into the anodic reservoir. After carefully balancing the fluid heights in both fluid reservoirs, an electric field of 10 V/cm was applied. It was found that the 500 nm particles migrate toward the cathodic reservoir, while the 4 pm particles are retained in the anodic reservoir. After 45 minutes, the two types of particles are separated with the 500 nm particles in the cathodic reservoir and the 4 urn particles in the anodic reservoir.

75s 70s 65s I I 20s 10s 0s I I 0>) "J

0 s 10 s 20 s I I 60s 65 s 80s

Figure 3.6. Trajectories of 500 nm (a) and 4 \x.m (b) particles in 1 mM KC1 at 10 V/cm. The region between two dashed lines represents the floating electrode. The arrows in (a) and (b) represent the directions of the corresponding particle motions. 36

To clearly show the opposite particle motions of the two types of particles in a microchannel with a floating electrode, the 500 nm particles were introduced into the anodic reservoir, while the 4^un particles were introduced into the cathodic reservoir.

Figure 3.6a shows the trajectories of 500 nm particles at 10 V/cm in 1 mM KC1.

These trajectories are obtained by superposing sequential images of many particles including one brighter one. At t=0, the particles are away from the anodic side of the floating electrode. As time increases, the particles move toward the floating electrode, then pass the floating electrode region and continue to move toward the cathodic reservoir at later times. Figure 3.6b shows the trajectories of the 4 urn particles under the same condition of Figure 3.6a. As time increases, the focused particles move from the cathodic reservoir toward the floating electrode region, pass the metal strip and move on toward the anodic reservoir.

3.1.3.2 Double Floating Electrodes

3.1.3.2.1 Trapping and Depletion

At a relatively low electric field, the particle motion in a microchannel with two floating electrodes is similar to that in a microchannel without floating electrodes due to insignificant ICEO flow. When the electric field is relatively high, particles can be trapped between the two floating electrodes for a short period of time, as shown in

Figure 3.7 at 30 V/cm in 1 mM KC1 solution. As time increases, the trapped particles leak to the downstream. Figure 3.8 shows the fluorescent intensity distribution between the two floating electrodes at 30V/cm electric field in ImM KC1 after 30 s

(a), 1 min (b), and 10 min (c). 37

Figure 3.7. 500-nm particles distribution between two floating electrodes after 30 sec (a), 1 min (b), 7 min (c), and 10 min (d) at 30V/cm in ImM KCl solution. The dark regions on both ends represent the two floating electrodes.

0 250 500 750 1000 1250 1500

250 500 750 1000 1250 1500

IF

250 500 750 1000 1250 1500 Axial Distance (|im)

Figure 3.8. Fluorescent intensity distribution between two floating electrodes after 30 sec (a), 1 min (b), and 10 min (c) at 30 V/cm in ImM KCl solution. 38

Note that the axial distance shown in Figure 3.8 originates from the cathodic edge of the left floating electrode as shown in Figure 3.1b. The axial distances 0 -

500 um, 500 um - 800 (j.m, and 800 urn -1300 um represent, respectively, the region of the left floating electrode, the gap between the two floating electrodes, and the right floating electrode. The significant enhancement of the fluorescent intensity in the gap between the two floating electrodes indicates that particles are initially concentrated and trapped, as shown in Figure 3.8a. As time increases, the fluorescent intensity decreases, suggesting that the trapped particles deplete due to a slow leakage toward the cathodic reservoir. By comparing Figures 3.8a and 3.8b, the trapped particles show oscillations in the gap between the floating electrodes. In a channel with a single floating electrode at 30 V/cm in 1 mM KC1 solution, the particles were trapped and continuously held in the upstream region next to the anodic edge of the floating electrode (Figure 3.2a). Under the same conditions, in a channel with two floating electrodes, particles are no longer trapped in the upstream region next to the anodic edge of the right floating electrode. Rather, the particles are now partially trapped for some length of time between the two floating electrodes.

3.1.3.2.2 Particle Focusing

At a higher electric field such as 50 V/cm, the particles are concentrated between the two floating electrodes where the particles are nearly uniformly distributed along the channel width (i.e., 100 um), as shown in Figure 3.9a. The concentrated particles subsequently form a small stream along the channel centerline and migrate toward the cathode, as shown in Figure 3.9a. Figure 3.9b depicts the fluorescent intensity distribution along the cross-section of the channel as shown in Figure 3.9a. The 39

particles are focused to a stream of less than 20 um in width. The particle focusing thus achieved may be utilized, for example, in microflow cytometry.

20 40 60 80 100 Radial Distance (fun)

Figure 3.9. Snapshot (a) and fluorescent intensity distribution (b) along a cross- section shown in (a) at 50V/cm in ImM KCl solution. The dark regions on both ends represent the two floating electrodes.

3.2 On-Demand Particle Enrichment in a Microfluidic Channel by a Locally

Controlled Floating Electrode

3.2.1 Introduction

In the previous section, a versatile and facile method for electrokinetic particle

manipulations such as trapping, reversal of particle motion, enrichment/depletion,

separation, and focusing by floating electrodes (metal strips) attached to the channel 40 bottom wall of a straight microfluidic channel has been experimentally demonstrated .

In this strategy of particle manipulation, the ICEO flow on the metal strips is passively induced by the global DC electric potential difference applied to two electrodes positioned at the two ends of the straight microchannel, inducing a global

DC electric field that causes electroosmotic flow (EOF) as well as particle electrophoretic motion. If the imposed DC electric field is fixed, the particle manipulation by the ICEO flow on the floating electrodes is not controllable. In contrast, on-demand particle manipulations by local control of the local ICEO flow on the floating electrode will make such a method suitable and attractive for reconfigurable microfluidic systems that can perform several different functions with different states of external controls. The objective of this section is to propose and demonstrate a novel and flexible strategy for particle manipulation in microfluidics by the use of a locally controlled floating electrode which can be polarized to variable extents by locally changing the electric field across it even at a fixed global field across the microchannel. The scope and approach of employing a floating electrode for particle manipulations was greaty extended as proposed in Section 3.1 by patterning two micron-sized control electrodes, CEL and CER, positioned on the left and right side of the floating electrode, as schematically shown in Figure 3.10. These control electrodes govern the degree of polarization on the floating electrode and can thus control the locally induced EOF, electrophoresis as well as ICEO flow in the vicinity of the floating electrode positioned in the central region of the channel bottom wall. A global DC electric field directed from the anodic reservoir to cathodic reservoir is also imposed by applying a potential difference across the two electrodes positioned in the two fluid reservoirs at both ends of the microchannel. Clearly, even a low voltage applied across the control electrodes induces a very high local electric 41 field across the floating electrode because the distance between the control electrodes is very small (i.e., 600 um in this study). Since the ICEO is proportional to the square of the overall electric field, the ICEO can be easily manipulated by tuning the magnitude and polarity of the control voltage. This strategy allows a far greater degree of flexibility in particle manipulation as compared to a floating electrode polarized only by the global field across the channel. The developed sample enrichment technique is useful for many applications in analytical chemistry, clinical diagnostics, forensics, food safety, and drug development in which the target analyte is present in low concentration and needs to be concentrated in order to be detected by standard analytical techniques.

3.2.2 Experiment

The PDMS/glass microfluidic channel with/without floating electrodes was fabricated using the standard soft-lithographic method, and its detailed fabrication procedure is given in Chapter 2 Section 2.1. The straight microchannel is 1 cm long with a uniform cross-section of 8 um (depth) x 100 urn (width), and connects two fluid reservoirs of 5 mm in diameter on either end. The microchannel and fluid reservoirs are made in PDMS. The floating and control gold electrodes are fabricated on a clean glass slide. The lengths of the floating and control electrodes are, respectively, 500

(j.m and 300 um. The dielectric gap between the floating electrode and each control electrode is 50 um. The floating electrode is positioned in the central region of the channel bottom wall. The microchannel side of the PDMS slab and the glass slide with the patterned floating and control electrodes were treated by 30-second oxygen plasma (Femto Science, Korea). Immediately following the oxygen plasma treatment, the two treated surfaces were bonded to form the microchannel with patterned 42 electrodes on the channel bottom wall. Figure 3.10a schematically shows the top view of a microchannel with floating and local control electrodes positioned in the central region of the channel bottom wall, and Figure 3.10b shows a picture of the

fabricated microchannel used in this work.

L L

(a) ( Cathode ) P j ! h 7 [ Anode CE,'—' ^JCE„ L

ft* .** IT it

Figure 3.10. Schematic top view of a straight microchannel with one floating electrode and two control electrodes patterned on the channel bottom wall (a), and a picture of the microfluidic channel (b). L=l cm, d=100 (im, the depth of the channel is 8 um, LE= 500 pm, LCE= 300 urn, and a= 50 um.

Spherical polystyrene fluorescence particles (Invitrogen, Eugene, OR) of 500 nm in diameter were used in the experiments. The particles were suspended in ImM

KCl solution. Sodium Dodecyl Sulfate (SDS) (Fisher Scientific, Fair Lawn, NJ) was added at a volume ratio of 0.05% to the particle solution for reducing the particle adhesion to the microchannel walls. 43

EOF and electrophoresis inside the entire channel was generated by applying a

DC voltage drop between two platinum electrodes of 1.25-mm in diameter that were placed into the two fluid reservoirs, filled with the particle solution. The DC voltage was supplied by a high-voltage DC power supply (PNCYS, EP5001). The DC voltage drop across the control electrodes was supplied by a low-voltage DC power supply (SMtechno, SDP50-3D). Pressure-driven flow was carefully eliminated before each experiment by balancing the liquid heights in the two reservoirs. The particle concentration and their motions were visualized and recorded using an inverted optical microscope (Nikon Eclipse Ti, Nikon Instruments, Japan) equipped with a

CCD camera (Pixelink, P1-E421CU).

3.2.3 Mathematical Model

Externally and locally imposed electric field around a floating electrode inside the rectangular microfluidic channel is simulated by commercial COMSOL software.

When an electric field is imposed through the channel, electroosmotic flow will be generated in the channel and vortices will be produced near the conducting floating electrode because of the induced non-uniform surface charge on the conducting surfaces.

The flow field is obtained by numerically solving a 2D Stokes equations in the vertical plane of the microchannel since the channel width is much larger than its depth and the Reynolds number of the electrokinetic flow is very small (i.e., Re«l).

A straight microchannel is considered with height h and length L as shown in Figure

3.11. The domain of the electrolyte is represented by the region bounded by the outer boundary ABCDEFGHIJA, the floating electrode GH, the control electrodes EF and 44

IJ, external electrodes AB and CD. On the surface of the channel wall,

Smoluchowshi slip velocity is used as the boundary condition. On the surfaces of the floating electrodes and dielectric walls, induced zeta potential and zeta potentials of glass and PDMS are used to calculate the slip velocity. The details of the mathematical model have been described by Wu and Li [58, 59]. The model is briefly summarized below.

Figure3.11. Schematic of micro fluidic channel with locally controlled floating electrodes

The applied electrical potential in the liquid, , is governed by the Laplace's equation.

VV=0 (1) with the boundary conditions

nV^=0 at BC, DE, FG, GH, HI, JA (2)

=t at CD (3)

<^=1 atEF (4)

= 0 at AB and IJ (5)

The flow field is obtained by solving the Continuity and the Navier-Stokes equations

Vu = 0 (6) 45

p Wt+"v2l= ~vp+^vZ"+^pe (7) where u is the velocity vector, VP is the pressure gradient, fj. is the viscosity, p is the

—» density of the fluid, pe is the local net charge density, E = V^ is the local applied electric field strength. The transient term can be dropped due to steady state flow inside the microfluidic channel. Since the local net charge density is not zero only in the electrical double-layer (EDL), the driving force for electroosmotic flow, Epe, exists only in EDL. The electroosmotic flow velocity changes sharply in a thin layer of the liquid near the solidwall. Therefore, the driving force term can be dropped off and Helmholtz-Smoluchowski slip velocity is applied as a boundary condition [58,

59].

Zeta potential (Q of the dielectric channel wall is constant. On the conducting surfaces C, is replaced by the local induced zeta potential. The corresponding boundary conditions for the velocity are

ux = -^Ex,uy = -^Ey at BC, DE, FG, HI, JA (8)

E E ux = - -^Ex,uy = - -^Ey atGH (9)

In this study, the fluid flow is generated by voltage drop between two reservoirs, and no pressure gradient is considered. The pressures at the two ends of the microchannel are specified as zero

P=0 at AB and CD (10)

3.2.4 Results and Discussion

The electrokinetic particle transport experiments were first conducted in the microchannel without the floating electrode, i.e., without the metal strips on the channel bottom wall. The top and side PDMS channel walls, as well as the bottom 46 glass channel wall, are negatively charged. The 500 nm fluorescence particles are also negatively charged. The experiments in the microchannel without the metal strips show the expectation that particles electrokinetically migrate from the anodic reservoir toward the cathodic reservoir. Since the zeta potential of the bottom channel wall made of glass is much higher than that of the particles, the electroosmotic flow directed to the cathode dominates over the electrophoretic motion directed toward the anode, thus dragging the negatively charged particles toward the cathode. As the

imposed electric field increases, the particle electrokinetic velocity, which is a net outcome of the fluid electroosmosis and particle electrophoresis, increases.

JEL_ S . e —o_. JQ „Q -. ©..„ a —,e, *.,.x3 «n*™™Gfc ««< w .ii.iiiiu w .. .™.JC? «,,fc*««,fc« fc? v «s3«« far <« >7 «r fat

Figure 3. 12. Flow field and streamlines in the region of the three floating electrodes when the external electric field is 10 V/cm (a) and 30 V/cm (b).

When the two control electrodes are not connected to an external power supply, they also act as floating electrodes and the microchannel in this case effectively has three floating electrodes on the channel bottom wall. Under the external electric field, Eext, imposed by applying a DC voltage across the two electrodes positioned in the two fluid reservoirs, each floating electrode is polarized 47 resulting in negative (positive) induced charge near the anodic (cathodic) side with a zero net induced charge. The induced charges on the floating electrodes induce spatially nonuniform distribution of the zeta potential (surface charge) on the channel bottom wall. Figure 3.12 shows the flow field and streamlines near the three floating electrodes when Eext=10 V/cm (a) and 30 V/cm (b).

Note that the model did not consider the distortion of the flow field and electric field by the presence of the particles, and the particle's velocity is different from the fluid's velocity due to the fluid-particleinteraction . To take into account the full fluid-particle-electric field interactions, one needs to simultaneously solve the

Stokes equations and the Laplace equation in an Eulerian reference frame and the particle's motion (including both translation and rotation) in a Lagrangian frame using the arbitrary Lagrangian Eulerian (ALE) technique. When the imposed electric field is relatively low (i.e., 10 V/cm in Figure 3.12a), there are counterclockwise vortices formed near the cathodic side of each floating electrode, where the induced charge is positive and the induced ICEO flow velocity is opposite to the dominant EOF. Since the ICEO flow is proportional to the square of the electric field imposed, as the external electric field increases, the ICEO flow increases faster than the EOF and electrophoretic flow. When the electric field is relatively high (i.e., 30V/cm shown in

Figure 3.12b), the induced zeta potential on the floating electrodes is much higher than that of the dielectric channel wall, and the resulting ICEO flow significantly distorts the EOF flow. Clockwise (counterclockwise) vortices are generated near the anodic (cathodic) side of each floating electrode, and the strength and area of the circulating flow increases with increasing the electric field imposed. Obviously, the

ICEO flow affects the overall flow field, and consequently the hydrodynamic force acting on the particle and the particle motion. When the imposed electric field is 10 48

V/cm, the negatively charged particles still migrate toward the cathodic reservoir by the dominant EOF since the ICEO flow is not sufficiently strong. However, when the imposed electric field is 30 V/cm, the particles are trapped near the anodic side of the right control electrode which is floating, and the front of the enriched particles moves toward the anodic reservoir. The particle trapping arises from the induced clockwise vortices near the anodic edge of the floating electrodes. As time increases, more particles are trapped by the right control electrode, CER, leading to the increase in the particle concentration and consequently the fluorescent intensity. Particles are continuously supplied from the anodic reservoir by the dominant EOF in the upstream of the floating electrodes, leading to the movement of the front of the enriched particles toward the anodic reservoir. The final front position of the enriched particles is the junction of the microchannel and the anodic reservoir. In the downstream of the channel between the cathodic reservoir and the left control electrode, CEL, the initial fluorescent particles (before the electric field is applied) are carried by the net EOF toward the cathodic reservoir.

3.2.4.1 On-Demand Control of Particle Enrichment

Next, how the local control electric field, ECont, is studied across the central floating electrode affects the particle enrichment and motion. In the absence of the control

(i.e., the control electrodes are also floating), particles are not trapped/enriched at low external electric field, Eext=10 V/cm, due to insignificant ICEO flow. To enrich particles at Eext=10 V/cm, a control electric field opposite to the external electric field is applied. Figure 3.13 depicts the fluorescent intensity (IF) of 500 nm fluorescent particles near the right control electrode in 1 mM KC1 when Eext=10 V/cm and the oppositely directed control electric fields are: Econt»-3.33 V/cm (a); -6.66 V/cm (b); 49

-10 V/cm (c); and -13.33 V/cm (d). The IF is the deviation of the cross-sectional averaged fluorescent intensity at time t from that at t=0 when Eext is imposed. The time interval between the external and control electric fields is zero. The origin of the axial distance is the edge of the right control electrode as shown in Figure 3.10. In marked contrast from the case when the control electrodes are floating, the 500 nm fluorescent particles continuously migrate from the anodic reservoir toward the cathodic reservoir by the dominant EOF in the upstream, and are enriched in the upstream region of right control electrode. As time increases, the front of the enriched particles moves toward the anodic reservoir, and the directed motion of the enriched particles increases as the control electric field increases.

250 500 750 1000 1250 1500 1750 0 250 500 750 1000 1250 1500 1750 120

250 500 750 1000 1250 1500 1750 250 500 750 1000 1250 1500 1750 Axial Distance (|un) Axial Distance (pm)

Figure 3.13. Fluorescent intensity distribution in ImM KC1 electrolyte when Eext=10 V/cm and EC0„,«-3.33V/cm (a), -6.66V/cm (b), -lOV/cm (c), and -13.33V/cm (d). The time interval between Econt and Eext is 0. 50

Figure 3.14 depicts the sequential images of the enriched particles under the condition of Figure 3.13c, showing the movement of the enriched particles as a front toward the anodic reservoir. Similar results are obtained for other control electric fields. Figure 3.15 depicts the flow field and streamlines when Eext=10 V/cm and

ECOnt= -6.66V/cm (a); -lOV/cm (b); and -13.33V/cm (c). In order to capture the essentials of the process, we neglect the polarization on the control electrodes, and assume the zeta potential of the control gold electrodes is zero. Comparing Figure

3.15 to Figure3.12a without any control, the polarity of the induced charge on the floating electrode is reversed when the magnitude of the opposite ECOnt is higher than that of Eext, as shown in Figure 3.15b and Figure3.15c. For ECOnt= -lOV/cm and

-13.33V/cm, the overall electric field in the region of the floating electrode is dominated by Econt, directed from the left CE toward the right CE, leading to the left side of the floating electrode closed to CEL being negatively charged while the other side closed to CER being positively charged. Due to this reversal of both the induced charge and the electric field, the direction of the resulting ICEO flow is the same as that for the case of |Eext|>|ECOnt|- Due to the absence of charge along the control electrodes (zeta potential is zero), the flow in the region of the two control electrodes is driven by the induced pressure gradient. In the upstream region between the anodic reservoir and CER, the flow is driven by both electroosmosis and the induced adverse pressure gradient. It is the same in the downstream region between the cathodic reservoir and CEL. In the floating electrode region, the flow is the net result of the

ICEO and the induced pressure-driven flow. Compared to the case without local control (Figure 3.12a), clockwise vortices are now generated in the right side of the floating electrode closed to CER. As the control electric field increases, the strength and area of the clockwise vortices increase. Under the same conditions, particles are 51 not trapped by the control electrodes in the absence of the floating electrode.

Therefore, the mechanism of the particle trapping/enrichment is due to the ICEO flow in the right side of the floating electrode closed to the right control electrode, CER, which is opposite to the upstream pressure-driven flow in the region of the right control electrode. Particles will be trapped by the ICEO flow when the opposite

ICEO flow is stronger than the upstream pressure-driven flow.

-15— ~1 («) Tjti»«i ••!• AftiitrtlMtfi (*) «i **hi W

W if)

(g)

Figure 3.14. Sequential images of the enriched particles in the upstream of the right control electrode after 10 s (a), 20 s (b), 30 s (c), 40 s (d), 50 s (e), 60 s (f), and 70 s = = (g) under Eext 10 V/cm and Eco„t -10V/cm. The left side of the dashed line represents the right control electrode.

(a) 0 -^JOL-^-JP © Q Q- Q w P ~~ a.. a t a s. e t a g e .j^ v

5 e •<^.\Wm4^^SS4^M& ;J^zi*i:i

(b) e a a a e , ..a a a . e a a "a a—a , a—a—a_j3—a—e , e e]

(c) 9 A P>AftflfiA«<=»«|_flfifiAO(=lRO a a <=s

9 e *« '^x&i^T^&yMyykM^^mAM^f^ s 1 a e Figure 3.15. Flow field and streamlines in the region of the control and floating = electrodes when Eext 10 V/cm, EC0„,=-6.66V/cm (a), -lOV/cm (b), and -13.33V/cm (c). 52

3.2.4.2 On-demand Control of the Position of Enriched Particles

By dynamically modulating the control electric field, the enriched particles can also be kept stationary at a prescribed position inside the channel where other substance which needs to interact with the target samples or sensor is positioned. Figure 3.16 depicts the fluorescent intensity (IF) of 500 nm fluorescent particles in 1 mM KC1 when Eext= 30 V/cm and Econt~31.67 V/cm after 1 min (a), 3 min (b), 5 min (c), and 8 min (d). The direction of the control electric field is the same as that of the external electric field, and Econt is actuated after Eext has been turned on for 15 seconds. Figure

3.17 shows the sequential images of the enriched particles under the condition of

Fig.3.16. The front of the enriched particles can be kept stationary for a longer time.

Figure 3.18 depicts the flow field and streamlines in the region of the floating and control electrodes. Under this condition, the ICEO flow in the region of the floating electrode dominates over the EOF in the upstream and downstream of the floating electrode. The clockwise (counterclockwise) vortices in the anodic (cathodic) region of the floating electrode almost occupy the entire cross section of the microchannel, and act like a valve to trap particles in the upstream of the floating electrode. 53

IF 20 -

0 250 500 750 1000 1250 1500 1750 0 250 500 750 1000 1250 1500 1750

500 750 1000 1250 1500 1750 500 750 1000 1250 1500 1750 Axial Distance (|im) Axial Distance (|im)

= Figure 3.16. The fluorescent intensity in 1 mM KC1 when Eext 30 V/cm and ECOnt~31.67 V/cm after 1 min (a), 3 min (b), 5 min (c), and 8 min (d). Both Eext and Econt are directed from the anodic reservoir toward the cathodic reservoir, and the time interval between Econt and Eext is 15 seconds.

Figure 3.17. The sequential images of the enriched particles after 20 s (a), 40 s (b), 1 min (c), 2 min (d), 3 min (e), 4 min (f), 5 min (g), 6 min (h), 7 min (i), and 8 min (j). The left side of the dashed line represents the right control electrode. The condition is the same as that in Figure 3.16. 54

Fig.3.18. Flow field and streamlines in the region of the control and floating electrodes when Eext=10 V/cm and Econt=31.67V/cm.

The positioning of the front of the enriched particles can be controlled by the

magnitude of the control electric field as well as the time interval between Eext and

ECOnt- For example, Figure 3.19 depicts the spatial distribution of the normalized

fluorescent intensity (IF) of 500 nm fluorescent particles after 1 min (a), 3 min (b), 5

min (c), and 8 min (d). Figure 3.20 depicts the sequential images of the enriched

particles under the same condition in Figure 3.19. The time interval between Eext and

ECont is 5 seconds and all other conditions are the same as the case of Figure 3.17.

Comparing Figure 3.19 to Figure 3.16 and Figure 3.20 to Figure 3.17, it is clear that

the enriched particles can be kept closer to the right control electrode by reducing the time interval between Eext and Econt. Thus, a versatile control of the location of the

enriched particles can be achieved by dynamically controlling the magnitude and

polarity of the voltage applied to the control electrodes. 55

40 IF 40 20 20

250 500 750 1000 1250 1500 1750 250 500 750 1000 1250 1500 1750

60

40

20

250 500 750 1000 1250 1500 1750 250 500 750 1000 1250 1500 1750 Axial Distance (fim) Axial Distance (|im)

Figure 3.19. The fluorescent intensity in 1 mM KC1 when Eext= 30 V/cm and Econt^l^? V/cm after 1 min (a), 3 min (b), 5 min (c), and 8 min (d). Both Eextand Econt are directed from the anodic reservoir toward the cathodic reservoir, and the time interval between Econt and Eext is 5 seconds.

Figure 3.20. The sequential images of the concentrated particles after 1 min (a), 2 min (b), 3 min (c), 4 min (d), 5 min (e), 6 min (f), 7 min (g), and 8 min (h). The condition is the same as that in Figure 3.19. 56

3.3 Particle Deposition onto the Floating Electrode under AC Electric Field

3.3.1 Introduction

In the previous sections, several paticle manipulations via inserting floating electrodes inside the microfluidic channel under DC electric field have been discussed discussed.

In addition to several particle manipulations, electrokinetic phenomena including electroosmosis, electrophoresis, and dielectrophoresis play an important role in facilitating both particle deposition and particle alignment in micro- and nano-fluidic lab-on-a-chip devices [126-158].

Electrophoretic deposition is essentially a two-step process. In the first step, particles suspended in a liquid are forced to move toward an electrode by applying an electric field to the suspension. In the second step, the particles collect at one of the electrode and form a coherent deposit on it [128]. To date, however, studies on electrokinetic deposition have all been limited to microfluidic devices with dielectric walls possessing a nearly uniform surface charge or zeta potential, and particles are deposited onto the driving electrodes

The objective of this section is to propose and demonstrate a novel strategy for particle deposition onto the floating electrode under AC electric field. Although electrokinetic particle manipulations such as trapping, reversal of particle motion, enrichment/depletion, separation, particle focusing by floating electrodes (metal strips), and concentration enrichment and its position control inside the microfluidic devices by locally controlled floating electrode attached to the channel bottom wall of a straight microfluidic channel under DC electric field have been experimentally demonstrated in the previous sections, particle deposition onto the floating electrode 57 under DC electric field was not observed. Thus floating electrode was positioned between two micron-sized control electrodes. An AC electric field was imposed to control electrodes CEL and CER, by applying a potential difference across the two micron-sized control electrodes.

3.3.2 Experiments

The PDMS/glass closed cavity microfluidic device with/without floating electrodes was fabricated using the standard soft-lithographic technique, and its detailed fabrication procedure for electrode patterning is given in chapter 2. The floating and control gold electrodes are fabricated on a clean glass slide. The lengths of the floating and control electrodes are, respectively, 500 um and 300 (xm. The dielectric gap between the floating electrode and each control electrode is 50 ^m. The floating electrode is positioned in the central region of the cavity's bottom wall. Finally, the

PDMS slab of 6 mm in diameter circular closed 2.5 mm deep cavity and the glass slide with the patterned electrodes were treated by 30 second oxygen plasma (Femto

Science, Korea). Immediately following the oxygen plasma treatment, the two treated surfaces were bonded to form the microfluidic device with floating electrode and control electrodes in between circular closed cavity. Figure 3.21 schematically shows the top view of a microfluidic device.

For particle deposition, again spherical polystyrene fluorescence particles

(Invitrogen, Eugene, OR) of 500 nm in diameter were used in the experiments. The particles were suspended in lmM KC1 solution. In each experiment the closed cavity was filled with 50 \xl volume of particle and KC1 mixture. The AC voltage drop across the control electrodes was supplied by a Function Generator (Stanford 58

Instruments). The particle deposition onto the floating electrode was visualized and recorded using an inverted optical microscope (Nikon Eclipse Ti, Nikon Instruments,

Japan) equipped with a CCD camera (Pixelink, P1-E421CU). The SEM images were taken by using Hitachi S4200 cold field emission SEM microscope (Hitachi, Japan).

y A y

)

Figure 3.21. Schematic top view experimental setup of one floating electrode and two control electrodes patterned on the glass slide with circular PDMS cavity on top of electrodes. LCE= 300 |wm, LFE= 500 urn, R=3mm, and a= 50 urn.

3.3.3 Results and Discussion

3.3.3.1 Without Floating Electrode

Firstly the particle deposition experiments were conducted for different frequencies in the closed cavity without floating electrode on the glass wall. The dielectric PDMS closed cavity walls as well as the bottom glass wall is negatively charged. The 500 nm fluorescence particles are also negatively charged. The gap between the driven electrodes is 600 urn, and the electrodes are 300 urn wide. At lower frequencies particles are trapped between electrodes, then at higher frequencies particles are repelled outside the electrodes. Figure 3.22 depicts the particle motion at different 59 frequencies. As seen from Figure 3.22, initially particles are uniformly distributed, then at low frequencies particles are trapped between electrodes, at higher frequencies particles are not trapped between the electrodes anymore, instead repelled outside the electrodes. Since we focused on the particle deposition onto the floating electrode, the detailed results of particle motion, trapping without floating electrodes are not shown here.

Figure 3.22. Particle motion between driving electrodes when no floating electrode is used at 100Hz (a), 100kHz (b), 1MHz (c), and 10MHz (d).

After each experiment the electrode surfaces have been washed with DI water for 1 minute and dried with nitrogen to remove the non-deposited particles. After washing the closed cavity, no particle deposition has been onserved onthe dielectric glass surface.

The flow pattern for AC-EOF, electrothermal flow, and positive-negative DEP is shown in Figure 3.23. At lower frequencies AC-EOF is dominant, and at higher frequencies AC-EOF is not dominant anymore, instead electrothermal flow starts to be dominant. The Clasius-Mossotti factor k(w) is calculated as:

G*—G* 60 where m defines the medium, p defines the particle, and G* is defined as G* =G + —

. Here G = 78*8.85e"12 , and 2.55*8.85e"12 defines the permittivity of medium and particle, a = 0.0026 and 0.01 defines the conductivity of medium and particle, and w is the angular frequency of the applied electric field. The real part of the Clasius-

Mossotti factor shows that for 500 nm size particles, DEP force changes from positive to DEP at a frequency of 1.4 MHz. Figure 3.23 shows the positive and negative DEP regions and corresponding flow patterns. When positive DEP occurs the force is toward the high electric field, and the particles collect at the electrode edges. The converse of this is negative DEP, the force is in the direction of decreasing field strength, and the particles are repelled from the electrode edge. As the imposed frequency increases, the particles experiences from positive DEP to negative DEP, but in any case particles are not deposited to dielectric glass surface when no floating electrode is used between control electrodes.

0.5 , Jzfamw%Xmti'i& ?VM

fc mi

-0.5 10" 10' 10" 10 frequency (Hz) Figure 3.23. Real part of the Clasius-Mossotti factor of 500 nm dielectric particles. 61

3.3.3.2 With Floating Electrode

Under the externally imposed AC electric field from two micron-sized electrodes located on both sides of the floating electrode, half of the floating electrode is negatively polarized, and the other half is positively polarized with a zero net induced charge over the floating electrode. Due to the AC electric field, positively-negatively induced surface charge continuously switches on the floating electrode. The induced charges on the floating electrodes induce spatially non-uniform distribution of the zeta potential (surface charge). Subsequently, deposition of the 500 nm fluorescent particles onto the floating electrode in a microfluidic device has been experimentally investigated at ImM KC1 solutions under various frequencies and electric fields.

Figure 3.24 shows the ICEO flow, AC EOF, electrothermal flow, and DEP directions on the electrodes. A significant feature of ICEO flow is its dependence on the square of the electric field amplitude. This has important consequences for AC fields: if the direction of the electric field in the above picture is reversed, so are the signs of the induced surface charge and screening cloud [23]. Therefore, induced-charge electro- osmotic flows insist even in an AC applied fields, as long as the frequency is sufficiently low that the induced-charge screening clouds have time to form. Thus at lower frequencies ICEO flow becomes more dominant compared to higher frequencies. Thus there is a critical frequency exist, in which below the critical frequency ICEO flow is more domimnant. Critical frequency is calculated as:

T = , t = - D ' J T where T is the time scale for induced charge electroosmosis, a=500 nm is the

9 2 characteristic length, XD = 10 nm is double layer thickness, D = 2*10" m /sec is the 62 characteristic ionic diffusivity, and / is the critical frequency[23]. When critical frequency is calculated, it is found as 400kHz for that microfluidic system, thus below

400kHz ICEO flow will be dominant. It was already mentioned that at lower frequencies AC-EOF is dominant, and at higher frequencies AC-EOF is not dominant anymore, instead electrothermal flow starts to be dominant [154].

Electrothermal Flow Electrothermal Plow a

Figure 3.24. Addition of ICEO flow pattern at low frequencies (a), high frequencies

(b).

Next, the floating electrode affects on the particle deposition onto its surface under AC electric field was studied. In the absence of floating electrode particles are not deposited to dielectric glass surface under AC electric field. Particle deposition experiments were performed for different frequencies to see the effect of positive 63

DEP, negative DEP, and ICEO flow on particle deposition. Figure 3.25 depicts the snapshot images of 500 nm fluorescent particles deposited onto the floating electrode in ImM KC1 under 2 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min

(c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f) after washing the floating electrodes and dielectric walls between electrodes. As seen from

Figure 3.25, as the time passes, more particles are deposited onto the floating electrode and distribution becomes more uniform. It is understood from Figure 3.25 that no particles are deposited onto the dielectric glass surface. To characterize the particle deposition onto the floating electrode, cross-sectional averaged fluorescent intensity (IF) distribution was drawn. Figure 3.26 depicts the fluorescent intensity

(IF) of 500 nm fluorescentparticle s deposited onto the floating electrode in ImM KC1 under 2 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp

1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f). As seen from Figure

3.26, as time increases, more particles are deposited more uniformly onto the floating electrode. Figure 3.26 shows that, particles are more uniformly deposited everywhere except in the corners. At 1MHz frequency positive DEP occurs, positive DEP pushes the particles towards the surface of the electrodes, at the same time ICEO flow is also effective on the floating electrode, thus particles are pushed away from the electrode corners. Another reason is at, that as seen from Figure 3.23, 500 nm fluorescent particles switch from positive DEP to negative DEP around 1.4 MHz. Thus at 1 MHz frequency, positive DEP is not that strong to trap the particles at the corner of the electrodes. Since DEP force reverses around that frequency range, and starts to push the particles away from the electrodes, the particles are not deposited uniformly near the floatingelectrod e corners. 64

Figure 3.25. Snapshot images of deposited particles onto the floating electrode after washing the electrodes under 2 Vpp IMHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp IMHz AC electric field after 5 min (d), 10 min (e), 20 min (f).

After obtaining more uniform deposition with respect to longer time, different voltages and frequencies were used to show the effect of frequency on particle deposition onto the floating electrode. Figure 3.27 depicts the IF of deposited 500 nm particles onto the floating electrode after 20 min, under 2 Vpp 100Hz (a), 100kHz (b),

IMHz (c), 10MHz (d); and 5Vpp 100Hz (e), 100kHz (f), IMHz (g), and 10MHz (h). 65

100 200 300 400 500 100 200 300 400 500

100 200 300 400 500 100 200 300 400 500

100 200 300 400 500 100 200 300 400 500 Length orFE(nm) Length of l'K(^m) Figure 3.26. Fluorescent intensity distribution of deposited particles onto the floating electrode under 2 Vpp 1MHz AC electric field after 5 min (a), 10 min (b), 20 min (c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f).

From Figure 3.27, it is understood that particles are generally repelled from the electrode edges. Figure 3.27a, 3.27b, 3.27e, 3.27f show that the particles are not deposited more near the electrode edges at lower frequencies. Critical frequency shows that below 400kHz ICEO flow will be dominant, also AC-EOF is dominant at low frequencies. So ICEO flow pushes the particles away from the floating electrode edges, at the same time dominant AC-EOF direction is also away from the electrode edges. These flows push the particles away from electrode edges, and at the same 66 time positive DEP pushes the particles towards the electrode surface. Thus at lower frequencies all flows push the particles away from the electrodes. This means that although positive DEP flow field is towards the electrode corners (Figure 3.23 and

Figure 3.24), ICEO flow pattern is always towards the center of the electrode even though the direction of the electric field is reversed (Figure 3.24) and since ICEO flow is dominant below the critical frequency, flow field will still be towards the electrode center. Figure 3.27c, 3.27d, 3.27g, 3.27h depicts that, similar to lower frequencies, particles are not deposited to the corners of the floating electrode at higher frequencies. At 1 MHz frequency positive DEP occurs. The real part of the

Clasius-Mossotti factor shows that for 500 nm size particles, DEP force changes from positive to DEP at a frequency of 1.4 MHz, thus the corresponding flow direction changes (Figure 3.23 and Figure 3.24). Positive DEP pushes the particles towards the surface of the electrodes, at the same time ICEO flow is effective on the floating electrode, and also electrothermal flow becomes dominant after 1 MHz frequency.

ICEO flow pushes the particles toward the center of electrodes, but instead electrothermal flow tries to push the particles away from the electrode edges, at the same time positive DEP tries to push the particles toward the surface of the electrode.

Again particles are not deposited to floating electrode edges uniformly. At 10 MHz frequency, particles start to experience negative DEP. Negative DEP pushes the particles away from electrode edges. But at the same time electrothermal flow becomes more dominant at higher frequencies, again particles are not deposited onto the electrode edges more uniformly. 67

50

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0 100 200 300 400 500 100 200 300 400 500 Length of FE((im) Length of FE(um) Figure 3.27. Fluorescent intensity distribution of the deposited particles onto the floating electrode after 20 min, under 2 Vpp 100Hz (a), 100kHz (b), IMHz (c), 10MHz (d); and 5Vpp 100Hz (e), 100kHz (f), IMHz (g), and 10MHz (h). 68

(d)

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Figure 3.28. SEM images of the deposited particles onto the floating electrode under 0 5 Vpp IMHz AC electric field after 5 min (a), 10 mm (b), 20 mm (c); and 5Vpp IMHz AC electric field after 5 min (d), 10 min (e), 20 min (f). .,*•-,»-,*_,.••

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Although particle deposition on to the floating electrode is characterized via

fluorescent images and IF distributions, to clearly show the particle deposition and

particle packaging and to understand the effect of frequency and voltage on

deposition, SEM images of samples were taken. For SEM image analysis, an

additional 0.5Vpp with different frequencies was imposed to see particle clustering at

at different voltages. Since IF distribution will be intensity based, it is impossible to

characterize the particle deposition and clustering for voltage difference, but instead

voltage difference on particle deposition can be more clearly visualized via SEM

imaging. Figure 3.28 depicts the SEM images of the deposited particles onto the

floating electrode under 0.5 Vpp 1 MHz AC electric field after 5 min (a), 10 min (b),

20 min (c); and 5Vpp 1MHz AC electric field after 5 min (d), 10 min (e), 20 min (f).

As seen from Figures 3.28a, 3.28b, 3.28c, at lower voltages, more particles are

deposited and clustered to each other when compared to higher voltage in Figures

3.28d, 3.28e, 3.28f. Figure 3.28 depicts that, at lower voltages, particles become more

clustered to each other and forms many layers, instead at higher voltages even after

longer times particles are still on a single layer and not clustered more, instead spread

around on the floating electrode. Figure 3.29 depicts the SEM images of the deposited particles onto the floating electrode after 20 min. under 2 Vpp 100Hz (a),

100kHz (b), 1MHz (c), 10MHz (d); and 5Vpp 100Hz (e), 100kHz (f), 1MHz (g), and

10MHz (h). As understood from Figures 3.29a, 3.29b, 3.29e, 3.29f at lower frequencies, more particles are deposited onto the floating electrode and also clustered to each other. So at lower voltages even at higher frequencies (Figures 3.28a, 3.28b,

3.28c) and at higher voltages even at lower frequencies (Figures 3.29a, 3.29b, 3.29e,

3.29f) more particles are deposited and particles are clustered more to each other.

ICEO flow is more dominant below critical frequency; that effect can be seen on 71 particle deposition. More particles are deposited at lower frequencies because induced charge zeta potential also becomes higher below critical frequency. In standard electro-osmosis, the zeta potential is typically taken to be constant. In contrast, ICEO flows (around conducting or polarizable surfaces) involve a charge cloud that is induced by the applied field itself, giving a non-uniform induced zeta potential, thus the floating electrode surface has higher induced charge at lower frequencies and particle has always fixed charge. Due to that surface charge difference, more particles are deposited onto the floating electrode. 72

CHAPTER IV

ELECTRODIFFUSIOPHORETIC MOTION OF A CHARGED SPHERICAL

PARTICLE IN A NANOPORE

4.1 Diffusiophoretic Motion of a Charged Spherical Particle in a Nanopore

4.1.1 Introduction

If a charged particle is positioned in a nanopore connecting two fluid reservoirs

(Figure 4.1) containing a dilute electrolyte solution with different concentrations, counterions are accumulated adjacent to the particle surface due to the electrostatic interactions between the ionic species present in the electrolyte solution and the surface charge on the nanoparticle. This counterion accumulation forms an electrical double layer (EDL) of thickness typically of the order of 10 nm. The basic idea and literature review for diffusiophoresis is given in Chapter 1. Briefly, due to the presence of the imposed concentration gradient, electrolyte ions diffuse in the nanopore. When the diffusive mobilities of anions and cations are unequal, a net diffusive flux of charge happens. As a result, an electric field, E

The generated electric field, Ediffusivity, through its action on the counterions accumulated in the EDL, creates a body force that, in turn, induces an electroosmotic flow. In addition, a secondary electric field is induced by the induced dipole moment, a consequence of the double layer polarization (DLP). Note that the DLP considered here is the consequence of the imposed concentration gradient without accounting for the polarization or relaxation of the EDL by the induced electric field, particle motion, and fluid convection. 73

c 1-

b D Nanopore E J ---<£i! a

I

^esoftfwr R£SQ-\5*r u

Figure 4.1. Schematic of a nanopore of length L and radius a connecting two identical reservoirs on either side. A concentration gradient of electrolyte solution is applied across the two reservoirs. A charged spherical particle of radius ap bearing uniform surface charge density, op, is positioned at the center of the nanopore.

Because of the imposed concentration gradient, the concentrations of both counterions and co-ions on the high-concentration side of the particle are higher than those on the low-concentration side, thus the thickness of the EDL on the high- concentration side is thinner than that on the low-concentration side. As a consequence, the center of charge inside the EDL, dominated by the counterions, shifts away from the particle's center. Together with the charge of the particle and the charge of the EDL, a dipole moment is induced, resulting in an electric field which reaches beyond the limits of the EDL arising at its positive pole and terminating at the negative pole. The concentration polarization inside the EDL by the imposed concentration gradient is called the Type I DLP, and its resulting electric field by the induced dipole moment is named ELDLP, the direction of which is opposite to (the same as) that of the applied concentration gradient when the particle is negatively

(positively) charged. Near the outer boundary of the antisymmetric EDL, co-ions dominate. Co-ions concentration on the high-concentration side is higher than that on 74 the low concentration side such concentration polarization is called the Type II DLP.

Similar to the induced dipole moment and generated electric field (EH-DLP) inside the

EDL, a dipole moment and its accompanied electric field, ED-DLP, are induced by the

Type II DLP. The direction of the ED-DLP, is opposite to EI.DLP- Therefore, depending on the operating conditions, the interactions between the net charge in the

EDL and the induced overall electric fields, established by the difference of ionic diffusivities (Ediffugvity) and the DLP (EI.DLP and ED-DLP), generate electroosmotic flow. In addition, an osmotic pressure gradient is generated within the EDL due to the chemiosmotic effect; it induces a fluid flow from higher to lower electrolyte concentration regions.

4.1.2 Mathematical Model

The mathematical model and nondimensionalization process was given in Chapter 2, thus it is not explained here again.

4.1.3 Results and Discussion

Fluid flow affects the ionic mass transport through the convection, and the concentration and electric fields affect the electrostatic forces acting on the net charge in the electrolyte solution and the charged particle. The fluid flow and the particle motion are coupled through the velocity boundary condition along the particle's surface. A direct numerical simulation was used to understand the diffusiophoretic motion and the associated fluid dynamics with realistic choice of control parameters.

The commercial package COMSOL version 3.5a (www.comsol.com), installed in a high-speed workstation with 96 GB RAM, was chosen to integrate the system with a finite-element method. Quadratic triangular elements with variable 75 sizes were used to accommodate finer resolutions near the particle surface where EDL is present. Solution convergence is guaranteed through mesh-refinement tests on conservation laws. The mathematical model and its implementation with COMSOL were validated by comparing its results of electroosmotic, diffusioosmotic, and electrophoretic flows with the corresponding approximate analytical solution and experimental results obtained from the literature [82, 32-35].

In this section, numerical results are presented of the diffusiophoretic motion of a charged spherical nanoparticle in a nanopore under various conditions. The focus is on the effects of the ratio of the particle size to the EDL thickness, scap, the ratio of pore size to the particle size, a/ap, and the dimensionless surface charge density of the particle, ap. A representative case of the numerical simulation corresponds to a nanopore with length L = 0.5 //m connecting two reservoirs of LR = 0.15 /um and b =

0.15 fiva. and particle radius of ap = 5 run. The temperature of the electrolyte solution in the reservoirs and the nanopore is 300 K. While an intensive parametric study in dimensionless terms is performed, two different salts (NaCl and KC1) are considered to clearly illustrate the effect of the induced electrophoresis by the generated electric field, Ediffusivity, stemming from the difference in the diffusivities of the anions and cations. The diffusion coefficients of the ions K+, Na+, and CI' are, respectively, 1.95

X 10"9, 1.33 X 10"9, and 2.03 X 10"9 m2/s. The concentration ratio is fixed at a =

CR/CL = 1000 in the current study.

In an unbounded medium, the contribution of the induced electrophoresis by

Ediffusivity is usually higher than that of the chemiphoresis, which is higher than that of the electrophoresis generated by the DLP-induced electric field, if the ionic diffusivities are unequal. Since the diffusive mobilities of anions and cations in KC1 76

are of the same order of magnitude, the induced electric field arising from the

difference of ionic diffusivities, Ediffusivity* is very small, and the chemiphoresis due to

the induced osmotic pressure gradient is dominant. Consequently, the chemiphoresis

propels the particle toward higher concentrations of KCl, regardless of the sign of

charge on the particle. Since the chloride ions have a higher diffusion coefficient than

sodium ions, an electric field arising from the difference in ionic diffusivities is

induced, and the generated electric field, Ediffusivity, is directed from higher to lower

NaCl concentration. Due to the induced electrophoresis by the generated Ediffusivity, a

negatively charged particle in an infinite medium typically migrates toward higher

salt concentration in NaCl. It should be noted that these trends can change in a

confined electrolyte medium. As will be shown in the present study, the

diffusiophoresis can be mainly controlled by the induced electrophoresis arising from

the DLP-induced electric field due to the imposed concentration gradient and the

presence of the nanopore wall.

4.1.3.1 Effect of KHP, the Ratio of Particle Size to EDL Thickness

Figures 4.2 and 4.3 show, respectively, the dimensionless particle translocation

1 velocity, scaled by UQ = ^Ti/ifMpF ), as a function of /cap, for KCl and NaCl when

a/ap = 2 and ap ~ -27.3 (solid line with open triangles), -13.7 (dashed line with open

squares), 13.7 (dashed line with solid squares), and 27.3 (solid line with solid

triangles). For up* > 0 (wp* < 0), the particle moves toward higher (lower) salt

concentration. When /cap is relatively small (thick EDL), the diffusiophoretic

velocity wp* is negative. The particle thus moves toward lower salt concentration regardless of the sense of the particle charge and of the type of salt, suggesting that 77 the chemiphoretic effect due to the induced osmotic pressure gradient, which always propels the particle toward higher salt concentration, is very small compared to the induced electrophoretic effect. The magnitude of up* increases with /cap until it reaches a maximum and then decreases. For sufficiently high /cap, the diffusiophoretic velocity can become positive, and the particle can move toward higher salt concentration. Since the diffusiophoresis mainly stems from the electrophoretic effect generated by the induced electric fields arising from both the difference in the ionic diffusivities and the DLP, the magnitude of the diffusiophoretic velocity depends on the type of salt, surface charge density of the particle, /cap, and the boundary effects.

Figure 4.2. Dimensionless particle velocity as a function of kap for KCl solution with cfp« -27.3 (solid line with open triangles), -13.7 (dashed line with open squares),

13.7 (dashed line with solid squares), and 27.3 (solid line with solid triangles). a/ap=2, and a= 1000. 78

For salt, KC1, (Figure 4.2), the electrophoretic effect by Ediffusivity is negligible because the diffusivities of cations (K+) and anions (CI) are almost identical.

Consequently, the effect of the particle surface charge density on the particle velocity is not significant. The resulting negative diffusiophoretic velocity suggests that the chemiphoretic effect is very small compared to the electrophoretic effect induced by

EI.DLP and EH-DLP- Figure 4.2 shows that both negatively and positively charged particles typically move toward lower salt concentration with up* < 0, suggesting that the electrophoretic effect by the electric field from the Type II DLP, EH-DLP, is dominant under the considered conditions. When /cap is relatively small (i.e., thick

EDL), the thickness of the EDL surrounding the nanoparticle is larger than the distance between the nanoparticle surface and the nanopore wall. The EDL thus touches the nanopore wall and is compressed by the impervious nanopore wall.

Under this condition, the effect of the Type I DLP is induced by both the imposed concentration gradient and the EDL compression by the boundary, and the latter dominates when tcap is relatively small. The EDL compression enhances the effect arising from the Type I DLP and increases the driving force propelling the particle toward higher salt concentration [111, 114, 117, 121]. Therefore, for a relatively small value of /cap under which the EDL is significantly compressed by the nanopore wall, the magnitude of the particle velocity increases with /cap due to the decrease in the opposite driving force arising from the Type I DLP by EDL compression. Once

/cap exceeds a critical value, the double layer compression by the nanopore wall becomes insignificant, and the Type I DLP arising from the imposed concentration gradient then dominates over that due to the double layer compression. For a relatively thin EDL (i.e., /cap is large), usually, the electric field generated by the 79

Type I DLP, EI_DLP, becomes stronger, and the generated electric field by the Type II

DLP, EII-DLP, becomes weaker as /cap increases if the double layer compression by the nanopore wall is insignificant. The electric field arising from the Type II DLP dominates over that from the Type I DLP if the surface charge or surface potential of the particle is relatively high [121]. Since the direction of the accompanying electrophoretic motion generated by the Type I DLP is opposite to that generated by the Type II DLP, the net electrophoretic motion generated by the two competing opposite electrophoretic effects obtains a local maximum and then decreases as /cap further increases.

Figure 4.3. Dimensionless particle velocity as a function of kap for NaCl solution with CT « -27.3 (solid line with open triangles), -13.7 (dashed line with open squares),

13.7 (dashed line with solid squares), and 27.3 (solid line with solid triangles). a/ap=2, and a= 1000. 80

For salt, NaCl, (Figure 4.3), a negative axial electric field, Ediffusivity, directed toward lower salt concentration is generated arising from the difference of the ionic diffusivities, leading to positively (negatively) charged particles electrophoretically moving toward lower (higher) salt concentration due to the induced electrophoretic effect by Ediffusivity. In addition, the particle will move toward higher (lower) salt concentration due to the electrophoretic effect arising from the generated electric fields by the Type I (II) DLP. The net diffusiophoretic velocity is mainly determined by the three competing driving forces. Figure 4.3 shows that both negatively and positively charged particles typically move toward lower salt concentration, suggesting that the electrophoretic effect by the electric field from the Type II DLP,

EH-DLP, is dominant over the electrophoretic effects by Ediffusivity and EI-DLP- The same as the KC1 salt, the increase in the particle velocity with /cap for a relatively small value of /eap is due to the decrease in the degree of EDL compression. As /cap increases further, the effect of the EDL compression on the Type I DLP is not significant, while the Type I DLP from the imposed concentration gradient dominates.

The effect of the Type I (II) DLP then increases (decreases) with /c ap, leads to the decrease in the magnitude of the particle velocity. The effect of the particle surface charge density on the diffusiophoretic velocity is significant due to the electrophoretic effect generated by the induced electric field Ediffusivity- Due to the electrophoretic effect by Ediffusivity, the magnitude of up* of the positively charged particle is higher than that of the negatively charged particle since the generated electrophoretic motion of the positively charged particle by Ediffusivity is in the same direction as that induced by the Type II DLP. For a positively charged particle, the higher the particle's surface charge density, the higher the driving force due to the electrophoretic effect by 81

Ediffusivity, which moves the positively charged particle toward lower salt concentration. Meanwhile, more counterions are attracted within the EDL as the electrostatic interaction between the positively charged particle and counterions gets stronger as the surface charge density increases, resulting in an increase of the driving force for particle moving toward higher salt concentration due to the Type I DLP. As the surface charge density increases, more co-ions are depleted from the EDL and accumulate at the outer boundary of the EDL, leading to an increase in the driving force arising from the Type II DLP. Therefore, the induced electrophoretic motions by Ediffusivity, EI.DLP, and ED-DLP are enhanced with the increase in the surface charge density of the positively charged particle, resulting in a higher diffusiophoretic velocity since the enhancements of the electrophoretic effect by Ediffusivity and EU-DLP prevail over that by EI.DLP- For a negatively charged particle, similarly, the magnitude of the diffusiophoretic velocity increases with the increase in the magnitude of the particle surface charge density. The effect of the particle surface charge density on the net diffusiophoretic motion will be elaborated in detail in next section.

4.1.3.2 Effect of ap, the Particle Surface Charge Density

Figures 4.4 and 4.5 depict, respectively, the diffusiophoretic velocity as a function of the particle surface charge density for KC1 and NaCl when a/ap = 2 and /cap = 0.1

(solid line with squares), 1 (dashed line with triangles), and 3 (dash-dotted line with circles). These lines demonstrate that the diffusiophoretic motion highly depends on the particle surface charge density and the type of salt. A neutral particle (i.e., ap = 0) does not move under an externally imposed concentration gradient due to the lack of

EDL. Generally, as the magnitude of the particle surface charge density increases, 82 more counterions are attracted within EDL, and more co-ions are repelled away from the charged particle to be accumulated at the outer boundary of the EDL, resulting in dominance of the Types I and II DLP. The effect arising from the Type II DLP dominates over that from the Type I DLP if the surface charge density of the particle is relatively high. When the diffusivities of the anions and cations are unequal, the electrophoretic effect by EdiiTusivity also increases with the magnitude of the particle surface charge density.

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-0 025

-30 -20 -10 0 _ 10 20 30 a,

Figure 4.4. Dimensionless particle velocity as a function of o^for KCl solution with kap=0.l (solid line with squares), 1 (dashed line with triangles), and 3 (dash-dotted line with circles). a/ap=2, and a=1000.

For salt, KCl, (Figure 4.4), the electrophoretic effect by EdiWiisivity is very small because the diffusion coefficients of both anions and cations are almost identical, which leads to almost symmetric velocity profile about the particle surface charge 83 density. The velocity of a positively charged particle is slightly higher than that of a negatively charged particle, which arises from the small electrophoretic effect by

Edifrusivity since the diffusion coefficient of the anions (Da = 2.03 X 10"9 m2/s) is slightly higher than that of cations (Z)R+ =1.95 X 10"9 m2/s). For a fixed value of

/cap, the magnitude of the diffusiophoretic velocity increases with the particle surface charge density because the enhancement arising from the Type II DLP effect is more significant than that from the Type I DLP effect. Again, the negative diffusiophoretic velocity suggests that the chemiphoretic effect is insignificant, and the diffusiophoretic motion is mainly driven by the electrophoresis induced by the Type II

DLP-induced electric field, EH.DLP-

1 ,.-Q~ ! ! , o .-©'• —° 5L * ' ri n ii /^.^* Q—* '' -*^ MW \\ s \ n 1=1* CI / / \ \ ^TJ U / / 'P 4 \ \ / \ \.Q .

,t # A / \ \ y ^ A' »\ %• / ®s -0.01 .' \ X s* X A'

-0.02

1 i i i i

-0.03

-30 -20 -10 0 10 20 30 Figure 4.5. Dimensionless particle velocity as a function of apfor NaCl solution with kap=0A (solid line with squares), 1 (dashed line with triangles), and 3 (dash-dotted line with circles). a/ap=2, and

For salt, NaCl, (Figure 4.5), the magnitude of the diffusiophoretic velocity increases with the increase in the magnitude of the particle surface charge density,

|

For the case of /cap = 3, the magnitude of the negative diffusiophoretic velocity increases with the particle surface charge density when the particle is positively charged, and the negatively charged particle moves toward higher salt concentration when the magnitude of the surface charge density is relatively small because the electrophoretic effects by Ediffusiviiy and EI.DLP are opposite to that by ED-DLP- The particle motion is reversed, and its velocity increases as the particle surface charge density further increases due to the increase in the electrophoretic effect arising from the Type II DLP. The particle velocity is asymmetric about the particle surface charge density. Typically, the positively charged particle has a higher particle velocity than that of the negatively charged particle due to the electrophoretic effect by Ediffusivity- The velocity of a positively charged particle is enhanced by the electrophoretic effect arising from Ediffusivity because the direction of the driving force arising from the electrophoretic effect by Ediffusivity is the same as that from the Type

II DLP. On the contrary, the velocity of a negatively charged particle is reduced by the opposite driving force of the electrophoretic effect by Ediffusivity-

4.1.3.3 Effect of ala9, the Ratio of Pore Size to Particle Size

Figures 4.6 and 4.7 depict, respectively, the particle velocity as a function of the ratio of the nanopore size to the particle size, a/ap, for KC1 and NaCl when /cap = 0.1

(lines with squares), 1 (lines with triangles), and 3 (lines with circles). Diverse effects 85 of the nanopore wall are illustrated. The distance between the particle surface and the nanopore wall increases as the ratio a/ap increases. For a relatively small value of

KOP (e.g., /cap = 0.1), the EDL is compressed by the nanopore wall for a/ap ranging from 1.6 to 4.0. The difference in the diffusiophoretic velocities of positively (solid symbols) and negatively (open symbols) charged particles in KCl solution is very small due to the negligible electrophoretic effect by Edjflusivity Compared to the results of KCl solution, the difference in the velocities of positively and negatively charged particles in NaCl solution is larger due to the electrophoretic effect generated by EdjffiisJvUy.

o

-0.01

» o. 3

-0.02

-0.03 1.5 2 2.5 3 3.5 4 a/a P

Figure 4.6. Dimensionless particle velocity as a function of a/ap for KCl solution with kap=0A (lines with squares), 1 (lines with triangles), and 3 (lines with circles) when ap=-273 (solid lines with open symbols) and 27.3 (dashed lines with solid symbols). a=1000. 86

In KC1 solution (Figure 4.6), for a relatively small value of /cap (e.g., xap =

0.1, a thick EDL), the magnitude of the negative particle velocity increases with the distance between the particle and the nanopore wall, and the particle speed increases with a/ctp since the effect of the Type I DLP arising from the EDL compression decreases as alap increases. For Kap = 1, the particle velocity does not increase monotonously with the distance between the particle and the nanopore wall. A maximum exists in its magnitude. For a relatively large value of /cap (e.g., /cap = 3), the particle velocity is negative, and the particle moves toward lower salt concentration when the gap between the particle and the nanopore wall is narrow. As the gap increases, the particle velocity decreases, and the particle motion can change its direction to migrate toward higher salt concentration. The overall behavior of the particle velocity versus the ratio a/ap for NaCl (Figure 4.7) is similar to that of KC1 solution, and their difference arises from the electrophoretic effect induced by

J^diffusivity

The aforementioned phenomena can be explained from the competition between the hydrodynamic hindrance owing to the presence of the nanopore wall, electrophoretic effects by Ediffusivity, and the DLP-induced electric fields. Generally, as the distance between the particle and the nanopore wall increases, the hydrodynamic hindrance stemming from the stationary nanopore wall decreases, and compression of the EDL by the presence of the impervious nanopore wall also decreases. 87

0.01 T ' 1 1 1 r

0

-0.01

• Q. 3

-0 02

-0.03

-0.04

1.5 2 2.5 3 3.5 4 a/a p

Figure 4.7. Dimensionless particle velocity as a function of alap for NaCl solution with kap=0.\ (lines with squares), 1 (lines with triangles), and 3 (lines with circles) when a =-213 (solid lines with open symbols) and 27.3 (dashed lines with solid symbols).

For a large value of /cap (i.e., /cap = 3), the compression of the EDL by the nanopore wall is not significant since the relative distance between the particle surface and the nanopore wall is larger than the EDL thickness. As the gap between the particle and the nanopore wall increases, the counterion distribution within the EDL surrounding the particle becomes more concentric to the particle, and the effects arising from DLP reduce. Therefore, as the ratio alap increases, the driving forces arising from both Ei_DLp and EH.DLP decrease, and the electrophoretic effect by

Edifrusivity becomes more significant. For KC1 solution (lines with circles in Figure

4.6), due to the negligible electrophoretic effect by Edifrusivity, the magnitude of the particle velocity decreases as the ratio a/ap increases from 1.6 to 4.0 due to the 88

decrease in the driving force from the Type II DLP. For NaCl solution, as alap increases, motion of the negatively charged particle (solid line with open circles in

Figure 4.7) is reversed due to the decrease in the driving force from the Type II DLP, and the generated electrophoretic motion by Ediffusiviiy drives the negatively charged particle toward higher salt concentration. For the positively charged particle (dashed line with solid circles in Figure 4.7), the particle motion does not change direction because the driving forces from the Type II DLP and Ediffusivity both direct the positively charged particle toward lower salt concentration. The magnitude of the particle velocity slightly decreases as alap increases mainly due to the reduction of the driving force from the Type II DLP. The difference in the velocities of the negatively and positively charged particles increases as the ratio alap increases due to the increase in the contribution of the electrophoretic effect by Ediffusivity-

For /cap = 1, the thickness of the EDL is larger than the gap between the particle surface and the nanopore wall when the ratio alap is relatively small. The

EDL surrounding the particle thus touches the nanopore wall and is compressed due to the presence of the impervious nanopore wall. As the ratio alap decreases, the EDL compression becomes more significant, and the effect of the Type I DLP is enhanced

[111, 114, 117, 121], leading to the decrease in the particle velocity. For NaCl and

KC1 solutions, the magnitude of the particle velocity increases as the ratio alap increases, mainly due to the decrease of the Type I DLP effect arising from the EDL compression. As the gap between the particle surface and the nanopore wall increases further, the EDL surrounding the particle is detached from the nanopore wall, and the

Type I DLP due to the EDL compression becomes insignificant. The particle velocity is then governed by the competition of the decrease in the Types I and II DLP effect induced by the imposed concentration gradient. The particle velocity attains a 89 maximum value when the gap is larger than the EDL thickness and then decreases, as the ratio alap further increases because the decrease in the driving force arising from the Type II DLP is more significant than that arising from the Type I DLP. As a/ap—*cc, the electrophoresis by Ediirusivity dominates.

For a relatively small value of /cap (i.e., /cap = 0.1), the EDL surrounding the particle is significantly compressed due to the presence of the impervious nanopore wall. The particle motion is mainly governed by the electrophoresis generated by the

DLP induced electric field, and the Type I DLP primarily arises from the EDL compression by the nanopore wall. As the distance between the nanoparticle surface and the nanopore wall increases, the degree of EDL compression decreases resulting in the decrease in the effect of the Type I DLP. The magnitude of the particle velocity increases with alap for both KC1 and NaCl primarily due to the decrease in the driving force moving the particle upward by the Type I DLP. The EDL compression is the dominating factor in this case.

4.2 Electrodiffusiophoretic Motion of a Charged Spherical Particle in a

Nanopore

4.2.1 Introduction

In this section, electrophoretic motion of a charged nanoparticle in a nanopore connecting two fluid reservoirs filled with different electrolyte concentrations are studied, for the first time. In addition to the electrophoretic and electroosmotic flows arising from the imposed electric field, diffusioosmotic and diffusiophoretic flows are generated in response to the imposed electrolyte concentration gradient [99-121]. As discussed in Section 4.1, the diffusiophoretic motion is induced by the generated electric field and osmotic pressure gradient arising from the imposed concentration 90 gradient. The generated particle motion by the imposed electric field and concentration gradient is called electrodiffusiophoresis. One might slow down the nanoparticle translocation process in a nanopore by adjusting the solute concentrations in the two fluid reservoirs when the induced diffusiophoretic motion is opposite to the particle's electrophoretic motion. In the current section the electrodiffusiophoretic motion in a nanopore is presented.

4.2.2 Mathematical Model

The mathematical model and nondimensionalization process was given in Chapter 2, thus it is not explained here again.

i5 e- — -

D Na-iooote _! r~AE nrz^vc

L^ ;<„ 4

Figure 4.8. Schematics of a nanopore of length L and radius a connecting two identical reservoirs on either side. The surface charge density along the wall of the nanopore is CTW. A charged spherical particle of radius ap bearing uniform surface charge density ap is positioned at the center of the nanopore. A concentration gradient of electrolyte solution and an electric field are applied across the two reservoirs. 91

4.2.3 Results and Discussion

A particle's velocity wp* is also unknown a priori and is determined iteratively using the Newton-Raphson method to estimate the offset correction starting from an appropriate initial guess. With an initial guess of the particle's velocity, the coupled system is simultaneously solved using a commercial finite element package,

COMSOL version 3.5a, installed in a workstation with 96 GB of RAM. On the basis of the obtained solution of the various fields, the net axial force acting on the particle is evaluated using Eqs. 29 and 30 which are shown in Chapter 2. The resulting net force acting on the particle is not likely to satisfy the force balance Eq. 28 that is shown in Chapter 2, and the particle's velocity is then corrected using the Newton-

Raphson method. This iterative process is repeated until the magnitude of the net axial force becomes smaller than the absolute error bound, 10"6.

Quadratic triangular elements with variable sizes are used to accommodate finer resolutions near the charged particle surface UK and the wall of the nanopore

DE where EDLs are present. The mathematical model and its implementation with

COMSOL have been validated by many benchmark tests. For example, the ionic mass transport near a charged planar surface in the absence of any external field using the Poisson-Nernst-Planck (PNP) equations without convection results were given in literature, and the numerical results are in good agreement with the analytical solution

(Figure 2 in Ref 159). The numerical results of the electroosmotic flow in a cylindrical nanopore driven by an externally imposed electric field obtained from the coupled PNP and Navier-Stokes equations are also in good agreement with the analytical solution (Figure 3 in Ref 159). The electrophoretic motion driven by the externally imposed electric field (e.g.,ct =CR/CL= 1) is also simulated using the model, 92 and the numerical results are consistent with the corresponding approximate analytical solution and experimental results obtained from the literature [32-35].

The focus is on the effects of the EDL thickness, /cap, the ratio of the nanopore's surface charge density to that of the particle, /? = ow/av, and the bulk concentration ratio, a, on the particle's translocation velocity in three different electrolytes (NaCl, KC1, and HC1). The diffusion coefficients of the ions K+, Na+, H+, and CT are, respectively, 1.95 X 10-9, 1.33 X 10~9, 9.53 X 109, and 2.03 X 10"9 m /s. The temperature of the electrolyte solution in the reservoirs and the nanopore is maintained at 300 K. The schematic of the nanopore is shown in Figure 4.8. In the numerical simulations, the following parameters are used: L = 0.5 ^m, ap = 5 nm, alap

2 = 4, LR = 0.15 //m, b = 0.15 ^m,

NaCl KC1 HC1 Figure 4.9. Particle's electrophoretic velocity in the absence of the concentration gradient (i.e., a = 1) as a function of the type of electrolytes when /cap = 1 (lines with open symbols) and /cap = 3 (lines with solid symbols)

Figure 4.9 depicts the particle's electrophoretic velocity in NaCl, KC1, and

HC1 solutions in the absence of the axial concentration gradient (i.e., a = 1) for /? = 1

(lines with triangles), 0 (lines with circles), and -1 (lines with squares) under the conditions of /cap = 1 (open symbols) and icav = 3 (solid symbols). When the wall of the nanopore is not charged (e.g., /? = 0), as expected, the negatively charged particle electrophoretically migrates toward the anode. The electrophoretic velocity

in HC1 solution is lower than that of KC1, which is lower than that of NaCl, which arises from the difference in the diffusivities of the cations. The diffusion coefficient of H+ is higher than that of K+, which is higher than that of Na+. Cations are accumulated in the EDL surrounding the negatively charged spherical particle (Figure

4.10b), while the anions are repelled away from the negatively charged particle

(Figure 4.11b), and the resulting EDL is spherically symmetrical without an external 94 field. Under the effect of the external electric field directed along the positive z direction, the mobile cations in the EDL move along the particle surface from the bottom hemisphere to the top hemisphere. The electrolyte concentration slightly decreases at the bottom hemisphere since the counterions (cations) migrate from the bulk to the diffuse layer (weak lateral flow of co-ions can be neglected) and increases at the top hemisphere since cations come from the diffuse layer to the adjoining bulk of the electrolyte solution [99]. The concentration polarization in the EDL results in ion diffusion flows directed to the surface of the bottom hemisphere where the concentration is decreased and from the surface of the top hemisphere where the concentration is increased (Figure 3 in ref 99). The induced ion diffusion flow is proportional to D+/D~, where D+ and D' are the diffusivities of the cations and anions, respectively. The diffusion flow is opposite to the direction of the particle motion and thus retards the movement of the particle. Since D(ft) > DilC) >D(Na+), the retardation force by the induced diffusion flow arising from the double layer polarization in HC1 is higher than that in KC1, which is higher than that in NaCl.

Consequently, the magnitude of the electrophoretic velocity in NaCl is higher than that in KC1, which is higher than that in HC1. As /cap increases (i.e., the EDL thickness decreases), the EDL becomes more symmetrical, and the retardation effect by the induced ion diffusion flow decreases, resulting in an almost identical particle velocity for the three different electrolytes (i.e., the case of /cap= 3, solid circles in

Figure 4.9). For the same electrolyte, the particle velocity decreases as KCLP increases. This behavior is attributed to the wall effects, which become more significant with the increase of the double layer thickness. 95

When the nanopore wall is charged (i.e., /? ± 0), EDLs form in the vicinity of the charged nanopore wall and the charged nanoparticle. The net charge, which is proportional to the concentration difference between the cations and anions, surrounding the negatively charged nanoparticle will be increased (Figures 4.10a and

4.11a) or decreased (Figures 4.10c and 4.11c) if the nanoparticle and the nanopore carry the same or opposite surface charges. For (5 = 1 (lines with triangles in Figure

4.9), both the nanoparticle and the nanopore wall are negatively charged. Comparing to the case of the uncharged nanopore (circles in Figure 4.9), the positive net charge surrounding the particle is increased due to the presence of the excess cations in the

EDL near the nanopore wall (Figure 4.10a). The direction of the particle's motion is reversed, and the negatively charged particle moves in the same direction as that of the applied electric field. Under this condition, the interaction between the applied axial electric field and the enriched net charge surrounding the particle and in the gap between the particle and the nanopore wall induces a strong electroosmotic flow

(EOF) directed toward cathode. The induced strong EOF drags the particle toward the cathode, resulting in a positive electrophoretic velocity. Under all other same conditions, the net charge surrounding the particle and in the gap between the particle and the nanopore wall decreases as /cap increases, resulting in lower hydrodynamic driving force from the EOF and thus lower particle velocity for /cap = 3 compared to the case of /cap = 1. For /?= -1 (lines with squares in Figure 4.9), the particle is negatively charged, while the nanopore wall is positively charged. Compared to the case of /? = 0, the concentration of the cations (anions) surrounding the particle and in the gap between the particle and the nanopore wall is decreased (increased) due to the opposite charges in the two EDLs, as shown in Figures 4.10c and 4.11c, which 96 decreases the positive net charge surrounding the negatively charged particle and thus reduces the retardation force arising from the electroosmotic flow, which is opposite to the direction of the particle motion. In addition, the net charge near the positively charged nanopore wall is negative because the concentration of the anions is higher than that of the cations, shown in Figures 4.10c and 4.1 lc, resulting in an EOF in the gap, the direction of which is the same as that of the particle electrophoretic motion.

In addition to the electrical driving force arising from the interaction between the electric field and the charge on the particle, the generated EOF also provides a driving force for the particle to move toward the anode. Therefore, the magnitude of the negative electrophoretic velocity is higher for /? = -1 compared to that for /? = 0 due to the reduction of the retardation force and the additional driving force arising from the

EOF in the gap between the particle and the nanopore wall. For the same electrolyte, as /cap increases, the magnitude of the negative net charge near the positively charged nanopore wall increases due to the decrease in the effect of the opposite i charges in the EDL of the nanoparticle, leading to an increase in the EOF in the gap between the particle and the nanopore wall and thus an increase in the magnitude of the electrophoretic velocity. Therefore, when the nanopore wall is uncharged, the electrostatic force acting on the particle is the driving force for the electrophoretic motion. The particle is driven by the generated EOF if the surface charge density of the nanopore wall is relatively high. 97

Figure 4.10. Spatial distribution of the dimensionless concentration of the cations around the particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 1 in KCl solution.

4 0 Figure 4.11. Spatial distribution of the dimensionless concentration of the anions around the particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 1 in KCl solution. 98

Figure 4.12 depicts the particle's translocation velocity as a function of the imposed concentration ratio, a, for a KC1 electrolyte solution when /cap = 1 (a) and 3

(b). The solid lines with circles, dashed lines with triangles, and dash-dotted lines with squares represent, respectively, the results when (3 = 0, 1, and -1. In Figure

4.12b, since the particle velocity at B = 0 is very small compared to those at B = ±1, its magnitude is multiplied by a factor of 10 to enhance visibility. Similar results are obtained for NaCl and HCl solutions, and their results thus are not shown. For the case of a =£ 1, a negative axial concentration gradient is imposed for a < 1 and vice versa.

0.04

«',

0.02

<

0

I -0.02

J 1 i i i i. "»" • i i • • io"J io* ao"1 io° IO1 ~ io* io5 io'J io"2 ao"1 io° IO1 ~ ao2 io3

Figure 4.12. Electrodiffusiophoretic velocity as a function of the concentration ratio, a, in KC1 solution when /cap = 1 (a) and 3 (b). The solid lines with circles, dashed lines with triangles, and dash-dotted lines with squares represent, respectively, the results of/? = 0, 1, and -1.

Figure 4.13 depicts the deviation of the particle electrodiffusiophoretic velocity from the electrophoretic velocity without imposing a concentration gradient, 99

X = wp*( a) - up*( a = 1), as a function of the imposed concentration ratio, a, for KC1 electrolyte solution when /cap = 1 (a) and 3 (b). The conditions are the same as those in Figure 4.12. Since the imposed electric field is fixed, the resulting electrodiffusiophphoretic velocity versus a, shown in Figure 4.12, is similar to the diffusiophoretic velocity as a function of the imposed concentration ratio, shown in

Figure 4.13.

When the nanopore wall is uncharged and /cap = 1 (solid line with circles in

Figure 4.12a), as a decreases from a = 1, the magnitude of the particle's velocity decreases, and the particle translocation process is slowed down by imposing a negative axial concentration gradient. The direction of the particle's motion is even reversed when a is smaller than a critical value, etc, at which the particle's velocity is

0. As the concentration ratio further decreases, the negatively charged particle migrates toward the cathode, and its velocity increases due to the increase in the imposed concentration gradient. When the concentration ratio is smaller than a certain value, the ionic concentration in the bottom reservoir is ci* = C2* = 2/(1 + a)

-* 2, and that in the top reservoir is c\* = ci* = 2 a /(l + a) -* 0, leading to the saturation of the concentration gradient and thus the particle diffusiophoretic velocity.

On the contrary, the electrophoretic velocity is accelerated by the diffusiophoresis when a > 1. As a increases from a = 1, the particle velocity increases and becomes independent of a when the latter is large enough. When a is large enough, the concentration in the bottom reservoir is c\* = C2* = 2/(1 + a) -»0, and that in the top reservoir is c\* = C2* = 2 a/(l + a) -* 2, resulting in the saturation of the imposed concentration gradient and consequently the particle motion, which is dominated by the generated diffusiophoresis. When the nanopore wall is uncharged and /cap = 3 100

(solid line with circles in Figure 4.12b), the EDL thickness is smaller than that of K ap

= 1, and the particle translocation process is slowed down by applying a concentration gradient, regardless of the direction of the imposed concentration gradient. Under this condition, the direction of the particle's motion is not reversed. Obviously, two diverse effects are obtained for /cap = 1 (relatively thick EDL) and /cap = 3

(relatively thin EDL) when a positive axial concentration gradient is applied (i.e., a

> 1), which arises from the opposite directions of the generated diffusiophoretic motion at /cap = 1 and 3, shown in Figure 4.13, and will be elaborated in the following.

The driving mechanism behind diffusiophoresis is given in Section 4.1, thus here in this paragraph it is summarized to briefly explain the electrodiffusiophoretic motion. The diffusiophoresis is induced by the chemiphoresis and the induced electrophoresis. The former is generated by the induced osmotic pressure gradient around the charged particle, which propels the particle toward a higher salt concentration region, regardless of the sense of the particle's charge. The latter is induced by the generated electric fields arising from the difference of ionic diffusivities and from the double layer polarization (DLP) under the effect of the imposed concentration gradient. When the diffusive mobilities of anions and cations are unequal, an electric field, Ediffusivity. is induced so that the diffusion of high- mobility (low mobility) ions is decelerated (accelerated). For example, since the diffusion mobilities of the anions and cations in KC1 electrolyte are almost identical, the induced electric field arising from the difference in the ionic diffusivities is very small in KC1 solution. Since the anions have a higher diffusion coefficient than the cations in NaCl solution, an electric field, EdJHbsivity, is induced and directed from 101 higher NaCl concentration to lower concentration. In contrast, an electric field,

Eaiffusivity, directed from a lower electrolyte concentration to a higher electrolyte concentration is generated in the HCl solution because the cations have a higher diffusion coefficient than the anions. Similar to the externally imposed electric field, the electric field, Ediirusivity, generated on account of the difference in the ionic diffusivities generates electrophoretic motion. With the imposed concentration gradient, inside of the EDL, the amount of the counterions on the high concentration side is higher than that on the low concentration side of the particle, resulting in an electric field, EI.DLP, the direction of which is opposite to (the same as) that of the applied concentration gradient when the particle is negatively (positively) charged.

This kind of DLP is called a Type I DLP, and its resulting electric field is named as

EI.DLP- On the other hand, the concentration of the co-ions near the outer boundary of the EDL on the high concentration side is higher than that on the low concentration side of the particle, which is called the Type II DLP. This generates an electric field,

EH-DLP, the direction of which is opposite to that established by the counterions inside of the EDL, EI.DLP- Therefore, when a concentration gradient is imposed, an electric field is generated by three mechanisms; the first one, Ediffusivity, is established by the difference in the ionic diffusivities; the second one, EI.DLP, is established by the Type

I DLP inside of the EDL; and the third one, EO-DLP, is generated by the Type II DLP near the outer boundary of the EDL. The induced electrophoresis stems from the interaction between the particle's charge and the generated electric fields, Edurusivity,

EI.DLP, and En-DLP- As mentioned before, the induced EI.DLP from the Type I DLP always propels the particle toward higher electrolyte concentration, while EO-DLP generated by the Type II DLP always drags the particle toward lower electrolyte concentration, regardless of the sign of charge on the particle. Usually, the induced 102 electrophoretic effect generated by Ediffusivity is more significant if the boundary effect is insignificant (i.e., large a/ap and /eap) and the ionic diffusivities are unequal. In the present study, the electrophoretic effect arising from the DLP-induced electric fields dominates since the EDL thickness, the particle size, and the nanopore size are of the same order of magnitude.

The degree of the aforementioned Type I and II DLPs arising solely by the imposed concentration gradient will be further affected by the externally imposed electric field. For a < 1, the concentration near the bottom hemisphere is higher than that near the top hemisphere. Inside of the EDL, the concentration of the counterions

(cations) near the bottom hemisphere is higher than that near the top hemisphere.

Under the externally imposed axial electric field, the cations are displaced from the bottom hemisphere toward the top hemisphere, which reduces the counterions' concentration difference between the bottom and top hemispheres and consequently reduces the electric field generated by the Type I DLP effect. Howewer, the co-ions at the outer boundary of the EDL are displaced from the top hemisphere toward the bottom hemisphere, which increases the co-ions' concentration difference at the outer boundary of the EDL near the bottom and top hemispheres and thus increases the

Type II DLP effect. Therefore, for a < 1, the DLP arising from the imposed electric field reduces the degree of the Type I DLP and increases the Type II DLP. The imposed axial electric field reduces the degree of the Type II DLP and increases the degree of the Type I DLP when a > 1.

For KC1, the generated Ediffusivity is very small due to the small difference in the diffusion coefficients of the cations and anions. For an uncharged nanopore (i.e.,

/?= 0) and /cap = 1 (solid line with circles in Figure 4.13a), the electrophoretic effect 103

arising from EH-DLP dominates over that from EI.DLP- The generated EU-DLP propels the particle toward lower salt concentration, resulting in a positive diffusiophoretic velocity for a < 1 and negative diffusiophoretic velocity for a > 1, as shown in Figure

4.13a (solid line with circles). The results also indicate that the chemiphoretic effect is insignificant compared to the induced electrophoretic effect since the former one propels the particle toward higher salt concentration. As /cap increases, the electric field generated by the Type I DLP, EI.DLP, becomes stronger, and the generated electric field by the Type II DLP, EH.DLP, becomes weaker. For /cap = 3 (solid line with circles in Figure 4.13b), the diffusiophoretic velocity results from the competition of the two opposite DLP effects. For a < 1, the electrophoretic effect by

EU-DLP dominates over that by EI.DLP due to the increase in the Type II DLP and decrease in the Type I DLP by the DLP arising from the imposed electric field; thus, a positive diffusiophoretic velocity occurs, as shown in Figure 4.13b. When a > 1, the degree of the Type II DLP is reduced, and that of the Type I DLP is increased by the

DLP arising from the imposed electric field, and the induced electrophoretic effect by

EI.DLP dominates over that by EU-DLP. resulting in a positive diffusiophoretic velocity, as shown in Figure 4.13b.

When the nanopore wall becomes charged, the electrodiffusiophoretic velocity versusct, shown in Figure 4.12, becomes more complicated, which mainly arises from the complicated variation of the diffusiophoretic velocity as a function of a, shown in

Figure 4.13. Regardless of the polarity of the nanopore's charge, as a decreases from a = 1, the generated diffusiophoretic motion is directed from higher salt concentration toward lower salt concentration, and the magnitude of its velocity increases, obtains a local maximum, and then declines. As a further decreases, the direction of the 104 diffusiophoretic motion is reversed and is directed toward higher salt concentration.

When the direction of the imposed concentration gradient is reversed (i.e., a > 1), an opposite diffusiophoretic motion is induced. As a increases from a = 1, the diffusiophoretic motion is directed from the higher concentration side to the lower concentration side, and its magnitude increases, obtains a local maximum, and then decreases as the imposed concentration gradient increases. When a exceeds a certain value, the diffusiophoretic motion is reversed, and its magnitude increases as a further increases.

0.04 m X J\ 0.02 ^j/ \ / / f X I JL> A ( J e 1 10*^\ >sj I i 1 \ / i 1 / / -0.02 /A

• 1 • 1 2 i io lir i? lerio io*io* 1( -> 10 2 IO'1 1C 6 J- asv 10 10 Figure 4.13. Particle velocity deviation % as a function of the concentration ratio, a, in KC1 solution when /cap = 1 (a) and 3 (b). The solid lines with circles, dashed lines with triangles, and dash-dotted lines with squares represent, respectively, the results ofjff = 0, l,and-l.

When a nanopore wall is charged, an EDL forms in the vicinity of the charged nanopore wall. Figures 4.14 and 4.15 depict, respectively, the spatial distribution of the dimensionless concentrations of the cations and anions around the negatively 105

charged particle for /? = 1(a), 0 (b), and -1 (c) in KC1 solution with a = 0.001 and /cav

= 1. Figure 4.16 depicts the concentration difference between the cations and anions, ci* - C2*, under the same conditions as those shown in Figures 4.14 and 4.15. Similar spatial concentration distributions are obtained for a = 0.1 and thus are not shown.

Compared to the case of /? = 0, which corresponds to an uncharged nanopore wall

(Figures 4.14b, 4.15b, and 4.16b), both the nanoparticle and the nanopore wall are negatively charged for /? = 1, and the presence of the EDL of the nanopore wall enriches the concentration of the cations (Figure 4.14a) and depletes the concentration of the anions (Figure 4.15a), resulting in higher net charge surrounding the particle and in the gap between the particle and the nanopore wall, shown in Figure 4.16a.

For fi = -1, the concentration of the cations (anions) is decreased (increased), arising from the opposite charges of the nanoparticle and the nanopore wall. Compared to the case of a = 1 in the absence of the imposed concentration gradient (Figures 4.10 and 4.11), the contour lines of the ionic concentrations shown in Figures 4.14 and

4.15 become more asymmetric around the particle, implying significant DLP arising from the imposed concentration gradient. Since the electric field generated by the

Type II DLP dominates over that arising from the Type I DLP, the overall electric field is dominated by EH-DLP, which is directed toward higher salt concentration. 106

2 r* t Figure 4.14. Spatial distribution of the dimensionless concentration of the cations around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 0.001 in KC1 solution.

(c)

T •2 ' ./

I

2 f A 0 Figure 4.15. Spatial distribution of the dimensionless concentration of the anions around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 0.001 in KC1 solution. 107

For p = 1 and /cap = 1 (dashed line with triangles in Figure 4.13a), as a decreases from a = 1, the electrical driving force arising from the interaction between the negative charge of the particle and the generated EH-DLP drives the particle toward lower salt concentration, resulting in a positive diffusiophoretic velocity. The interaction between EH-DLP and the positive net charge surrounding the particle and in the gap between the particle and the wall generates electroosmotic flow, which is directed toward higher salt concentration. The direction of the generated electroosmotic flow is opposite to that of the diffusiophoretic motion. As a decreases, the concentration gradient increases, and the magnitude of the generated electric field

EH-DLP and the net charge, c\* - C2*, increase, which simultaneously increases the electrical driving force acting on the particle and the body force in the fluid, and the latter increases the opposite electroosmotic flow. The diffusiophoretic velocity attains a maximum due to the competition between the hydrodynamic force arising from the generated opposite electroosmotic flow and the electrical driving force acting on the particle. As a further decreases, the rate of increase in the hydrodynamic force is faster than the rate of increase in the corresponding electrical driving force, resulting in the decrease in the diffusiophoretic velocity. When a is smaller than a certain value (or the imposed concentration gradient exceeds a certain value), the hydrodynamic force arising from the induced electroosmotic flow becomes the driving force for the particle motion, and the particle is driven by the generated electroosmotic flow, leading to the reverse of the diffusiophoretic velocity, shown in

Figure 4.13 a. On the contrary, the generated EH-DLP is directed in the positive axial direction for a > 1. As a increases from a = 1, the electrical driving force stemming from the interaction between EH-DLP and the negative charge on the particle induces 108 negative diffusiophoretic velocity. The generated electroosmotic flow arising from the interaction between EH-DLP and the positive net charge is directed along the positive axial direction. As a increases, both the magnitude of EH-DLP and the net charge surrounding the particle and the gap increase, which leads to the increase in the electrical driving force and the hydrodynamic retardation force acting on the particle. When the rate of increase in the retardation force is faster than that of the electrical driving force, the magnitude of the diffusiophoretic velocity attains the maximum and then declines. As a further increases, the induced electroosmotic flow provides the driving force and drags the particle moving toward higher salt concentration. For /? = 1 and /cap = 3 (dashed line with triangles in Figure 4.13b), the variation of the diffusiophoretic velocity with a is similar to that under /cap = 1, except that the direction of the diffusiophoretic motion is not reversed. In addition, the magnitude of the diffusiophoretic velocity for /cap = 3 is higher than that for /cap

= 1. As /cap increases, the EDL thickness decreases, and the enrichment of the cations and the depletion of the anions surrounding the particle and in the gap become less significant. The net charge surrounding the particle and in the gap for K ap = 3 is lower than that under scap = 1, leading to relatively weaker electroosmotic flow for

/cap = 3. Consequently, the retardation force arising from the electroosmotic flow for

Kap = 3 is lower than that of /cap = 1, resulting in higher magnitude of the diffusiophoretic velocity. Since the generated electroosmotic flow is not strong enough, the particle is driven by the electrical driving force arising from the interaction between EH-DLP and the negative charge of the particle, and the direction of the diffusiophoretic motion is not reversed for KQP = 3. 109

Figure 4.16. Spatial distribution of the concentration difference, c\* - C2*, around the negatively charged particle when /? = 1 (a), 0 (b), and -1 (c). /cap = 1 and a = 0.001 in KC1 solution.

For /? = -1 and /cap = 1 (dash-dotted line with squares in Figure 4.13a), similar to the cases of p = 0 and 1, EH.DLP generated by the Type II DLP dominates.

The net charge is positive in the region surrounding the negatively charged particle and is negative in the region near the positively charged nanopore wall, as shown in

Figure 4.16c. The magnitude of the net charge increases as the magnitude of the imposed concentration gradient increases. For a < 1, EH.DLP is directed in the negative axial direction. As a decreases from a = 1, the electrical driving force arising

from the interaction between EH_DLP and the negative charge on the particle generates positive diffusiophoretic motion. The interaction between the generated EH-DLP and the positive net charge surrounding the particle generates electroosmotic flow which 110 is opposite to the particle motion. In addition to the fluid motion, which tends to retard particle motion, the interaction between EH-DLP and the negative net charge near the positively charged nanopore wall induces electroosmotic flow, the direction of which is the same as that of the particle diffusiophoretic motion, and thus enhances the particle motion. Therefore, the diffusiophoretic velocity for /? = -1 is higher than that of P = 1 since the electroosmotic flow near the positively charged nanopore wall provides an additional driving force while the electroosmotic flow near the negatively charged nanopore wall retards the particle motion. As a decreases, the generated electric field EH-DLP and the magnitude of the net charge increase, leading to the increase in the electrical driving force, the driving force from the electroosmotic flow near the nanopore wall, and the retardation force from the opposite electroosmotic flow near the particle. Similar to the case of /? = 1, as a decreases, the diffusiophoretic velocity increases, peaks, and then declines. The particle motion is reversed when the hydrodynamic drag arising from the fluid motion in the vicinity of the particle becomes the driving force. On the country, an opposite variation of the diffusiophoretic velocity with a is obtained when the direction of the imposed concentration gradient is reversed. As /cap increases, the influence of the EDL formed in the vicinity of the nanopore wall on the ionic concentration in the EDL surrounding the nanoparticle decreases, resulting in higher net charge and consequently stronger fluid motion surrounding the particle. Therefore, the magnitudes of the particle's velocity at a = 0.001 and 1000 under /cap = 3 are higher than those at /cap = 1, under which the particle motion is driven by the fluid motion surrounding the particle. Ill

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

5.1 Concluding Remarks

In the present study, two electrokinetic particle manipulation techniques in micro- and

nano fluidic devices have been studied. These particle manipulation techniques are:

Particle manipulation via floating electrodes and diffusiophoresis.

Therefore, particle manipulations were first studied using floating electrodes

attached to the bottom of a straight microchannel under an imposed DC or AC electric

fields. In contrast to a dielectric microchannel possessing a nearly-uniform surface

charge, a floating electrode is polarized under the imposed electric field. Such a non­

uniform electric field, in turn, generates an induced-charge electro-osmotic (ICEO)

flow near the metal strip. Since the ICEO flow highly depends on the imposed

electric field, and affects the overall hydrodynamic field inside the channel and

accordingly the particle motion, versatile particle manipulations have been easily

achieved by simply attaching one or multiple metal strips to the channel bottom wall

without requiring complicated fabrication process.

The demonstrations include,

1- Passive control of the floating electrode polarization by externally imposed

DC electric field from microfluidic reservoirs and obtaining particle

enrichment, movement, trapping, reversal of motion, separation, and particle

focusing via using single and double floating electrodes.

2- Active control of the floatingelectrod e polarization by adding two micron-size

control electrodes on both sides of the floating electrode and obtaining a 112

flexible strategy for the on-demand control of the particle enrichment and its

positioning via externally and locally imposed DC electric fields.

3- The particle deposition onto a floating electrode under an externally imposed

AC electric field.

In the second part of the study, another electrokinetic particle manipulation method, the diffusiophoretic and electrodiffusiophoretic motion of a charged spherical particle in a nanopore is computationally investigated. The charged particle experiences electrophoresis because of the imposed electric field and the diffusiophoresis is caused solely by the imposed concentration gradient. The diffusiophoresis is induced by chemiphoresis and induced electrophoresis.

Chemiphoresis is generated by the induced osmotic pressure gradient around a charged particle. Induced electrophoresis is induced by the generated electric fieldsarising from the difference of ipnic diffusivities and from the double layer polarization (DLP). Via imposed concentration gradient, particles' electrophoretic motion has been controlled inside the channel.

The investigations include.

1- Diffusiophoretic motion of a charged spherical particle in a nanopore for

different parameters; /cap (the ratio of particle size to pore size), ap (the

particle surface charge density), a/ap (the ratio of pore size to particle size) to

understand the induced electrophone field (EdiffuSivity, Ei_DLP, EH.DLP) and

chemiphoresis (osmotic pressure gradient) effects on the motion of the

particle.

2- The effect of diffusiophoresis on electrophoretic motion of the particle to; 113

• Enhance,

• Slow down,

• Reverse the particle motion in a nanopore by the superimposed

diffusiophoresis.

5.2 Recommendations for Future Research

The main objective of this dissertation was to develop particle manipulations for micro- and nano-fluidics via floating electrodes and diffusiophoresis. Micro- and nano-fluidics are multidisciplinary in nature and they potentially have wide applications in chemisty, biology, and colloidal science applications. If the following recommendations are considered in the future that utilize the current results, they should lead to many useful devices.

1- LOCs deal with the handling of extremely small fluid volumes down to less

than pico liters. So concentration enrichment, and particle trapping is very

important in LOC devices. The current floating electrode configuration can be

extended into, for example, biomedical research to enrich the concentration of,

say, DNA or RNA, and to increase their concentrations at a desired location.

2- In the present study, although the floating electrode was attached only to the

bottom wall of the channel, the particle leakage was minimized and particle

concentration and reversal of the particle motion was succeeded. By inserting

floating electrodes to the other walls of the microfluidic channel, it can be

used as a filtration device, thus the filtration can be achieved without blocking

the microfluidic channel and without any porous material.

3- In the present study, local control of the position of the particles is shown in a

straight microfluidic channel. By using many inlet and outlet channels and 114

inserting locally controlled floating electrodes to these channels, the polarity

of the floating electrode and direction of the electric field can be locally

controlled. Such a device can be used as a microfluidic valve: the particles

can be locally trapped in any desired location and the direction can be

switched as desired.

4- In the present study, particle deposition onto the floating electrode was

demonstrated under AC electric field. Since under AC electric field, floating

electrode polarity always switches with respect to time, the current system can

be used for nanocomposite material formation. Therefore, different types of

and opposite surface charge particles can be deposited onto the floating

electrode. This may even be possible for thin nanocomposite film formation

on the floating electrode.

5- In the present study, since it is seen that particles can be deposited onto the

floating electrode, the configuration can be extended for immobilization of

any desired sample. In many micro- and nano-fluidic applications, the sample

needs to be immobilized to conduct the study. Instead of single floating

electrode, many small floating electrodes can be inserted inside the

microfluidic device and, under applied electric field, the sample can be

immobilized on the floatingelectrode .

6- In the present study, particle's diffusiophoretic motion showed that, the

particle motion can be enhanced, slowed down, and even reversed. Thus, by

designing a continuous concentration-gradient-generator nanofluidic device

may be obtained for nanoparticle translocation process. This may achieve

nanometer-scale spatial accuracy sample sequencing by simultaneously

controlling the electric field and concentration gradient. 115

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VITA

Sinan Eren Yalcin Department of Mechanical and Aerospace Engineering Old Dominion University Norfolk, VA 23529

Sinan Eren Yalcin was born on May 3rd, 1980 in Istanbul, Turkey. He graduated from

Haydarpasa High School in 1998 and then admitted to Marine Engineering at Istanbul

Technical University (ITU) in 1998. He received his Bachelor of Science degree in

Marine Engineering at Istanbul Technical University in August 2003. Thereafter, he

was accepted to Mechanical Engneering Department Thermo-Fluids Division as a

master student at Istanbul Technical University in August 2004. While completing his

master studies he served as a Teaching Assistant at the same institution. He received

his Master of Science degree in Mechanical Engineering at Istanbul Technical

University in August 2006. Until 2007 he worked as a Teaching Asistant in the same

department. He was then admitted into the Aerospace Engineering Department at Old

Dominion University in August 2007 to pursue his Ph.D. study. During his Ph.D.

study, he was awarded a research assistantship by the Department. He was involved in research work pertaining to electrokinetics in microfluidics. From September 2009 to

September 2010 he was exchange student at Yeungnam University, South Korea.