Evaluating the Role of the Secondary Energy Minimum in Colloid Deposition and Release in Saturated Porous Media Thesis Presented

Evaluating the Role of the Secondary Energy Minimum in Colloid Deposition and Release in Saturated Porous Media

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Qing Ye, B.S. & B.Admin

Graduate Program in Civil Engineering

The Ohio State University

2011

Thesis Committee:

John J. Lenhart, Advisor

Harold Walker

Ethan Kubatko

Qing Ye

2011

Abstract

Transport and release of carboxylate-modified polystyrene microspheres of two sizes (36nm and 490nm) in saturated quartz sand under steady flow conditions were investigated in this study. The interaction energy profiles and classic DLVO framework were set up based on measurements and characterization of both particles and sand grains to evaluate and explain the colloidal behavior in the porous media. Emphasis was focused on the roles of the secondary energy minimum and effects of solution chemistry. It was found that the deposition of both colloids displayed apparent ionic strength dependence, and generally the higher ionic strength values were, the more deposition occurred. All the breakthrough curves had extended tailing, which was ascribed to the reversible colloid deposition (release from the secondary minimum) under hydrodynamic drag interactions. The 36nm colloids were observed to have retarded initial breakthrough at high ionic strength, similar to the reversible adsorption of solute species. This was interpreted to result from readily reversible deposition in the secondary minimum. The 490nm colloids did not have such delayed breakthrough and instead displayed slight size exclusion effects indicative of straining. The influence of heterogeneities on colloid deposition and release was also considered. For example, surface roughness appeared to be an important mechanism for 36nm colloid deposition at low ionic strength. At high ionic strength, however, the secondary and even primary minima dominate colloid deposition and release. Both straining and the secondary minimum were enhanced at greater ionic strength. The profile of retained colloids measured for the 490nm colloids transitioned from hyper-exponential to non-monotonic styles as the ionic strength increased. This reflects a transition from straining-dominated deposition to deposition involving both straining and the secondary minimum. Plausible release mechanisms were deduced based on experimental observations. The final release step, which involved the transition from the existence of the secondary minimum to no secondary minimum, was the most important step. During this transition, no secondary minimum association sites were available for colloid retention, and the only colloid retention

ii sites left were likely straining sites such as grain-grain contact points. The release behavior indicated that global release was the net of local release and subsequent redeposition. A conceptual model was developed to include the assumptions of non-contacting deposition, critical ionic strength ranges, distributed nature of interaction energies, as well as squeezing-induced local colloid release mechanisms.

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Dedication

Dedicated to the ones who love me and I love

Acknowledgement

I really appreciate the great patience and graceful help that my advisor, parents and the fellow graduate colleagues in the lab have offered me during the two-year journey of my pursuit of the Master’s Degree at

The Ohio State University.

Vita

Oct. 1986…………………………………...Born

Sep. 2003-Jun. 2008..………………………B.S. Environmental Science, Zhejiang University, China

Sep. 2003-Jun. 2007..………………………B.Admin. Business Administration, Zhejiang University, China

Sep. 2008-Aug.2010…………….………….Graduate Research Assistant, Civil and Environmental

Engineering, The Ohio State University

Fields of Study

Major Field: Civil Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgement ...... v

Vita ...... vi

List of Tables ...... x

List of Figures ...... xi

CHAPTER 1: INTRODUCTION AND BACKGROUND ...... 1

1.1 An introduction into colloidal systems ...... 1

1.2 Interactions between colloidal particles ...... 2

1.2.1 DLVO and XDLVO (extended DLVO) theories ...... 2

1.2.2 Colloid stabilization and aggregation ...... 4

1.3 Environmental behavior of colloidal particles ...... 5

1.3.1 The existence of colloidal particles in natural environments ...... 5

1.3.2 Colloid-facilitated transport of pollutants in porous media ...... 5

1.3.3 Colloid transport and release in saturated porous media ...... 6

1.3.3.1 Mechanisms inducing colloid deposition during transport ...... 7

1.3.3.1.1 Heterogeneity ...... 7

1.3.3.1.2 Straining ...... 9

1.3.3.1.3 Deposition within the secondary energy minimum ...... 11

1.3.3.2 Colloid release from saturated porous media ...... 11

1.3.3.2.1 Release kinetics ...... 12

1.3.3.2.2 The role of transient conditions in ionic strength, pH or flow rate ...... 13

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1.3.3.3 Other influential factors for colloid deposition and release ...... 15

1.3.3.4 Mathematical description of colloid transport and release ...... 17

1.3.3.4.1 One dimensional transport modeling ...... 17

1.3.3.4.2 Colloid filtration theory ...... 18

1.3.3.4.3 Colloid deposition under unfavorable deposition conditions ...... 22

1.4 Research objectives ...... 23

CHAPTER 2: EVALUATING THE ROLE OF THE SECONDARY ENERGY MINIMUM IN COLLOID

DEPOSITION AND RELEASE IN SATURATED POROUS MEDIA: EFFECT OF SOLUTION

CHEMISTRY ...... 29

2.1 Introduction ...... 29

2.2 Materials and methods ...... 32

2.2.1 Model colloids ...... 32

2.2.2 Model porous media ...... 33

2.2.3 Column experiments ...... 34

2.2.3.1 Experimental setup ...... 34

2.2.3.2 Tracer experiment ...... 35

2.2.3.3 Colloid experiments ...... 36

2.3 Results and discussion ...... 37

2.3.1 Microsphere characterization ...... 37

2.3.2 Quartz sand characterization ...... 38

2.3.3 Interaction potential energy profiles ...... 39

2.3.4 Column experiments ...... 41

2.3.5 Conceptual model regarding colloid deposition and release ...... 50

2.3.5.1 Non-contacting and contacting deposition ...... 50

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2.3.5.2 Ionic strength spectrum where non-contacting deposition happens ...... 50

2.3.5.3 Correlating deposition kinetics with initial deposition ionic strength ...... 54

2.3.5.4 Local colloid release induced by decreasing ionic strength ...... 56

2.3.6 Summaries and implications ...... 58

CHAPTER 3 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK ...... 76

3.1 Conclusions ...... 76

3.2 Recommendations for future work ...... 77

References: ...... 79

Nomenclature ...... 92

List of Tables

Table 1. Models widely used for EDL and vdW calculations ...... 25

Table 2. Representative studies evaluating colloid release in saturated porous media ...... 26

Table 3. Manufacture’s reported details of both particles ...... 60

Table 4. A summary of colloid transport experiments performed ...... 60

Table 5. Zeta potentials of two colloids as a function of pH (ionic strength is 10mM) ...... 61

Table 6. Zeta potentials of two colloids as a function of ionic strength (pH is 6.7±0.1) ...... 61

Table 7. Zeta potentials of quartz sand as a function of ionic strength and pH ...... 61

Table 8. Summary of energy minima and maximum for 36nm colloid ...... 62

Table 9. Summary of energy minima and maximum for 490nm colloid ...... 62

Table 10. Characteristic parameters of 36nm colloid mass balance and deposition kinetics ...... 63

Table 11. parameters used to derive Table 8 and 10 ...... 63

Table 12. Characteristic parameters of 490nm colloid mass balance and deposition kinetics ...... 63

Table 13. Summary of cumulative colloid recovery based on the release experiments ...... 64

List of Figures

Figure 1. DLVO profile ...... 27

Figure 2. Retained profile ...... 27

Figure 3. Typical release curve ...... 28

Figure 4. Flow chart of the column experiment setup ...... 65

Figure 5.TEM images for (a) 40nm and (b) 500nm colloids ...... 65

Figure 6. SEM images of quartz sand at (a) 50x magnification and (b) 1000x magnification ...... 66

Figure 7. Total interaction potential energy profile of 36nm polystyrene microspheres and quartz sand ..... 66

Figure 8. Total interaction potential energy profile of 490nm polystyrene microspheres and quartz sand ... 67

Figure 9. The highlight of the secondary energy minima of 36nm ...... 67

Figure 10. The highlight of the secondary energy minima of 490nm ...... 68

Figure 11. Breakthrough curve for the tracer, bromide ...... 68

Figure 12. Breakthrough curves for the 36nm colloids as a function of ionic strength ...... 69

Figure 13. Release experiments of 36nm colloid at initial ionic strength 30mM and pH 6.7 ...... 69

Figure 14. Breakthrough curves for the 490nm colloids as a function of ionic strength ...... 70

Figure 15. Retained profiles of 490nm colloid ...... 71

Figure 16. Comparison of 490nm colloid deposition at different pH levels ...... 72

Figure 17. Release experiments evaluating the role of pH at initial conditions of 1mM NaCl and pH 6.7 ... 72

Figure 18. Release experiment at initial conditions of 3mM and constant pH 6.7±0.1 ...... 73

Figure 19. Release experiment at initial deposition conditions of 10mM and pH 6.7±0.1 ...... 73

Figure 20. colloid deposition processes and mechanisms known so far...... 74

Figure 21.the spectrum of ionic strength for colloid deposition ...... 74

Figure 22. The relationship between the apparent deposition rate coefficient and ionic strength ...... 75

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CHAPTER 1: INTRODUCTION AND BACKGROUND

1.1 An introduction into colloidal systems

A colloidal system consists of a phase of one substance dispersed microscopically and evenly throughout another one (Encyclopedia Britannica, 2010; Shen and Cheung, 2010). In this research, our colloidal system comprises one solid phase dispersed in a continuous aqueous phase, which is by definition a hydrosol (Encyclopedia Britannica, 2010). Although many familiar substances are similar colloidal systems, e.g., blood and ink, only those of environmental relevance are of interest in this research, such as those with naturally occurring colloids and engineered nanoparticles. Natural colloids are abundant in soil and groundwater systems, and are primarily composed of metal oxide precipitates and clay minerals sometimes coated by natural organic matter (Ryan and Elimelech, 1996). Engineered nanoparticles, e.g., metal nanoparticles, metal oxide nanoparticles and carbon nanoparticles, are produced through modern chemical processes, utilized for various purposes, and may inevitably be introduced into the natural environment. No matter the specific colloidal system, a common property shared by all is that the dispersed solid particles have a diameter between 1nm and 10μm (Saiers and Ryan, 2006), which is beyond the visibility of the human eyes.

As will be discussed in the following sections, the environmental behavior of colloidal particles is controlled by their physical properties and specific surface chemistry, as well as the physical and chemical conditions of their surrounding aqueous environment. Detailed information about the interactions among colloidal particles or between colloids and environmental media will be given, with an emphasis on colloid aggregation, transport, deposition and release. Colloid release is the focus of this research but understanding its impact requires introduction of other colloid interactions. A full understanding of these processes has field scale applications such as determination of removal rates by porous media and transport distances of many colloid-sized

1 particles in natural environment, e.g., contaminant-associated humic substances as well as biocolloids such as protozoa, bacteria and viruses.

1.2 Interactions between colloidal particles

1.2.1 DLVO and XDLVO (extended DLVO) theories

Colloids often have surface charge. This charge can be observed by applying an external electric field causing particles of the same sign dispersed in aqueous phase to migrate to the electrode of the opposite charge (Lyklema, 1995). From this measurement of particle electrophoretic mobility, the particle zeta potential can be calculated (Smoluchowski, 1903;

Huckel, 1924). The zeta potential is not the surface potential, instead it represents the electrokinetic potential at the slipping plane in the double layer (Haydon, 1960).

DLVO theory describes the forces between charged surfaces interacting through a liquid medium. It combines the effects of London van der Waals interactions (note: for simplicity, we use “vdW” as the notation) and electrostatic double layer (EDL) interactions. A positive value indicates a repulsive interaction and negative an attractive interaction. The EDL interactions arise when the diffuse layer of ions that accumulate near charged surfaces to balance the surface charge overlap (Ryan and Elimelech, 1996). When the two interacting surfaces are oppositely charged, the EDL interactions are attractive. The opposite occurs when the surfaces are of like charge. The

London van der Waals interactions arise from dipole-dipole interactions between surfaces, and they are typically attractive (Israelac and Tabor, 1972). These are considered long-range interactions and they are a function of the physical properties of the interacting surfaces and the intervening liquid (French, 2000). DLVO theory is named after the Soviet and Dutch authors of two seminal papers Derjaguin and Landau (1941) and Verwey and Overbeek (1948). Since its introduction in the 1940s, DLVO theory has been used to explain phenomena in colloidal science and many other fields. It is frequently represented by a DLVO interaction energy curve which delineates the total interaction energy (sum of EDL and vdW interactions) between two charged 2 surfaces as a function of their separation distances. Typical DLVO curves are shown in Figure 1.

In Figure 1, the x-axis is the separation distance (h) between a spherical colloid and the surface of a plate, and the y-axis is the interaction energy (ϕ) normalized by kT, where k is Boltzmann’s constant and T is the absolute temperature. In Figure 1A, curves for EDL repulsive interactions

(electrostatic line) and vdW attractive interactions (van der Waals line) are drawn. Summing these interactions results in the net interaction energy (net interaction line). Noting the EDL interaction energy as ϕEDL and the vdW interaction energy as ϕvdW, then the total interaction energy ϕT is expressed as:

     T EDL vdW (1)

Various efforts have been devoted to quantitatively derive equations to represent both EDL and vdW interaction energies. Table 1 summarizes the most widely used approaches. As general features, the total interaction potential energy (ϕT) profile as shown in Figure 1 presents an attractive primary energy minimum (ϕ1min) of theoretically infinite depth at short separation distances, a primary repulsive energy maximum (ϕMax) at a larger separation distance and a

comparatively smaller attractive secondary energy minimum (ϕ2min) at an even larger separation distance (Canseco et al., 2009). The energy barrier to deposition frequently noted in the literature refers to the difference between ϕMax and ϕ2min. This energy must be overcome in order for a colloid to deposit within the primary minimum. Based on DLVO theory, increasing ionic strength makes the secondary energy well deeper and reduces the height of the primary energy maximum.

Increasing colloid size deepens the secondary energy well and raises the height of the primary energy maximum.

In theory, the primary energy minimum has an infinite depth at zero separation distance, which suggests the probability of colloid escape from the infinitely deep primary minimum is zero. However, experimental observations of colloids detached from collector surfaces

(Ruckenstein and Prieve, 1976), and evidence of the existence of short range repulsive forces

(Barouch et al., 1987), both indicate this depth should not be infinite. The short range forces, although still not fully understood, are assumed to originate from either hydration or steric repulsion (Ryan and Elimelech, 1996) and could play a significant role at close distance because they define a finite depth in the primary energy minimum. Beyond the near surface region, these forces are no longer dominant. As classic DLVO theory does not include these forces, they are called non-DLVO forces. Extended DLVO (XDLVO) theory considers these non-DLVO forces in addition to the classic DLVO interaction forces, i.e. EDL and vdW. A Born repulsion potential energy (ϕBorn) is often proposed to account for those non-DLVO interactions (Ruckenstein and

Prieve, 1976). The total interaction energy under the framework of XDLVO theory is:

       T EDL vdW Born (2)

1.2.2 Colloid stabilization and aggregation

A stable colloid suspension is one that resists aggregation, and it is reached only under certain conditions. Electrostatic stabilization and steric stabilization are the two main mechanisms that impact colloid stabilization (Napper and Netschey, 1971). Electrostatic stabilization is based on the mutual repulsion of like-charged interfaces, and an unstable colloid suspension forms flocs as the particles aggregate due to interparticle attraction. This occurs either by adjusting the ionic strength or pH of the colloid suspension or adding a charged polymer flocculant. For the former, increasing the ionic strength or adjusting the pH near the pHPZC to neutralize or “screen” the surface charge of the colloid suspension reduces the electrostatic barrier which prevents aggregation. Therefore, repulsive forces which keep colloidal particles separate are overwhelmed by attractive vdW forces and aggregation of the particles occurs. Polymer flocculants destabilize colloid systems by bridging individual colloidal particles (Dickinson and Eriksson, 1991). Steric repulsive stabilization of colloidal particles arises when molecules such as high molecular weight

4 natural organic matter (NOM) adsorb on the particle surfaces, resulting in the production of a repulsive interaction (Mosley et al., 2003). This can be comprised of both an osmotic energy term to account for water exclusion around the molecule protruding from the particle surface and an elastic energy term due to the compression of the adsorbed molecule and its subsequent loss of configurational entropy (Mylon et al., 2010). Steric repulsion is dominant at very small separation distances (<10nm), at high ionic strength, as well as at pH values near the pHPZC when electrostatic repulsion is absent or minimal (Mosley et al., 2003).

1.3 Environmental behavior of colloidal particles

1.3.1 The existence of colloidal particles in natural environments

The environment of interest in this research is the subsurface which is comprised of a porous medium where solid, liquid and even air phases co-exist, such as is present in soils and groundwater systems. Colloids, no matter the origin, are abundant in such porous media environments. Such colloids could originate from natural processes as well as industrial, municipal or other anthropogenic sources and could be inherently toxic or pathogenic (McCarthy and Zachara, 1989; Wiesner et al., 2006). Colloids can also facilitate the migration of sparingly- soluble chemicals and pollutants (McCarthy and Zachara, 1989; Honeyman, 1999). Hazardous pollutants including many heavy metals, metalloids, radionuclides and hydrophobic organic contaminants are strongly sorbing substances which usually associate with solid phases, and consequently their aqueous concentration in pore water are small (Hofmann and Wendelborn,

2007; Persson et al., 2008; Hofmann and von der Kammer, 2009). The bulk solid matrix is stationary or migrates very slowly in the subsurface, so the associated pollutants would pose no or very little health risk at distant locations where drinking water sources or croplands are located.

However, colloidal particles can be mobile and act as vectors to enhance the migration of associated strongly bound contaminants.

1.3.2 Colloid-facilitated transport of pollutants in porous media 5

Although colloid-facilitated transport can occur in fractured media characterized as having a wide-range of hydraulic apertures facilitating colloid movement and limited matrix permeability hindering colloid movement (Saiers and Ryan, 2006; Zvikelsky and Weisbrod, 2006;

Zvikelsky et al., 2008; Missana et al., 2008; Zheng et al., 2009; Tang and Weisbrod, 2009, 2010), in this research the emphasis is on transport through granular porous media. Such media could be natural (e.g., gravel aquifer media (Walshe et al., 2010), sediment beds (Chen et al., 2009) and oil reservoirs), artificial (e.g., granular filters (Ternes et al., 2002)), or even membranes such as those used in drinking water treatment (Lee et al., 2000, Auset et al., 2005). Natural porous media grains are primarily silicate minerals and in laboratory conditions, people usually study colloid- facilitated transport by packing this porous media in a column. Other techniques can be used to study colloidal phenomenon, such as an impinging jet cell (Bayoudh et al., 2009; Tong and

Johnson, 2006), radial stagnation point flow systems (RSPF, Liu Y. et al., 2009), parallel-plate channels (Adamczyk et al., 2009; Kline et al., 2008) and micromodels (Kim et al., 2010; Auset and Keller, 2006), but their use in evaluating colloid-facilitated transport is quite limited.

Numerous studies have verified facilitated transport of colloid associated pollutants in field and packed bed column experiments (Kersting et al., 1999; Grolimund et al., 1996; Corapcioglu and

Jiang, 1993; Roy and Dzombak, 1997; Novikov et al., 2006). The main evidence of colloid- facilitated transport from these studies and others includes: (1) significant amounts of contaminants detected at farther distances than predicted by solute transport models (e.g.,

Utsunomiya et al., 2009) and (2) significant concentration of those contaminants associated with and detected in colloid phase (e.g., Delos et al., 2008).

1.3.3 Colloid transport and release in saturated porous media

The basic framework for describing the transport and deposition of colloid-sized particles in saturated porous media was developed in the 1970s by engineers primarily interested in improving the performance of packed bed filters used in water treatment (Yao et al., 1971; 6

Rajagopalan and Tien, 1976). Often when studied in the laboratory, a model porous media (e.g., glass beads, silica or quartz sand) is used instead of “real” natural porous media to minimize heterogeneities thereby allowing the study of specific colloid deposition and release mechanisms.

The selection of the colloid depends on the objectives of the study. For the purposes of evaluating specific mechanisms, ideal artificial colloids such as silica (Johnson et al., 1996) or latex microspheres (Liu et al., 1995; Tong and Johnson, 2007; Bradford et al., 2007; Tufenkji and

Elimelech, 2005b) are often used due to their homogeneous size and uniform chemical properties.

Colloids deposit on the surface of porous media either reversibly or irreversibly. Under favorable conditions, colloid deposition is well described by colloid filtration theory (CFT). Favorable means “favorable for deposition” and vice versa. In environmental contexts, unfavorable deposition conditions are typical and energy barriers hindering deposition exist due to the adsorption of natural organic matter to grain surfaces or other processes (Gupta et al., 2009).

Under such unfavorable conditions CFT does not work well (Bowen and Epstein, 1979; Gregory and Wishart, 1980; Tufenkji and Elimelech, 2004b, 2005a) and thus describing deposition and release processes under such conditions is a great challenge and it has been the center of intensive research.

1.3.3.1 Mechanisms inducing colloid deposition during transport

1.3.3.1.1 Heterogeneity

Heterogeneity in the colloid population or porous media is one of the most common reasons why colloids deposit during transport. Heterogeneities induce “holes” in the energy barriers where the barrier is reduced or eliminated. Sources of heterogeneity are diverse and include: (1) physical and chemical heterogeneities, (2) heterogeneities in the colloid population and grain media, and (3) heterogeneities in the flow conditions.

Physical and chemical heterogeneities are common on the surfaces of porous media grains and they can be patchwise in nature as well as nanoscale in size. Surface roughness of the 7 porous media, which may be etch pits with varying depth and density or surface steps distributed on grain surfaces, is one example of a physical heterogeneity (Shellenberger and Logan, 2002).

Smaller particles are more vulnerable to be deposited on rough surfaces, and etch pits more easily attract colloids than do surface steps (Darbha et al., 2010). Rough surfaces also perturb the fluid streamlines and result in an increase in the frequency of colloid-grain collisions (Saiers and Ryan,

2005) and strongly decrease hydrodynamic interactions (Bradford and Torkzaban, 2008). Surface irregularities may also lower the repulsive colloid-grain interactions thereby increasing the probability of attachment (Auset and Keller, 2006). Morales et al. (2009) investigated the role of the grain surface roughness on colloid deposition in the vadose zone, and found that grain roughness may influence colloid transport more in unsaturated porous media than saturated. In either case, smoother grain surfaces retained fewer colloids. Locally favorable charged sites on the surface of porous media grains due to the presence of metal oxide coatings is one example of a chemical heterogeneity. These can be evident by the release of previously deposited colloids upon altering the pore water pH (Alonso et al., 2009). Typically, the greater the extent of surface area covered by chemical heterogeneity, the greater is colloid deposition. Further evidence of the impact of heterogeneity is provided by Litton and Olson (1993) and Shani et al. (2008). They evaluated the role of grain surface preparation methods on grain surface properties and colloid deposition and found that colloid deposition was much higher with natural collectors than it was with the washed counterparts. Comparison of physical and chemical surface properties between the two implied that washed grains had changes (e.g., surface charge) resulting from cleaning procedures that resulted in less colloid deposition.

Natural colloids and mineral grains are inherently inhomogeneous in size, structure and hence physical and chemical properties. Tong and Johnson (2007) and Li et al. (2006a) demonstrated retained colloid profiles that decreased in a manner exceeding that predicted from

CFT (see Figure 2). Termed a “hyper-exponential profile” this behavior is thought to result from 8 heterogeneities in the colloid population. Tufenkji and Elimelech (2005a) attributed similar deviations from CFT to heterogeneities in the surface characteristics of either the colloid population or the porous media grains. This result was not consistent with that of Johnson and Li

(2005), however, because collector heterogeneities do not automatically generate the deviation observed in Figure 2. The influence of such heterogeneities also depend on flow rates, with

Chatterjee et al. (2010) reporting the deposition rate coefficient (kdep) for a heterogeneous colloid population only matching the predicted one from CFT under low flow velocities. At high velocities deviations result, and CFT overestimates kdep for big colloids (>2μm) and underestimates kdep for small colloids (<1μm). Size non-uniformity also contributes heterogeneities in grain media, but its impact is poorly understood and seems more important for unsaturated porous media (Mishurov et al., 2008).

Heterogeneities in flow conditions occur in hydraulically transient systems such as the vadose zone (Saiers and Lenhart, 2003) as well as in the complex pore space that exists in heterogeneous water-saturated natural porous media. Flow heterogeneities can induce different local velocities in the flow fields, characterized as mobile liquid zones, low velocity zones and immobile or flow stagnant zones (Bradford et al., 2009). This heterogeneity is the foundation of other colloid retention mechanisms such as deposition within the secondary energy minimum which will be discussed in detail later.

1.3.3.1.2 Straining

Straining in porous media is increasingly found to strongly influence colloid transport.

Straining includes not only colloid removal by pores smaller than the size of the colloid, but also incorporates removal at grain-grain and grain-wall contacts (Li et al., 2006b, Xu and Saiers, 2009;

Zhuang et al., 2005). Flow into grain-grain and grain-wall contacts can be sufficiently energetic to induce colloids to cross surface energy barriers at the grain surfaces and the colloids can be subsequently trapped (Li et al., 2006a), a phenomenon sometimes referred to as “wedging” 9

(Johnson et al., 2010; Kim et al., 2010). In general, straining happens when the size ratio of the particle to collector (dp/dc) is above a critical value (Knappett et al., 2008; Pelley and Tufenkji,

2008), and colloid straining rates increase with larger dp/dc (Xu et al., 2008). Various critical dp/dc values are reported, e.g., 0.005 (Johnson et al., 2007a; Ma et al. 2009), 0.003 (Bradford et al.,

2007), 0.008 (Xu et al., 2006) and 0.0017 (Bradford et al., 2002). Differences in this threshold dp/dc may reflect, but are not limited to, differences in flow velocities in the respective studies since straining increases at higher flow velocities (Johnson et al., 2007a). However, a seemingly different conclusion is made by Bradford et al. (2007), who proposed that increasing the system flow rate tends to decrease the amount of straining.

The occurrence of straining has many implications for colloid transport in porous media.

Generally the deviation in the deposition profile from CFT induced by straining tends to increase with increasing colloid size or decreasing grain media size (Bradford et al., 2006). Straining is depth-dependent and it is mainly observed at column inlets (Gargiulo et al., 2007; Johnson et al.,

2007b; Bradford et al., 2006). Straining is also dependent on the concentration of strained colloids, with Xu et al. (2006) observing that straining rate coefficients exponentially decrease with increasing concentration of strained colloids.

The occurrence of straining is also controlled by many chemical, physical and hydrodynamic factors. Shen et al. (2008) evaluated the role of solution ionic strength on colloid straining, and confirmed that the critical dp/dc is significantly reduced at higher ionic strength due to additional straining induced by colloid retention, predominantly in the grain-grain contacts.

This straining enhancement resulting from the change of solution chemistry may also help to explain the wide range in the reported critical values of dp/dc, especially under unfavorable conditions. Similar results are also reported by Torkzaban et al. (2008a), who asserted more colloids are retained in the secondary energy minimum at higher ionic strength. These retained colloids are prone to be translated to low velocity and flow stagnation zones, e.g., rear stagnation 10 points on the downstream side of grains and asperities (Li et al., 2006a) or leeward sides of protrusions (Johnson et al., 2007b) where grain-grain contacts or dead-end pores form, where they are more readily trapped. Other studies have different explanations for the effect of ionic strength on straining. Bradford et al. (2006) indicated at high ionic strength that colloids in small pores may experience attractive interactions up to five times larger than that predicted by DLVO theory. These enhanced interactions result in increased straining.

1.3.3.1.3 Deposition within the secondary energy minimum

Weakly adhesive interactions happen at zones where the fluid drag is low and overcome by secondary energy minimum interaction (Liu Y. et al., 2009; Li et al., 2010; Johnson and Tong,

2006). As the ionic strength increases, the magnitude of the secondary minimum is also enhanced and may be sufficient to not only overwhelm hydrodynamic drag forces but also exceed colloidal

Brownian diffusion forces (Torkzaban et al., 2007). The secondary minimum is also enhanced at pH values close to pHPZC (either colloid or grain media), as the surface potential as well as EDL interaction is very small at such condition. Under these conditions, the attractive vdW interactions dominate and the secondary energy minimum depth is increased (Johnson et al., 1996; Ryan et al.,

1999; Elimelech et al., 2000; Quevedo and Tufenkji, 2009). Colloids that associate with the secondary energy minimum are considered reversibly attached. Evidence in support of reversible attachment in the secondary minimum are found in studies that intentionally evaluate colloid release by perturbing system conditions, e.g., eluting column with low ionic strength solution after deposition (Canseco et al., 2009; Hahn et al., 2004; Ryan and Gschwend, 1994b).

1.3.3.2 Colloid release from saturated porous media

Colloid release (or mobilization) is an important, but poorly understood process that controls colloid migration in natural porous media. Under steady-state or equilibrium conditions

(Compere et al., 2001), the rate at which colloids are released is very slow. Fast release is observed, however, as the result of a disturbance in the system (Bridge et al., 2009; Zhuang et al., 11

2007; Abadzic and Ryan, 2001). For example, hydrodynamic or physicochemical perturbations resulting from rain infiltration, artificial recharge or drainage events can induce the detachment of existing or previously deposited (in-situ) colloids from their contacting points within the porous media into the pore fluid. If the released colloids are stable, they can travel significant distances.

For saturated systems, rapid colloid release is usually in response to a perturbation of solution chemistry or flow conditions in the system. In general, under unfavorable conditions, colloid release is associated with an increase in fluid velocity (Johnson et al., 2010) or variation in solution chemistry. The latter includes alteration of pH (Hahn et al., 2004) or reduction in ionic strength (Lenhart and Saiers, 2003). This results in an increase in the height of the energy barrier and a decrease in the depth of the secondary minimum. The depth of the primary minimum is only slightly affected (see Figure 1) and thus released colloids presumably are only those held within the secondary minimum. Figure 3 (Canseco et al., 2009) is a typical summary depiction of how stepwise changes in ionic strength induce stepwise colloid release in saturated porous media.

The colloid release is often studied in column systems by depositing colloidal particles under designated initial deposition conditions and subsequently changing a particular system parameter of interest (e.g., ionic strength) from the initial state to the desired state. Coincident with the passage of the perturbation, a pulse of released colloids is observed (see Figure 3).

1.3.3.2.1 Release kinetics

Recognition of the significance of release to colloid transport has resulted in extensive research of the governing processes, however, many questions remain. Early studies focused on the role of interaction potentials on release rates assuming colloids overcame the energy barrier and were released to bulk solution phase (Ruckenstein, 1978). The influence of the secondary minimum was ignored. Work at this time also emphasized release induced by hydrodynamic forces (Dahneke, 1975). Particle release under these conditions was described as being a first order reversible process as influenced by diffusion across the interaction potential (Ruckenstein 12 and Prieve, 1976). Grolimund and Borkovec (1999, 2006) evaluated the release of colloidal particles from natural porous media over long time periods, and reported the release process was not based on simple first order kinetics (exponential style) because the experimental effluent concentration decayed not in an exponential fashion but rather seemed to follow a power law.

Various studies simulated the release kinetics as a function of changes in ionic strength; however, the differing kinetic expressions make direct comparisons difficult. For example, Grolimund and

Borkovec (2006) observed that the release rate coefficient used in a power law kinetics expression increased with decreasing ionic strength. Roy and Dzombak (1996) used a first-order expression and observed that the release rate constant was insensitive to changes in ionic strength, and they attributed this result to colloid population heterogeneity. Lenhart and Saiers (2003) explicitly considered heterogeneity of interaction energies between deposited colloids and grain surfaces by dividing the immobile colloidal group into several compartments with each one assigned a critical release concentration based upon a distribution in attractive interactions. This distributed approach fits well the pulse type releases induced by stepwise variations in ionic strength. The resulting release rates appeared to primarily depend on the initial colloid deposition conditions. Tosco et al. (2009) performed research similar to that of Lenhart and Saiers (2003) but applied a transient dual site (unfavorable and favorable attachment sites) model so as to relate release rate coefficients with ionic strength. It should be noted that none of the above studies explicitly considered the dominant role of the secondary energy minimum on colloid release kinetics, and that specific knowledge regarding release rates is still lacking and thus colloid release phenomena warrant further investigation.

1.3.3.2.2 The role of transient conditions in ionic strength, pH or flow rate

The phenomenon of colloid release induced by a reduction in ionic strength has recently been attributed to the release of colloids previously deposited in the secondary energy minimum

(Hahn and O’Melia, 2004). These colloids are depicted as having only a “loose” association with 13 collector surfaces (Johnson et al., 2007c) and since the secondary minimum associated colloids are believed to be reversibly retained (Johnson et al., 2007a), they can be spontaneously released to bulk solution when the potential energy level in the secondary minimum is comparable to the average Brownian kinetic energy (McDowell-Boyer, 1992). Such a comparison was quantitatively realized by a Maxwell model utilized by Hahn and O’Melia (2004) and Shen et al.

(2007) to evaluate the role of the secondary energy minimum on colloid deposition and reentrainment.

Changes in solution pH also can induce colloid release. This is thought to occur for two reasons. For heterogeneous porous media, small portions of deposited particles can be eluted upon the introduction of a high pH solution because this solution is thought to reverse the charge on localized patches of attractive surface interactions. Increasing the pH to the extent that it exceeds the pHPZC of these attractive patches presumably reverses the electrostatic interaction producing the subsequent colloid release (Johnson et al. 2007b; Abudalo et al., 2005). Increasing pH can also increase the energy barrier height and decrease the secondary minimum depth thereby spurring release (Canseco et al., 2009). In the context of DLVO theory, however, the former explanation ignores the fact that colloids held within a primary energy minimum are unavailable for release.

Transients in flow are also known to spur colloid release, with flow rate increases normally leading to greater amounts of released colloids (Ryan and Gschwend, 1994a; Shang et al., 2008). Bergendahl and Grasso (2000) describe this physically based colloid detachment as originating from the primary energy minimum and reported half detachment flow rates based on a moment analysis between applied and resisting torques. Previously deposited particles can inhibit the further deposition of particles due to electrostatic repulsion, and increasing flow velocity could enhance this effect and even induce colloid detachment (Johnson et al., 2007b). This phenomenon was termed by Ko and Elimelech (2000) as the hydrodynamic “shadow” effect. 14

Initial deposition is not expected to occur within such hydrodynamic shadows, but colloid translation following initial deposition may “concentrate” colloids on leeward sides of grain surfaces, and detachment of a particle increases the hydrodynamic drag forces experienced by adjacent attached colloids (Ko and Elimelech, 2000). Johnson et al. (2007b) summarized three possible mechanisms of colloid re-entrainment by hydrodynamic drag: (1) increased diffusion

“out” of the secondary minimum driven by increased colloid concentration gradient away from accumulation zones (e.g., rear stagnation points); (2) increased magnitude of hydrodynamic collision between mobile and surface-associated colloids; and (3) increased dominance of hydrodynamic drag torques relative to adhesive torques.

Table 2 summarizes the representative studies evaluating colloid release in saturated porous media, and we see that these studies either ignored the dominant role of the secondary energy minimum on colloid release, or failed to quantitatively relate the magnitude of colloid release with the extent of perturbation (e.g., decrease in ionic strength). These areas are the focus of this research.

1.3.3.3 Other influential factors for colloid deposition and release

In addition to the previously mentioned processes, there also exist a number of other factors that contribute to colloid transport and release in porous media. These are mainly physical differences in the materials or system studied that may or may not induce chemical differences.

Obviously, colloid transport depends upon the properties of the colloids and porous media, but subtle differences in the materials may modify the resulting behavior. For example, quartz sand packed columns are thought to have more grain-grain contacts than equivalently sized glass beads due to enhanced angularity of the sand which increases grain-grain contacts and the percentage of smaller pores (Li et al. 2006a, 2006b; Liu XY. et al., 2009).

Grain and colloid shape also influence transport, with non-spherical grain shapes influencing the transport of small and large colloids more than those considered mid-sized (1- 15

2μm) (Saiers and Ryan, 2005; Knappett et al., 2008). The colloid shape is also important, with rod-like colloids being strained to a lesser extent than similarly-sized spherical particles (Liu et al.,

2010). As the aspect ratio increases, however, removal also tends to increase (Salerno et al.,

2006).

Size exclusion, pore blocking and filter ripening are additional physical factors that influence colloid transport. Size exclusion occurs commonly in natural porous media (Delos et al.,

2008) and is the result of the preferential transport of colloids through large flow channels. This results in the breakthrough of a portion of the colloid suspension prior to solute molecules which presumably sample the complete spectrum of available flow channels (Bradford et al., 2006).

Over longer transport distances, however, size exclusion becomes less of a factor (Ahfir et al.,

2009). Pore blocking and filter ripening are both related to the influence of deposited colloids on the continued deposition of additional particles. In the case of pore blocking, deposited colloids act to inhibit additional deposition due to electrostatic or steric effects (Rijnaarts et al., 1996;

Camesano and Logan, 1998). Filter ripening has the opposite effect and it reflects enhanced deposition resulting from attractions that may exist between deposited particles and those within the pore fluid (Nascimento et al., 2006; Shiratori et al., 2007). Filter ripening is often triggered by an increase in ionic strength or decrease in flow velocity (Tong et al., 2008).

Finally, natural organic matter (NOM) also influences colloid transport, as it can alter or control the surface characteristics of surfaces upon which it adsorbs. Depending upon the specific system, adsorbed NOM can significantly modify surface charge and in some instances it can completely reverse it (Abudalo et al. 2010; Ryan and Elimelech, 1996). This is one of the reasons that natural colloidal substances almost always have a negative surface charge (Schafer et al.,

2000). This adsorbed layer of NOM can subsequently alter electrostatic interactions as well as steric interactions, typically increasing both (Sirk et al., 2009), resulting in a decrease in colloid deposition (Phenrat et al., 2010; Johnson RL et al., 2009; Wang et al., 2008; Domingos et al. 2009; 16

Walshe et al. 2010).

1.3.3.4 Mathematical description of colloid transport and release

1.3.3.4.1 One dimensional transport modeling

Laboratory experimental systems using packed bed columns typically employ columns with an inner diameter smaller than the length and thus transverse dispersion is negligible. To describe colloid transport under such unit gradient flow conditions it is typical to use the one- dimensional form of the convective-dispersive model for solute transport supplemented with expressions to describe colloid deposition and release. First-order deposition and release terms are most commonly used resulting in the following equations (Johnson et al., 2007b):

C  2C C  S  D  v  b t x 2 x  t (3) where C is the aqueous concentration of colloid (number of particles mL-1), x is the transport distance from the column inlet (m), t is time (s), v is average pore water velocity (m s-1), D is the hydrodynamic dispersion coefficient (m2 s-1), θ is porosity, ρ is the bulk density of the porous b media (g mL-1), and S is the concentration of deposited colloids (number of particles g-1). The average pore water velocity v is given by the ratio of Darcy velocity or approach velocity (U, m s-

1) and porosity:

U v   (4) v and D are derived by fitting a tracer (an inert, conservative, non-sorbing and nonreactive solute) breakthrough curve to equation (3) modified to remove the influence of deposition as follows:

C 2C C  D 2  v t x x (5) The fitted v should be quite close to that calculated based on the Darcy velocity. Usually we assume D is the same for both colloid and tracer solute, and this assumption should be valid since

Brownian movement is negligible compared with the pore fluid movement, so D is just a property 17 of porous medium only (Baumann et al., 2010). The solid concentration of deposited colloids is related with the deposition and release terms by:

b S b  kdepC  k relS(1 firr )  t  (6)

-1 where kdep is the apparent deposition rate coefficient (s ), krel is the apparent release rate

-1 coefficient (s ), firr accounts for the fraction of deposited colloids which are irreversibly attached.

Equation (6) demonstrates that the accumulation of deposited colloids on grain surfaces is the net of particle deposition and release.

1.3.3.4.2 Colloid filtration theory

Colloid filtration theory (CFT) utilizes a pore space geometry called Happel’s sphere-in- cell model (Happel, 1958). This model describes porous media as a solid sphere encircled by a larger spherical fluid shell, the thickness of which is chosen such that the unit cell porosity is equal to porosity of the whole packed bed. CFT does very well in capturing processes of fluid flow and colloid transport in porous media in the absence of energy barriers. It provides a quantitative prediction of particle removal as a function of particle and collector size, fluid velocity and other parameters, and it describes removal as a two-stage process: colloid collision or contact with the grain and colloid attachment to the grain. The probabilities of occurrence for these two stages are known as η (collector or contact efficiency), which is the ratio of number of colloids colliding with the collector to number approaching the collector, and α (collision or attachment efficiency), which is the ratio of number of attached colloids to number of colloids colliding with the collector, respectively (Bales et al., 1991). The contact efficiency is calculated based on physical principles and certain assumptions about the porous media, such as perfect sphericity and uniform grain size. For many years, researchers have been improving the predictability of η by modifications of its empirical equation. One of the earliest and most widely

18 used equations was proposed by Rajagopalan and Tien (1976) and it is sometimes noted as the R-

T equation:

  4A 1/ 3N 2/ 3  A N 1/8N 15/8  0.0038A N 6/ 5N 2/ 5 s PE s Lo R s G R (7)

As is the parameter for Happel’s sphere-in-cell model, as defined by:

5 1 2(1  ) where   (1 ) 3 As  5 6 (8) 2 3  3  2

NPE is the Peclet number, which is the ratio of the colloid advection rate by fluid flow to the diffusion rate, and it is given by the equation below with dc (μm) equal to the diameter of the collector.

Ud c NPE  D* (9)

D* is bulk molecular diffusion coefficient in pore space (m2 s-1) and it is calculated using the

Stokes-Einstein equation (Baumann et al., 2010):

kT D*  3d p (10) where μ is the viscosity of the water. NLo is the London number and it combines the influence of vdW attraction and fluid velocity on particle deposition rate due to interception.

4A N  Lo 9d 2 U p (11)

The Hamaker constant (A) is calculated based on a colloid1-collector2-solution3 system, and the number 1,2,3 are the subscripts. One equation to calculate A is shown as (Elimelech et al., 1995):

A  A A 132 131 232 (12)

A131, A232, and A132 are the Hamaker constants for the colloid-solution-colloid, collector-solution- collector, and colloid-solution-collector, respectively. NR in equation (7) is the aspect ratio or interception number, which is the ratio of colloid diameter to that for the collector, dp/dc. NG in

19 equation (7) is the gravity number, which is the ratio of the Stokes particle settling velocity to the

-3 fluid approach velocity. The equation for NG is shown below with ρp and ρf (kg·m ) representing the densities of the particle and fluid, respectively.

(   )gd 2 N  p f p G 18U (13)

g is the acceleration due to gravity. The R-T equation is the sum of three independent transport mechanisms, diffusion, interception and gravitational sedimentation, and it has been widely used for years to estimate colloid transport and deposition in saturated porous media under favorable conditions. Tufenkji and Elimelech (2004a) proposed a new equation that modifies the original R-

T equation by considering hydrodynamic interactions and universal vdW attractive forces. It

incorporates these interactions into the traditional dominant transport mechanisms: diffusion,

interception and sedimentation, and therefore improves predictions of the collector efficiency

over a wide range of conditions encountered in natural or engineered aquatic systems. This correlation equation (T-E equation), which will be applied in this research, is depicted as follows:

  2.4A 1/ 3N 0.081N 0.715N 0.052  0.55A N 1.675N 0.125  0.22N 0.24N 1.11N 0.053 s R PE vdW s R AT R G vdW (14)

This expression includes parameters from the R-T equation plus NvdW, which is the van der Waals number, and NAT, the attraction number. The van der Waals number is the ratio of the vdW interaction energy to the particle’s thermal energy:

A N vdW  kT (15) The attraction number is very similar to the London number:

3 A N  N  AT 4 Lo 3Ud 2 p (16)

Alternative expressions have also recently been presented by Johnson and Ma based on a pore space geometry called Hemispheres-in-cell model (Ma et al., 2009; Ma and Johnson, 2010), and

20 by Long and Hilpert (2009) based on a numerical Lattice-Boltzmann simulation for Brownian particles (size 50-300nm). All of the expressions depict mid-sized particles (1-2μm) as being least attached in porous media since these colloids experience less diffusion relative to smaller colloids and less gravitational settling relative to larger colloids (Gupta et al., 2009).

After derivation of η, the collision efficiency (α) which depends on the solid surface and aqueous chemistry, can be calculated by fitting an empirical equation to the early-stage breakthrough of a colloid suspension under clean bed conditions (Bales et al., 1991; Zhang et al.,

2010):

C 3(1 )L ln eff   C 2d 0 c (17) where L (m) is the column length or transport distance at the monitoring point, and Ceff is the total effluent colloid concentration (number of particles mL-1). Given calculated values for η and those for α based on fits to experimental data allows for the calculation of the rate constant for deposition, kdep, based on first-order kinetics (Bales et al., 1991):

3(1 )v k  dep 2d c (18)

The theoretical retained profile S(x) at a given time period t0 (duration of deposition run) is expressed as (Foppen et al., 2007):

t C k k S(x)  0 0 dep exp( dep x)  v b (19)

In the event that particles are also retained in a reversible equilibrium fashion, equation (3) can be supplemented with a hydrodynamic retardation factor R as follows:

C D  2C v C  S    b t R x 2 R x  t (20) where R is defined as:

b R 1 Kd  (21) 21

3 -1 In this expression, Kd (m kg ) is a partitioning coefficient that depicts the linear deposition of colloids in an equilibrium fashion.

1.3.3.4.3 Colloid deposition under unfavorable deposition conditions

Typical experimental studies (e.g., Li et al., 2008) show that theoretical collision efficiency, αthe, computed by DLVO theory are much lower than those calculated from fitting equation (17) to experimental breakthrough data. This discrepancy is often attributed to the fact that DLVO, hence CFT, fails to account for colloid deposition as the result of heterogeneity, straining, and attraction due to the secondary energy minimum interaction. This discrepancy has spurred considerable research interest. For example, straining can be incorporated into equation

(3) by adding an additional kinetic term, assuming depth dependent first-order removal (Choy et al., 2008; Bradford et al., 2003).

 S b Str  kStrStrC  t (22)

-1 -1 where SStr is the solid concentration of colloid deposited due to straining (g ), kStr (s ) is a first order straining rate coefficient, ψStr is a dimensionless straining function accounting for the depth- dependent straining behavior, which is given by the following expression where β is the fitting parameter, and SMaxi is the maximum concentration of colloid deposited due to straining:

S x   (1 Str )(1 ) Str S d Maxi c (23)

In a similar manner, kinetic expressions to account for particle deposition in the secondary energy minimum have been proposed (Shen et al., 2008).

 S  b Sec b  kSecSecC  k relSSec  t  (24) where SSec is the solid concentration of colloid deposited due to the secondary energy minimum

-1 -1 (g ), kSec (s ) is a first order secondary energy minimum associated rate coefficient, ψSec is a dimensionless colloid blocking function to account for the limited sites within the secondary

-1 minimum, and krel is the apparent colloid release rate coefficient (s ). This can be estimated assuming SMax is the maximum secondary energy minimum associated solid concentration of deposited colloids (g-1).

S  1 Sec Sec S Max (25)

1.4 Research objectives

Colloid deposition or removal during transport through saturated porous media has been extensively studied during the past decades; however, many questions remain regarding how the secondary minimum influences colloid deposition and release, particularly release. Therefore, in this research the roles of the secondary energy minimum in colloid deposition and release will be targeted, with the main research objectives being to:

(1) Both qualitatively and quantitatively describe the effects of solution ionic strength, pH, and particle size on colloid transport and release behaviors.

(2) Propose a conceptual model to fully describe both the global and local colloid release processes under the framework of the secondary energy minimum.

This thesis is organized into 3 chapters. In the first chapter the background and introductory material necessary to form a basis to understand the research is presented. In the second chapter, the body of the research effort is presented evaluating the transport of two different sized colloids through water-saturated quartz sand. Detailed properties of colloid and porous media are presented as are experimental results evaluating the transport of an inert tracer and the colloids. Supplementing these are data evaluating the spatial distribution of retained colloids and multistep colloid release experiments. Calculated interaction potentials for the colloid-sand system are presented and a conceptual model to capture how varying ionic strength results in colloid release due to shifts in the secondary energy minimum well is proposed. The

23 final chapter will discuss the deficiencies or limitations of the current theories and practices, and propose several research directions.

List of Tables in Chapter 1

Force Assumptions and constraints References sphere-plate model, assume constant surface potential Hogg et al., 1966 EDL sphere-plate model, assume constant surface charge Wiese and Healy, 1970 sphere-plate model, assume linear superposition approximation Verwey and Overbeek, 1948; Gregory, 1975 sphere-sphere model, assume linear superposition approximation Weronski et al., 2003 sphere-plate model, unretarded interaction at h<5nm Gregory, 1981 vdW sphere-plate model, retarded interaction at h>5nm Gregory, 1981 sphere-plate model, based on surface element integration, for small Li YS et al., 2008 spherical particles and h is the same order of magnitude with particle size Table 1. Models widely used for EDL and vdW calculations

No. Reference Colloid Release Details colloid type and size porous media type and parameters (flow velocity, size ionic strength or pH) perturbed to induce release 1 Ryan and hematite colloids quartz sand (210-300μm) ionic strength, pH and flow Gschwend, 1994a (150±35nm) velocity 2 Roy and natural colloids (60-70% natural sands (Lincoln ionic strength Dzombak, 1996 silica and 20-30% clay and Otis sand, 250 and minerals, <1μm); 550μm in average, polystyrene latex spheres respectively); glass (468nm) beads (400-520μm) 3 Bergendahl and carboxylate-modified glass beads (425-600μm) ionic strength, pH and flow Grasso, 2000 polystyrene latex velocity microspheres (1000nm) 4 Lenhart and amorphous spherical silica quartz sand (300-355μm) ionic strength Saiers, 2003 colloids (282±7nm) 5 Franchi and sulfate latex microspheres soda-lime glass beads ionic strength O’Melia, 2003 (98nm) (200μm) 6 Hahn et al., 2004 latex particles (72, 308, 683 glass beads (200 and ionic strength and pH and 1060nm); hematite 400μm) particles (80nm) 7 Tong and Johnson fluorescent carboxylate- soda-lime glass beads ionic strength and pH (2006) modified polystyrene latex (417-600μm) microspheres (100, 200, 500, 1000, 2000nm); amine- modified polystyrene latex microspheres (1000nm) 8 Shen et al. (2007) polystyrene latex particles quartz sand (300-355μm) ionic strength (20, 1156nm) 9 Tong and Johnson carboxylate-modified soda-lime glass beads ionic strength (2007) polystyrene latex (417-600μm) microspheres (100, 200, 500, 1000, 1100, 2000nm) 10 Tosco et al., 2009 carboxylate-modified latex natural sand (composed ionic strength microparticles (1.9μm) by quartz and a minor content of K-feldspar, 150-300μm) Table 2. Representative studies evaluating colloid release in saturated porous media

List of Figures in Chapter 1

150 20 electrostatic A B van der Waals 100 net interaction 100mM 10mM 10 ϕMax 1mM

50 secondary energy minimum

ϕ kT

/ 0 ϕ 0

-50 primary energy minimum

-100 -10 0 5 10 15 20 0 30 60 90 120 separation distance (nm) separation distance (nm)

Figure 1. (A) Typical repulsive, attractive and total interaction energy curves between a sphere and a flat plate based on DLVO theory assuming constant surface potential. ap=490nm, I=0.1M, T=298K. (B) Interaction energy curves of sphere-plate case for separation distances from 0 to 120nm at different ionic strength levels. Assuming constant surface potential interaction. ap=490nm, T=298K.

A B C

Figure 2. Representative experimental results and simulations from Tong and Johnson (2007), showing retained profiles for (A) 0.1μm, (B) 0.5μm, and (C) 2.0μm microspheres. The fluid velocity was fixed at 4m day-1. The ionic strength was 0.02M for the 0.1 and 0.5μm microspheres and 0.05M for the 2.0μm microspheres. The black solid line in each panel represents simulation with a single deposition rate coefficient and the blue dashed line represents simulation with a log- normally distributed deposition rate coefficients.

Figure 3. Deposition BTC followed by five release pulses performed at different ionic strengths

(Canseco et al., 2009)

CHAPTER 2: EVALUATING THE ROLE OF THE SECONDARY ENERGY MINIMUM IN COLLOID DEPOSITION AND RELEASE IN SATURATED POROUS MEDIA: EFFECT OF SOLUTION CHEMISTRY

2.1 Introduction

Colloids are ubiquitous in the subsurface and if mobile they can act to enhance the mobility of strongly sorbing contaminants, a phenomenon called colloid-facilitated contaminant transport (McCarthy and Zachara, 1989). Contaminants associated with mobile colloids could migrate faster and farther than predicted, and thus pose a potential risk to human health and groundwater resources (Grolimund et al., 1996; Flury and Qiu, 2008). Some colloid-sized particles such as pathogenic microorganisms are contaminants themselves. These microbes or mineral colloidal particles enter groundwater via crossing the water table from the vadose zone or by seeping from surface water bodies such as lakes and rivers (Ryan and Elimelech, 1996). The complex delivery and transport processes are controlled by a number of factors and processes including colloid deposition or immobilization, and colloid release from the stationary interfaces

(Saiers and Ryan, 2006). Laboratory and field studies have demonstrated that immobilized colloids are readily released into aqueous phase in porous media (Seaman et al., 1995). Processes responsible for rapid colloid release such as perturbation in aqueous phase chemistry have been identified (Swartz and Gschwend, 1998; Gao et al., 2006). The mass of colloids released appears to reflect the magnitude of ionic-strength reduction (Ryan and Gschwend, 1994a), and stepwise decreases in ionic strength produce multiple pulses of released colloids (Roy and Dzombak,

1996). Semi-empirical quantitative models have been proposed to assist in interpreting the release processes under saturated conditions (Lenhart and Saiers, 2003; Tosco et al., 2009); however,

29 these approaches do not explicitly account for the important contributions of the secondary energy minimum which has recently been highlighted to be a dominant process controlling colloid mobility in saturated porous media under unfavorable conditions (Hahn et al., 2004;

Franchi and O’Melia, 2003; Shen et al., 2007; Tong and Johnson, 2007).

Under unfavorable conditions when repulsion between colloid and collector exists and the energy barrier is present, colloid filtration theory (CFT) fails to explain colloid deposition behavior (Tufenkji and Elimelech, 2005a). Three major reasons have been proposed to account for the unexpectedly high colloid deposition under these conditions; heterogeneity, colloid straining, and retention within the secondary energy minimum (Song et al., 1994; Bradford et al.,

2002; Johnson et al., 2007c). Among these mechanisms, colloids retained via the secondary energy minimum are assumed to be reversibly attached to the collector surfaces (Johnson et al.,

2010). The nature of this association depicts colloids at the secondary minimum being capable of translating along the collector surfaces into relatively low flow drag or flow stagnation zones

(Johnson et al., 2007a). Colloids retained within the secondary energy minimum are thought to be able to be released based upon partial or full removal of the secondary energy minimum

(Torkzaban et al., 2010). Colloid release from the primary minimum, however, requires the colloids to overcome very high energy barriers (Bai and Tien, 1997) and this will occur at exceedingly low rates based upon an Arrhenius law type relationship (Canseco et al., 2009).

Therefore, one approach to explain reversible colloid deposition is based on deposition occurring between non-contacting surfaces that presumably occurs during secondary energy minimum governed association. Under highly unfavorable conditions, the secondary energy minimum is negligible and does not account for any colloid deposition. As the system conditions become more favorable for colloid interaction by increasing the ionic strength, for example, the height of the energy barrier is reduced and the secondary well is deepened (Canseco et al., 2009).

More colloids are deposited within the secondary energy minimum under these conditions 30

(Redman et al., 2004). When the ionic strength is high enough to reduce the energy barrier to less than 10kT (Hahn and O'Melia, 2004), the primary energy minimum starts to dominate colloid attachment. Dual mode deposition (Tufenkji and Elimelech, 2004b), which combines both the primary and secondary energy minima should happen from this point. Purely secondary energy minimum deposition should occur during the interval from its “emergence point” to the end point when the energy barrier height is 10kT. This emergence point is theoretically a particular ionic strength that corresponds to when the secondary energy minimum is just balanced by the

Brownian kinetic energy and hydrodynamic interactions. Under these conditions, the secondary minimum potentials should be sufficient in magnitude to overcome average fluid hydrodynamic drag and colloidal Brownian diffusion interactions in order to retain colloids within the secondary well (Torkzaban et al., 2007; Li et al., 2005). Compared with the relative clarity of this deposition process, rationalizing the inverse process that occurs when the ionic strength is decreasing is more elusive. Either sudden (one step decrease in ionic strength to deionized water) or gradual release (multiple step decrease from the initial ionic strength to deionized water) experiments have been conducted to evaluate the response of deposited colloids (Hahn et al., 2004; Canseco et al., 2009). These experiments have provided phenomenological insight into release patterns, for example, a single sharp peak or several peaks with extended tailing which may reflect different release kinetics. However, many unknowns remain regarding colloid transport during transient solution chemistry conditions and additional research is warranted to fully understand colloid release processes, kinetics and mechanisms.

In this study we carried out column experiments based on a model colloid-collector system in order to gain more insight into how the secondary energy minimum influences colloid release processes in saturated porous media. The experiments are conducted to study two different sized colloids at a series of ionic strength and pH conditions. A conceptual model was also developed to capture the processes of colloid release linking initial deposition. Three key 31 assumptions underlie this model. First, colloid release based on non-surface-contacting deposition

(i.e., separation distance larger than that to the primary energy maximum) controlled by the secondary energy minimum, occurs at a particular range of ionic strength values. Second, hydrodynamic and Brownian interactions as well as the secondary minimum attractive interaction all follow statistical distributions in local flow velocities, local colloidal Brownian motion velocity, and separation distances across the secondary well, respectively. Third, the local colloid release magnitude should be correlated to the extent at which the inducing parameters (e.g. solution chemistry, flow velocity) are varied and the corresponding modification of the secondary energy well. The approach balances local colloid release at specific locations with global release throughout the system. Local release is induced by squeezing the resident domains of retained colloids as the result of decrease in retention capacity of the secondary energy minimum, but global release could be much different as it combines multiple release and deposition processes.

2.2 Materials and methods

Unless otherwise specified, all analytical reagents used were ACS certified or better.

Deionized (DI) water (Milli-Q Plus, Millipore Corporation) was used in all experiments. Glass and labware for all experiments were subject to acid wash (10% HCl) overnight followed by DI water rinse and air-drying. All aqueous solutions were filtered by membranes with a pore size of

0.2μm (Whatman). All experiments were performed in duplicate or triplicate.

2.2.1 Model colloids

Two different-sized FluoSpheres® surfactant-free carboxylate-modified polystyrene microspheres (Invitrogen Life Technologies) with nominal diameters of 40nm and 500nm were used in this research (see Table 1 for a summary of manufacturer’s reported properties). These particles are yellow-green fluorescent and were received in an aqueous suspension. The 40nm and

500nm microspheres were received as 1mL and 10mL in volume, respectively. These suspensions were diluted with DI water by a factor of 50 to form 50mL and 500mL stock solutions, 32 respectively, and stored at 4℃. The 500nm microsphere suspension contained 2mM azide. This was removed prior to dilution by dialyzing (cellulose ester tubing, 100-500D, flat width 10mm,

Spectrum Labs) the original suspension against DI water. Transmission Electron Microscopy

(TEM) was used to collect images of the particles to confirm size and morphology. This was done by air-drying one drop of aqueous phase colloids (dialyzed to remove residual salts) at a particle concentration used for the transport experiments on a Formvar/Carbon coated grid. The particles were directly observed using a FEI Tecnai G2 spirit Biotwin TEM (FEI Worldwide Corporate) at

80kV. Images were collected digitally at a magnification of 98000x and 18500x for 40nm and

500nm colloids, respectively. The electrophoretic mobilities of the colloids were measured at

22±0.5℃ across the range of pH and ionic strength values studied using a Brookhaven Instrument

Corporation’s Zeta PALS instrument. In all instances, the microsphere suspensions were sonicated for 2 minutes prior to use in order to disrupt possible aggregates.

2.2.2 Model porous media

Quartz sand (Accusand 50/70, Unimin Corporation) was used as the model porous media in this research. The fraction of sand between 0.25mm and 0.3mm was isolated for use with stainless steel sieves. Prior to use, the sieved sand was thoroughly cleaned to remove all impurities following a procedure modified from Lenhart and Saiers (2002). The sand was first washed in deionized (DI) water until the rinse water was transparent, followed by an acid wash

(1L acid per 1kg sand) with 10% HNO3 for 48hrs. The sand was subsequently rinsed with DI water until a near neutral pH was reached. Finally, the sand was base washed (1L base per 1kg sand) with 5M NaOH for 48hrs and again rinsed repeatedly with DI water until the pH was stable.

The sand was finally dried at 60℃ for 24hrs and stored in a clean HDPE (high-density polyethylene) container for further use.

Prior to use, the sand was thoroughly characterized to determine its electrokinetic properties, specific density and surface morphology. A portion of the clean sand (around 10g) 33 was put in a beaker (250mL) filled by DI water, then the beaker was sonicated for 20mins in order to release colloid-sized fragments of sand. This supernatant containing the colloidal sand was collected and used to prepare a series of dilute suspensions at pH (5-11) and ionic strength

(0.05mM-100mM) conditions identical to those used to characterize the microspheres.

Electrophoretic mobility values were measured and zeta potentials were calculated for the bulk sand grains following Tufenkji and Elimelech (2004b). The hydrodynamic size of these particles was measured using dynamic light scattering (90 plus, Brookhaven Instrument Corporation).

Gravimetric analysis was carried out to determine the sand density and scanning electron microscopic (SEM) images were taken with an FEI Nova Nano-SEM 400 (FEI Worldwide

Corporate) for sand surface characterization. For the SEM images, sand grains were attached to double-sided carbon tape affixed to SEM stubs. Images were collected using an Everhart-

Thornley detector (5kV, 50x and 1000x magnification).

2.2.3 Column experiments

2.2.3.1 Experimental setup

All experiments were carried out using one-dimensional flow-through columns under conditions representative of subsurface water flow or engineered granular filtration systems using the system setup depicted in Figure 1. Glass chromatography columns (Chromaflex®, Kimble

Kontes) with an inner diameter of 1cm and length of 30cm were utilized in our column experiments. Each column was supplied with one fixed and one adjustable PTFE

(polytetrafluoroethylene) end fitting with porous HDPE bed supports of 20μm pore size. Flow to the column was provided by a digital isocratic pump (ISO-100 Chrom Tech, Inc.). PTFE tubing of 1/16 inch diameter and three way valves (Hamilton Company) were used to switch between the different influent solutions and to control flow pathways.

Sample solution was extracted for flow to the column by the pump from a beaker or bottle at a flow rate of 0.3mL/min. The solution was passed through a pulsation dampener and a 34 backpressure regulator (250psi) to achieve steady and uniform flow. Flow was directed to a vertically positioned column from the bottom. Prior to packing, the column was half filled to clear air bubbles from the flow path. The upward flow direction can influence gravitational deposition, but for the size of colloids examined here it has no significant impact (Chen et al.,

2010). Before placement in the column, a fraction of the clean sand (approximately 21g) was placed in a beaker with DI water and sonicated to remove colloid-sized sand particles. The wet sand was gradually introduced into the column with constant gentle tapping of the column until a depth of 15cm was reached. The sand was always below the solution level to ensure full saturation. The adjustable fitting was inserted in the column from the upper end until it touched the top flat surface of the wet packed sand. Excess solution was removed via tubing connected to the fitting. The average porosity of the sand pack, calculated from the total sand mass used in each column (20.8±0.2g) and the experimentally determined quartz sand density

(2.60±0.10g/cm3), was 0.321±0.019. This results in an average column pore volume of 3.78mL based on total sand pack volume (1cm diameter and 15cm height). The packed column was pre- equilibrated by pumping a sufficient volume of the background solution until the effluent pH was similar to the influent pH and the effluent turbidity was near that of DI water.

2.2.3.2 Tracer experiment

A tracer experiment using a solution of NaBr was carried out in duplicate to confirm flow was uniform and one-dimensional, and to determine the dispersion coefficient of the column. A background electrolyte of 10mM NaCl was used to pre-equilibrate the packed column at a flow rate of 0.3mL/min, and 20mL NaBr (10mM) was injected without pH adjustment. The effluent solution was collected by a fraction collector (Retriever® 500, Teledyne Isco, Inc.) based on a fixed time interval (4min). Before the desired sample collection, gravimetric analysis was carried out to make sure the actual effluent solution (using background electrolyte NaCl) flow rate matched the one displayed on the digital pump. Differences were generally no more than 1%. To 35 measure bromide, 1mL was extracted from each effluent sample (approximately 1.2mL in total based on a 4min interval) and diluted by 6-fold. The concentration was measured using a bromide electrode (Cole Parmer) based on a standard curve prepared beforehand by correlating a series of bromide concentrations (10-2, 10-3 and 10-4M) and their respective mV readings measured using a

Thermo Orion 720A plus pH/mV meter (Thermo Scientific). There was a linear relationship between the signals and log concentrations of bromide.

2.2.3.3 Colloid experiments

A series of colloid deposition and release experiments were performed for both the 40nm and 500nm colloids (see Table 2). Colloid suspensions for these experiments were prepared by diluting the stock solutions of 40 and 500nm microspheres 50 times. The average linear pore water velocity for all experiments was 1.98×10-4m/s and the injection volume of colloid suspensions was 10mL (about 2.6 pore volumes). The background electrolyte in all deposition

-5 experiments was NaCl as supplemented with 5×10 M NaHCO3 to provide a pH of 6.7±0.1 or with 10-4M NaOH to provide a pH of 9.6±0.1. The effluent colloid concentrations were determined using a fluorometer (RF-5301PC spectrofluorophotometer, Shimadzu) at pre- determined optimum wavelengths of excitation (505nm) and emission (520nm), respectively. At the 505/520nm conditions, both colloids displayed fluorescence intensity with colloid concentration within a linear range on the fluorometer, and a standard curve was prepared beforehand based on correlating the fluorescence intensity of a series of diluted suspension concentrations (C0, 1/6C0, 1/10C0 and 1/50C0), where C0 is the colloid input concentration of

7.8×1011 particles/mL or 1.2×108 particles/mL for the 40nm and 500nm colloids, respectively.

The total mass of colloids recovered was determined by summing the effluent colloid mass and the mass of colloids retained in the column. The retained colloid profile was determined upon dissecting columns at the conclusion of select experiments. Columns were dissected by pushing the sand out of the column into two or more discrete segments. Care was taken to 36 minimize disturbance of the spatial distribution of the retained particles. Each segment was immersed in 50mL of DI water and sonicated to release the deposited particles. The solution was decanted and the colloid concentration was determined as previously mentioned. This process was conducted a minimum of three times. Each segment of sand was subsequently dried at 60°C in an oven (737G ISOTMP, Fisher Scientific) and weighed.

Colloid release experiments were performed after select deposition experiments in a stepwise manner by introducing a pulse of pH 10 colloid-free electrolyte or by introducing pulses of lower ionic strength colloid-free water (see Table 2). Depending upon the initial deposition ionic strength, release may have involved multiple steps, e.g., for initial deposition at pH 7 and ionic strength 10mM, the stepwise release was 10mM3mM (release stage 1), 3mM1mM

(stage 2), and 1mM0.05mM (stage 3). For this example, the pH remains at 7.

2.3 Results and discussion

2.3.1 Microsphere characterization

The sizes of the carboxylate-modified latex microspheres measured using TEM (Figure

2) were quite consistent with what the manufacture reported (36nm and 490nm in average, respectively). The images also demonstrated that the particles were monodisperse and round with minimal deviation in size from their respective average diameters.

The zeta potential values of the particles were calculated from measured electrophoretic mobility (EPM) values as a function of pH at an ionic strength of 10mM (Table 3) and as a function of ionic strength at a pH of 6.7±0.1 (Table 4). For the 36nm particles, the EPM values were converted to zeta potentials by the Debye-Huckel approximation (Debye and Huckel, 1923).

This approach is valid for systems when the product of the inverse of Debye-Huckel screening length (κ) and particle radius (ap) is relatively small, which in this case applies since κap was less than 20 at all conditions of interest. In a similar manner, the zeta potentials for the 490nm particles were derived from measured EPM values by the Smoluchowski approximation (Sze et 37 al., 2003). This approach is valid for systems when κap is relatively high, which in this case applies since κap ranged from 5.7 to more than 250 at the conditions of interest.

The zeta potentials of 36nm and 490nm colloids were highly negative across the entire range of conditions studies (see Tables 3 and 4). In general, values for the 490nm colloids were more negative than those for the 36nm colloids, however, the magnitude of changes observed were higher for the smaller colloids. As pH increased and ionic strength decreased, the zeta potential values became increasingly negative. These trends are to be expected and are a reflection of pH-dependent changes in the charge of the colloid surface and compression of the electrostatic double layer (Elimelech et al., 1995; Pelley and Tufenkji, 2008). Values and trends similar to these have been reported by others (e.g., Shen et al., 2007; Johnson and Tong, 2006) for similarly-sized carboxylate-modified microspheres.

2.3.2 Quartz sand characterization

SEM images of the quartz sand demonstrate that the sand was well rounded with a clean surface devoid of obvious contamination (Figure 3). The average size of the particles determined from Figure 3a was approximately 270μm, which was in accordance with the expectation of an estimated size (dc) of 275μm based on the collection of the sieved fraction between 250μm and

300μm. At higher magnification (Figure 3b), evidence of surface roughness at a very small scale was observed, the magnitude of which may influence smaller colloidal particles more than larger particles (Darbha et al., 2010). The zeta potentials of quartz sand as a function of pH and ionic strength was determined from measured EPM values of colloid-sized particles using the

Smoluchowski approximation as the κap was once again relatively high (from 3.8 to about 170) at the conditions of interest (Table 5). The ap used (165nm) was that for the colloidal sand particles determined by dynamic light scattering. Similar to microspheres, the sand zeta potentials became less negative as pH decreased or ionic strength increased owing to a decrease in the grain surface charge or compression of the thickness of electrostatic double layer. These values and trends 38 compare favorably to those reported in literature (Shen et al., 2007; Torkzaban et al., 2008b) for median quartz sand of 327 and 205μm, respectively.

2.3.3 Interaction potential energy profiles

Interaction energy profiles were calculated at different values of pH and ionic strength based on DLVO theory by summing calculated values for vdW and EDL interactions.

For EDL, the sphere-plate expression of Hogg et al. (1966) assuming constant surface potentials was used:

1 exp(h) 2 2 EDL   0ra p[2cp ln( )  (c  p )ln(1 exp(2h))] 1 exp(h) (1)

The surface potentials, ψc and ψp (V), for both collectors and particles were approximated by their respective zeta potentials, ap is the particle radius (m), ε0 is the vacuum permittivity

-12 (8.854187817×10 F/m), εr is the relative permittivity of the medium or its dielectric constant

(80.18 for water at 20°C), and h is the separation distance (m) between colloid and collector, which is the distance from the center of colloid to the nearest collector surface minus colloid radius.

For vdW, the sphere-plate expression of Gregory (1981) was used:

Aap 5.32h  vdW   [1 ln(1 )] 6h  5.32h (2) where λ is a characteristic decay wavelength of the dielectric usually taken to be 100nm accounting for the retardation of vdW interaction (Sonin, 1995). A is the Hamaker constant

- (Hamaker, 1937) of a polystyrene(1)-water(3)-quartz sand(2), A132, system calculated as 8.88×10

21 -20 -20 J based on the following equation where A131 equals 0.95×10 J and A232 equals 0.83×10 J

(Hahn, 1995):

A  A  A A 132 131 232 (3)

The total interaction energy profiles for 36nm colloids are shown in Figure 4 and for

490nm colloids in Figure 5. Figures 6 and 7 highlight the secondary energy minima for the respective particles. As general features, the total interaction energy (ϕT) profiles for both 36 and

490nm colloids present a deep attractive primary energy minimum (ϕ1min) of theoretically infinite depth at very short separation distances, a primary repulsive energy maximum (ϕMax) at a larger separation distance and a comparatively smaller attractive secondary energy minimum (ϕ2min) at even larger separation distance. Tables 6 and 7 summarize the energy minima and maxima as well as the relevant separation distances for both 36 and 490nm colloids, respectively. The separation distance to the primary minimum was assumed to be 0.1nm after Weronski and

Elimelech (2008) in order to provide a finite energy value.

Values for ionic strength lower than 1mM are not listed in Tables 6 and 7 because the calculated secondary energy minima (ϕ2min) were negligible and the theoretical separation distances to ϕ2min were unrealistically large. As shown in these figures and tables, when the ionic strength increases, the energy barrier decreases and the secondary energy minimum increases for both colloids. Based on these calculations, the primary energy minimum should be relatively insignificant as a locus of colloid deposition in this research, as in most cases the energy barriers were very high (above 10kT) and should prevent deposition into or release from the primary energy minima. Thus, based on DLVO theory the secondary energy minimum should control colloid deposition and release in this research. All the energy extreme values for the 490nm colloid were larger than those of the 36nm colloid at equivalent ionic strength, which was in qualitative agreement with DLVO theory as both EDL and vdW interactions scale linearly with changes in colloid radius (ap). At any given ionic strength, distances to the primary energy maxima and the secondary energy minima were roughly the same between the two colloids. For example, at an ionic strength of 100mM, the two distances were 0.7 and 4.3nm for the 36nm colloids, and 0.7 and 5nm for the 490nm colloids, respectively. This was also consistent with 40

DLVO theory and upon examining equations 1 and 2, it can be noticed that the total interaction energy can be expressed as functions of ionic strength (I), colloid radius (ap) and separation distance (h), where f(h) and g(h,I) are functions based on vdW and EDL interactions, respectively.

ϕT= apf(h)+apg(h,I) (4)

The extreme values of ϕT happen upon setting the derivative of equation 4 with respect to h to 0:

g(h,I) df (h)   0 (5) h dh

Solutions to equation 5 include separation distances to the primary energy maximum and secondary energy minimum, which are independent of colloid radius ap. Distances to the primary energy maxima have a slowly increasing trend, and those to the secondary energy minima have a rapidly increasing trend as ionic strength increases (see Tables 6 and 7).

2.3.4 Column experiments

The breakthrough curve for bromide (Figure 8) was quite symmetrical with a flat plateau at a relative concentration (C/C0) of approximately 1 in the middle and rapidly rising and descending limbs at both sides. Tailing was not evident at the conclusion of the breakthrough curve, which was consistent with the conservative (non-sorbing) characteristic of solute tracers.

Overall 97% of the injected NaBr was recovered at the column outlet. The concentration at breakthrough corresponding to C/C0 equal to 0.5 was near 1 pore volume, confirming the uniform and steady nature of the flow.

As the ionic strength increased from 0.05mM to 100mM the extent of breakthrough of the 36nm colloids decreased (Figure 9) corresponding to an increase in retained colloids (Table

8). Similar to the breakthrough curve (BTC) of tracer bromide, the initial breakthrough of the colloidal suspension corresponded to 1 pore volume. Deposition was quite small up to an ionic strength of 3mM. Above this ionic strength deposition increased significantly and at the same

41 time the initial breakthrough shifted to later times. This became increasingly evident at an ionic strength of 30 and 100mM. Above 100mM no breakthrough was observed (data not shown). To exclude the possible formation of colloidal aggregates and undesired excess colloid removal

(Chatterjee and Gupta, 2009), all the solution chemistry conditions in this study were tested against hydrodynamic size measurements by dynamic light scattering, and were proved to be unfavorable for aggregation. The overall mass recovery for the systems varied between 83.8% and 99.4%, with lower recoveries measured as deposition increased. Likely this reflects difficulties experienced in the column dissection and colloid recovery process in ultrasonically removing colloids attached to the sand at high ionic strength values.

The observation of “retarded” breakthrough like that observed at ionic strength values in excess of 10mM is seldom reported in the colloid transport literature. Such behavior is most often associated with the reversible adsorption of solute species (Seaman et al., 1996) and it is also occasionally reported on in the literature evaluating microbe transport (e.g., Scholl and Harvey,

1992). However, results similar to those depicted in Figure 9 were presented by Shen et al. (2007) for a model system comprised of 30nm carboxylate-modified microspheres and quartz sand.

Larger sized particles did not exhibit the delay in breakthrough (Shen et al., 2007). Shen et al.

(2007) did not offer an explanation for this result, but one plausible explanation might be that the observed retardation may be evidence of secondary energy deposition which is supposed to be weak and reversible and thus may appear similar to solute adsorption. Another important feature commonly seen in colloid transport is extended tailing observed at the end of BTCs (even in colloid release experiments). Such tailing, as observed in Figure 9, is often not significant but still apparent and is typically ascribed to reversible colloid deposition (Johnson et al., 2007b). Such colloid reentrainment that occurs both in the presence and absence of flow or solution composition perturbations is thought to arise from release of colloids held within the secondary

42 minimum (Hahn and O’Melia, 2004) as well as from hydrodynamic interactions (Johnson et al.,

2007a).

The negligible colloid deposition at ionic strength values less than 3mM corresponds to conditions producing significant repulsive energy barriers and small secondary energy minima

(see Table 6). This suggests that deposition into either the primary energy minima or the secondary energy minima was negligible. The micro-scale surface roughness observed on the surface of the quartz grains in Figure 3b could influence deposition for the 36nm colloids, since surface roughness can result in interaction forces between colloids and irregular grain surfaces deviating substantially from forces between colloids and smooth, homogeneous surfaces

(Bhattacharjee et al., 1998; Walz, 1998). Grain surface roughness and irregular shape also influence deposition because they alter the prevalence of flow stagnation zones and the geometry of grain-grain or grain-wall contacts (Canseco et al., 2009; Bradford et al., 2007). The sand surfaces also did not exhibit obvious signs of contamination (see Figure 3a) and thus local favorably charged sites associated with metal oxide or organic contamination were likely not important in our experimental systems (Johnson et al., 1996).

Significant colloid deposition was observed at ionic strength values in excess of 10mM and the magnitude of deposition increased with ionic strength (see Table 8). Deposition under these conditions coincided with increasing depth in the secondary interaction energy well (see

Table 6), but the possible influence of surface roughness cannot be discounted as according to

Walz (1998) it could decrease the magnitude of the theoretical energy barrier of 15.382kT below the 10kT threshold thereby inducing deposition within the primary minimum.

Colloid deposition within the secondary energy minima is assumed to be reversible and a series of release experiments were performed to evaluate the extent of the role it played by eluting solutions with reduced ionic strength or increased pH at the conclusion of the colloid deposition experiments at 30mM and 100mM ionic strength. No colloids were released after deposition at 43

100mM, even though the secondary energy minimum depth of 0.656kT exceeded the one dimensional average colloidal Brownian diffusion kinetic energy of 0.5kT (Hahn and O'Melia,

2004). Under these conditions, the height of the energy barrier was only 4.652kT and according to Hahn and O'Melia (2004), primary minimum deposition becomes dominant when the energy barrier height is less than 10kT. Deposition into a shallow secondary energy minimum is not stable when the energy barrier is low as colloids weakly held in the secondary minimum can overcome the energy barrier and subsequently be strongly held in the much stronger primary energy minimum (Tufenkji and Elimelech, 2005b). Any colloids still retained in the secondary energy minimum were likely trapped at secondary energy minimum sites or funneled to small regions of pore space formed adjacent to grain-grain contact points which irreversibly retain colloids (Li et al., 2006a; Bradford et al., 2007). Very few colloids were released after deposition at 30mM as well and those that were released were only observed in the second step where the pH was increased from 6.7 to 9.6 (see Figure 10). Colloids deposited at 30mM NaCl faced an energy barrier of approximately 15kT. This was theoretically sufficient to hinder colloid transfer from the secondary minimum to the primary minimum, however, as earlier stated the roughness of the quartz surface likely influenced this energy value. The theoretical secondary energy minimum of 0.168kT was also less than the average particle Brownian energy suggesting attraction within the secondary energy minimum was easily reversed. Release induced by increasing pH has been attributed to charge reversal associated with metal oxide patches (Johnson et al., 2001), however, examination of interaction energy profiles suggests colloids held within primary minimum must be irreversibly retained, regardless of the perturbation in system chemistry, because the energy in the primary minimum is infinitely strong (Canseco et al., 2009).

Thus, release induced by pH change must be corresponding to colloids located further than the primary maximum separation distance (within the secondary well).

The lack of release observed likely pertains to reversible deposition within the secondary energy minimum. Colloids deposited within the secondary energy minimum during the initial deposition stage were not strongly held and could have easily been released or translated along the surface of the quartz grain where they encountered straining sites associated with grain-grain contacts. This provides some context for the observed retardation of the breakthrough (see Figure

9). These colloids were not available for release upon reduction in the pore water ionic strength.

A small population of the deposited colloids was available for release upon increasing the solution pH to 9.6 likely due to enhanced colloid-grain repulsion resulting from the further decrease in sand and colloid surface potential (see Tables 3 and 5).

As observed for the 36nm colloids, the deposition of the 490nm colloids exhibited a dependence on ionic strength (Figure 11). The overall mass recoveries were between 90.8% and

100.5% which were very acceptable. Only a few percent of the colloids deposited on the sand surfaces at low ionic strength values (0.3mM and below). This was in qualitative agreement with

DLVO theory, considering the energy barriers were very high and the secondary energy minima were too small to allow either primary or secondary energy minima deposition. These values are not listed in Table 7, but those listed for an ionic strength of 1mM can be used as a means of comparison. Thus, deposition at these ionic strength levels likely reflects straining mechanisms.

This is consistent with Shen et al. (2008) and Jaisi et al. (2008), interpreting incomplete breakthrough (0.9 < C/C0 < 1) of colloidal particles at low ionic strength levels as an indication of physical straining. Chemical heterogeneities on the quartz were likely insignificant and grain surface roughness playing a role for 36nm colloids may impact 490nm colloid much less (Darbha et al., 2010). Straining of colloids depends on colloid size (Bradford et al., 2002), consistent with the increased deposition of the 490nm colloid compared to the 36nm colloid at equivalent conditions. The ratio of the colloid and sand grain (dp/dc) in this system of 0.00178 was also consistent with the critical value reported by Bradford et al. (2002) of 0.0017. The initial 45 breakthrough of the 490nm colloids occurred at about 0.6 pore volume, which was in advance of the tracer and 36nm particles. Unlike the 36nm particles, it did not show evidence of retardation.

This provided evidence of colloid size exclusion (Grolimund et al., 1998), which often occurs along with straining (Bradford et al., 2005).

As the ionic strength increased to 1mM and above, physicochemical filtration was the dominant mechanism of colloid filtration and significant colloid retention was observed with at

10mM only 13.1% of the total colloids injected passing through the column (Table 10).

Contributing to the straining behavior observed for lower ionic strength values was the likely impact of deposition within the secondary energy minima, which increased to 0.689kT at 10mM

(see Table 7). At the same time, the energy barrier was still in excess of 400kT suggesting little deposition occurred within the primary minimum. There was no observable colloid breakthrough at 30mM and 100mM conditions, reflecting the strong retention at the secondary minima with respective well depth of 2.251kT for 30mM and 7.606kT for 100mM and associated straining.

This data was not shown in either Table 10 or Figure 11, and release experiments were conducted only until 10mM (discussed later), because clear relative magnitudes of initial colloid deposition and breakthrough are needed for comparison purposes.

Under conditions favorable for deposition, colloid filtration theory predicts a logarithm linear retained colloid profile. This is based on the determination of the solid concentration of retained colloids as a function of distance, S(x), and a spatially constant deposition rate coefficient (kdep) (Tufenkji and Elimelech, 2004b):

t C k k ln(S(x))  ln( 0 0 dep )  dep x (6) b v where x is the transport distance, t0 is the duration of the deposition run, v is the average pore water velocity, θ is porosity, C0 is input colloid concentration, and ρb is bulk density of sand porous media. The experimentally retained colloid profile as a function of ionic strength

46 determined at the conclusion of the colloid injections is shown in Figure 12. As the ionic strength increased, the profiles gradually transitioned from those characterized as “hyper-exponential” (Li et al., 2004) where the retained colloid concentration is decreasing along transport distance greater than the log-linear decrease predicted from colloid filtration theory to one characterized as

“non-monotonic” (Li et al., 2006a; Li and Johnson, 2005). Hyper-exponential profiles are suggestive of a straining-dominated colloid deposition environment (Bradford et al., 2006, 2007;

Li et al., 2006a) whereas non-monotonic retention is characteristic of deposition influenced by the coupled effects of colloid straining and the secondary energy minimum associated deposition (Li et al., 2006a). At low ionic strength, colloids retained due to the influence of surface heterogeneity or straining under unfavorable conditions do not translate down-gradient (Li et al.,

2006a). When the ionic strength increased, the colloids loosely retained within secondary energy minimum increased. Many of these were subjected to flow drag and able to translate down- gradient (Redman et al., 2004; Li et al., 2006a). A subset of these translating colloids were subsequently immobilized at grain-grain contacts where they may be trapped by wedging resulting in a depletion of translatable colloids and the observed peak in the profile at a distance down gradient from the column inlet as evident in Figure 12 at 10mM NaCl. Although heterogeneities in the colloid population or quartz sand may also produce a hyper-exponential deposition profile (Tufenkji and Elimelech, 2005a; Tong and Johnson, 2007), these factors were not evident in this system.

Experiments were conducted at an elevated pH of 9.6±0.1 in order to further interrogate the impact of surface heterogeneities on particle transport. Such an increase in pH by nearly 3 orders of magnitude had very little impact on particle transport as the breakthrough curves at

0.1mM NaCl and 1mM NaCl exhibited little dependence on pH (Figure 13). In a similar manner, colloid release induced by changes in the solution pH were also relatively minor, with very little measurable release observed upon increasing the pH and only a slight amount of released colloids 47 observed upon subsequently decreasing the ionic strength (Figure 14). This reflects that changes in ionic strength influence both the Debye length (κ-1) and zeta potential, whereas changes in pH only influence the zeta potential. Thus, at 0.1mM NaCl the primary mechanism of colloid removal was likely straining, but at 1mM NaCl both straining and deposition within the secondary energy minimum were in effect. The very little release observed upon changing pH

(Figure 14) indicates secondary minimum interactions were not dependent upon pH, because at

1mM NaCl and pH 6.7±0.1 and 9.6±0.1 the secondary minima depth are both nearly -0.052kT.

The lack of release observed upon increasing the pH from 6.7 to 9.6 and the more substantial release noted upon subsequently changing the ionic strength (Figure 14) confirmed the limited impact of surface chemical heterogeneity in this system. This also provides some insight into the relative importance of straining and secondary energy minimum deposition. At the conclusion of the first release step involving the pH increase at 1mM NaCl (noted as stage 1 in

Figure 14), the percent colloid recovery in the effluent was 87.2%, which was quite close to the

85.7% recovery measured directly during colloid deposition at pH 9.6 and 1mM NaCl (Figure

13). Decreasing the ionic strength to 0.1mM (noted as stage 2 in Figure 14) released sufficient colloids, presumably held within the secondary energy minimum, such that the cumulative recovery in the effluent of 90.8% again nearly matched that directly measured during the deposition at pH 9.6 and 0.1mM NaCl (91.4%). The slight difference likely reflects experimental deviations, but in theory some fraction of those colloids released from the secondary minimum during the decrease in ionic strength (stage 2) could have been further removed via straining.

Step-wise release experiments were also conducted at the conclusion of the colloid injection at 3mM and 10mM NaCl (Figure 15 and 16, respectively). In both instances, the final release step (decrease in NaCl to 0.1mM) released the largest amount of colloids. This result appears consistent with “colloid release hysteresis” described by Torkzaban et al. (2010). Colloid release hysteresis occurs when competing mechanisms simultaneously release and retain colloids. 48

In this case, significant deposition was measured during the initial injection at both 3mM and

10mM NaCl. Mechanisms responsible were likely straining and secondary minimum deposition.

The limited time for the injection and high interstitial velocity did not permit the system to attain equilibrium, especially for particles as large as several hundreds of nanometers (Canseco et al.,

2009). Colloids exiting the column under these conditions did not indicate the number of the retention sites in the column had become saturated. Column saturation is a complex function of system conditions such as colloid radius, solution chemistry and flow velocity, and is positively related to ionic strength but negatively related to flow velocity. At a lower flow velocity, the increased colloid residence time in the column pushes the system closer to equilibrium and more colloid deposition due to the secondary minimum and straining would occur (Johnson and Tong,

2006; Bradford et al., 2007). According to Torkzaban et al. (2010) a subset of the colloids weakly held by these mechanisms is more susceptible to system perturbations. Upon decreasing the ionic strength, weakly retained colloid populations were subject to release and upon traveling through the remainder of the column they could subsequently be removed. Some of these “released” particles were removed by straining, some exited the column, and the remainder and likely largest fraction were once again removed via deposition in the secondary minimum. Further decreasing the ionic strength produces a similar release and subsequently transfers weakly held colloids to stronger deposition locations. Those transferred during these steps to straining locations were irreversibly held, but those transferred to the secondary minimum were reversibly held. The net effect is that during the release steps, the actual amount of colloids associated with the secondary minimum at a particular release stage was more than that measured during direct deposition at equivalent systematic conditions. At the final decrease in ionic strength the two amounts should equal each other because the excess colloids residing in the secondary minimum from the previous stages theoretically all had to be released. However, colloid retention within the media appeared to increase as the ionic strength of deposition increased (Table 11). This suggests that 49 colloids initially deposited at elevated ionic strength released upon the addition of lower ionic strength solutions were more susceptible to straining. This is consistent with the ionic strength dependence in straining reported by Torkzaban et al. (2008a) and reflects the enhanced contribution of grain-grain contact points at elevated ionic strength. Colloids removed at these grain-grain contacts were trapped and not subjected to release as the ionic strength was lowered.

The extended tailing observed in all cases reflects that the time-scale for these processes varies due to corresponding variations in the strength of interactions for the different colloid populations.

2.3.5 Conceptual model regarding colloid deposition and release

2.3.5.1 Non-contacting and contacting deposition

Fast and significant colloid release should be attributed to reversible colloid deposition, which presumably occurs between “non-contacting” surfaces attached at separation distance beyond that to the primary maximum. Deposition within the secondary minimum is one such non-contacting deposition mechanism, and probably the most important one, while deposition due to straining and chemical heterogeneity is not. Therefore any systematic disturbance, such as reasonable variations in physical or chemical parameters like ionic strength, flow velocity and pH, which induces colloid release, results from non-contacting deposition, in particular secondary minimum deposition. A schematic flowchart (Figure 17) reviews the known colloid deposition processes and mechanisms and separates them on the basis of whether they are characteristic of contacting and non-contacting deposition.

2.3.5.2 Ionic strength spectrum where non-contacting deposition happens

In a well-defined ideal system, a homogeneous and monodispersed colloid suspension of size dp (perfectly round shaped) flows through a homogeneous and saturated porous media with grain size dc (perfectly round shaped) with a constant velocity v under a stable background solution of constant pH. Assuming the contribution to ionic strength (I) from pH buffers (e.g., 50

NaHCO3) is negligible, the influence of I from a 1:1 electrolyte on colloid deposition is the only independent variable. The total injected colloid number is N (C0*V) and no blocking or filter ripening occurs. When I is very low (DI water), secondary minimum association is negligible and colloid deposition should be purely due to straining (including grain-grain contacts). Colloids strained under these conditions are enumerated as Nstr.

Nstr (I = 0) > 0 (7)

Because gravity has a negligible influence on Brownian particles, secondary minimum association occurs when hydrodynamic drag interaction energy (ϕHyd) and colloidal Brownian diffusion kinetic energy (ϕBr) are balanced or exceeded by the attractive DLVO interaction energy.

In practice, both ϕHyd and ϕBr are distributed as the local flow and colloid Brownian motion velocities are not fixed values. Also according to Li et al. (2004), at any “observation” time the concave nature of the secondary well (see Figures 6 and 7) suggests the retained colloid population is distributed with the interaction energy across the separation distances, with the majority of the particles appearing at the secondary minimum separation distance (h2min), and fewer particles at separation distances deviating from h2min in both directions, especially toward the direction of increasing separation distances, considering it is much less steeper than the opposite direction (see Figures 6 and 7). The implication of this pattern is that the magnitude of the attractive energy experienced by colloid populations will differ as the separation distance varies.

Model studies, such as those performing torque balances calculations (Torkzaban et al.,

2008b; Johnson et al., 2007b), do not consider this fact and simply use the maximum energy in the secondary well (ϕ2min) to reflect the overall DLVO attractive energy level. Calculations were performed based on these methods comparing the relative magnitude of applied torque from the hydrodynamic drag force and resisting torque from the secondary minimum associated adhesive force. It turns out in our system that the resisting torques were one to several orders of magnitude 51 lower than the corresponding applied torques for both sized colloids across the range of solution chemistry conditions studied. This indicates that the particles should not deposit, which as discussed previously was not the case in our system. This deviation likely reflects that torque balance method, which is based upon a single secondary energy value may not be a robust way to evaluate deposition that is controlled by the secondary minimum energy, and further lends support for the idea to distribute the interaction energy. By distributing all the three energy terms colloid retention within the secondary minimum could happen for very small ϕ2min. This could also be the underlying reason why distributed deposition rate coefficients are observed among colloid populations.

After deposition occurs within the secondary minimum, colloids can be translated along the collector surfaces by tangential hydrodynamic interaction until they finally reside at low flow drag or flow stagnation zones. At these locations, colloids are less sensitive to hydrodynamic change than they are to chemical change. Although interaction energies are distributed, as a first approximation we assume an average energy level in this study for the sake of mathematical parsimony as well as in order to introduce the concept of critical ionic strength in a mathematical way. It is stipulated that the critical ionic strength, I1, corresponds to the ionic strength required to initiate secondary minimum deposition. I1 is a singular value reflecting the fixed average values assumed for the previously discussed energy terms, instead of a range likely found in reality. The colloid number corresponding to these conditions is termed Nsem.

Nsem (I = I1) = 0 (ϕ2min = ϕHyd+ ϕBr) (8)

As the ionic strength exceeds I1, Nstr also increases as colloids partially retained within the secondary minimum are translated to straining sites.

dN str  0(0  I  I ) (9) dI 1

dN str  0(I  I ) (10) dI 1 52

When the ionic strength increases above I1, secondary minimum associated deposition becomes active as a mechanism for colloid accumulation. The reported average one dimensional Brownian thermal energy is 0.5kT (Hahn and O'Melia, 2004), and while probably accurate from a statistical perspective it does not imply that the ϕ2min has to be greater than 0.5kT in order to retain colloids.

Colloid attraction likely occurs at ϕ2min below 0.1kT.

As the ionic strength increases, the energy barrier height a colloid must overcome to be deposited in the primary energy minimum is reduced. The second critical ionic strength, I2, corresponds to that required to reduce the barrier height to 10kT. According to the numerical simulation of Hahn and O’Melia (2004), this is the minimum value that will prevent deposition within the primary minimum. Thus, when the ionic strength is between I1 and I2, the secondary energy minimum dominates deposition, and when it is above I2, primary energy minimum will control. Under these conditions, a subset of the colloids deposited within the secondary minimum might be sufficiently energetic to translate the energy barrier to reach the primary minimum.

Thus, starting from I2, dual mode deposition (Tufenkji and Elimelech, 2005b), where both secondary minimum deposition and primary minimum deposition occur, dominates colloid transport.

ϕMax - ϕ2min = 10kT (I = I2) (11)

As the ionic strength increases above I2, the energy barrier decreases. The third critical ionic strength, I3, corresponds to that where the primary energy maximum equals 0 and under these conditions interactions between colloids and collector surfaces are attractive at any separation distance. Thus, dual mode deposition occurs between I2 and I3, but single mode, primary energy minimum associated contacting deposition occurs at I3 and above this value the secondary minimum deposition no longer occurs as the secondary minimum merges with the primary minimum.

ϕMax = 0 (I = I3) (12) 53

When the ionic strength continues to increase above I3, not only are the interactions between colloids and collectors favorable but also the interactions between the colloids themselves become favorable. The colloidal particles start to aggregate themselves at the CCC (critical coagulation concentration), which is the second critical ionic strength for the colloid-colloid deposition case.

c c c ϕ Max – ϕ 2min = 10kT (I = I2 = CCC) (13)

The superscript “c” refers to interactions between two colloidal particles. The critical ionic strength values depend on system specific conditions such as colloid size, collector size, flow velocity, solution pH and ion valence. Figure 18 summarizes the critical ionic strength relationships.

Based on this conceptual representation of the ionic strength dependence of the controlling mechanisms of deposition, we can assert with confidence that the deposition ionic strength exerts a great influence on the subsequent colloid release behavior. Colloid release, associated with the non-contacting deposition within the secondary minimum, generally occurs when the deposition ionic strength is within the range of I1 and I3, particularly between I1 and I2.

Release that happens between I2 and I3 should be rare and trivial, so we will focus on release when the deposition ionic strength is between I1 and I2. Note that the concept of release here specifically refers to the global release quantified by measured concentrations at a particular downward monitoring point, rather than local release such as that which occurs when a colloid translates along the collector surface. Therefore, global colloid release is the net result of local colloid release, colloid translation and colloid redeposition.

2.3.5.3 Correlating deposition kinetics with initial deposition ionic strength

At the conclusion of colloid deposition experiments at ionic strength values between I1 and I2 the total retained colloid population (Ndep) would be the sum of those retained via straining and secondary minimum deposition. 54

Ndep = Nstr + Nsem (I1 < I < I2) (14)

Since the total mass of grain media in the column is considered to be constant, Ndep should be related to the term S in the governing advection-dispersion equation (ADE):

C  2C C  S  D  v  b (15) t x 2 x  t where the last term on the right side could be expressed as follows:

 S  b b (16)  kdepC  k relS(1 firr )  t 

Alternatively, we could explicitly account for straining and secondary minimum deposition as follows (Bradford et al., 2003; Shen et al., 2008):

 S  S  S b  b Str  b Sec (17)  t  t  t where

b SStr SStr x  (18)  kStrC(1 )(1 )  t SMaxi dc and

 S S  b Sec Sec b (19)  kSecC(1 )  k relSSec  t SMax 

Substituting equations (18) and (19) into (17) gives:

b S SStr x  SSec b  kStrC(1 )(1 )  kSecC(1 )  krelSSec  t SMaxi dc SMax  (20)

Substituting this into equation (16), and recognizing that SSec equals S(1-firr) by definition hence the last term on the right hand side of equation (20) equals that of equation (16), we determine that:

S x S Str  Sec (21) kdep  kStr (1 )(1 )  kSec (1 ) SMaxi dc SMax

The above equations could be used to fit the experimental colloid breakthrough curves in order to derive the straining rate coefficient (kstr) and secondary minimum association rate coefficient 55

(ksem). From this, the relationship between these two coefficients and the initial deposition ionic strength could be modeled and the relative contribution of the two mechanisms could be compared at different initial ionic strength values. Theoretically, the apparent deposition rate coefficient (kdep) as presented by Bales et al. (1991) could be used to construct relationship with ionic strength.

(22)

The collision efficiency α is determined from the clean-bed portion of the colloid breakthrough curves using the following expression (Zhang et al., 2010):

(23)

where the ratio Ceff/C0 equals Ndep/N. Following this approach, we related kdep and ionic strength using the data for both 36nm and 490nm colloids (Figure 19). Tables 8-10 list all the parameters needed to calculate kdep. As we can see, kdep linearly increased with ionic strength for both sizes of colloids, with a larger slope for the 490nm colloid. This trends indicate that colloid deposition kinetics can be simply correlated with solution ionic strength for the experimental setup of current study.

2.3.5.4 Local colloid release induced by decreasing ionic strength

Recognizing that the global release, corresponding to nearly all instances of release appearing in the literature, is actually the net effect of local release and various redeposition processes. The phenomenon of local release is essentially unknown, but may proceed in a manner that follows.

Considering an initial ionic strength (I) between I1 and I2 for secondary minimum dominated deposition, the occurrence of release due to reduction of I to a target value below I1 where no secondary minimum deposition occurs. The number of steps to realize such reduction can be one or more than one. Regardless of the number of steps, the final step, which involves a

56 transition from an ionic strength above I1 to one below I1, is the most important one. As the secondary minimum no longer exists at this juncture all the remaining colloids reversibly attached have to be released, and a relatively high peak should be observed. Heights and extent of tailing in releasing peaks depend upon the increment of ionic strength change and other system conditions such as grain media type (e.g., quartz sand and glass bead). Increased colloid size and flow rates should enhance the non-equilibrium release processes and promote global release. The number of colloids available for global release are related to initial deposition ionic strength, not the number of release steps.

Local release is assumed to be instantaneous in response to the change of ionic strength.

The magnitude of release is directly proportional to the increment of change in I and reflects the corresponding change of the secondary energy well. Due to the distributed nature of the secondary minimum associated colloid, each deposited particle has local movement within the secondary well theoretically bounded by two separation distances, termed hA and hB. These distances correspond to the edges of the attractive secondary energy well. Colloids located at different separation distances between these two distances experience different attractive forces as follows.

h  h  h (24) A 2min B

(h A )  (h B )  0 (25)

When the ionic strength decreases, the ϕ2min becomes smaller and the h2min becomes larger, so the whole secondary energy well diminishes in magnitude and moves to greater separation distances.

The distance between hA and hB is smaller during this process and becomes almost zero when the ionic strength is reduced to the first critical ionic strength I1. The energy distribution for deposited colloid populations also become narrower as the area covered by the secondary well is smaller.

Therefore, the overall attractive energy experienced by colloid populations is reduced, and the

57 active domain of retained colloid population is squeezed and finally disappears as hA , h2min and hB

* approach one another. This critical maximum separation distance h2min corresponds to that when the ionic strength is I1. The ionic strength reduction should be proportional to a certain amount of local colloids released, which is an instantaneous process, concomitant with the change in secondary well mentioned above. While at any particular state, it is unpredictable how many colloids could be retained at specific depth of secondary minimum, what we can predict is the change of those parameters. Excess colloids have to be released in order for the remaining particles to reach a new equilibrium distribution across the new secondary well when ionic strength is reduced.

2.3.6 Summaries and implications

Previous studies investigating colloid detachment from porous media either neglected the thermodynamic roles of the secondary energy minimum (Bergendahl and Grasso, 1999) or did not go deep into the mechanisms regarding its participation in colloid release. Instead of constructing colloid release processes based on detachment from the primary energy minimum using extended-DLVO theory (Bergendahl and Grasso, 2003), secondary energy minimum associated reversible deposition was adopted in this study and explored as a more plausible explanation under the framework of classic DLVO theory. The effects of parameters influencing colloid deposition and release, such as colloid size, flow velocity, and especially ionic strength, were discussed in detail in this study. A conceptual model was proposed to explain the experimental phenomena observed and may provide some guidance for future work evaluating both local and global colloid release. The influence of pH change on colloid release at constant ionic strength was also raised as a question deserving further study, because the surface charge reversal by pH variation should not readily release colloids held in the primary minimum. Neither does it affect the secondary minimum depth.

Results obtained from this research using model colloids have practical implications for field scale application. The microspheres used herein were valid colloid tracers for evaluating the transport potential of pathogenic microorganisms and mineral colloids of similar size in field- scale experiments (Passmore et al., 2010), since solute tracers would greatly overestimate the transport time for many environmentally relevant microorganisms (e.g., Cryptosporidium parvum oocysts, Harvey et al., 2008).

List of Tables in Chapter 2

Properties 40nm colloid 500nm colloid Actual particle size 36±5nm 490±75nm Number concentration 1.95 × 1015 particles/mL 3.09 × 1011 particles/mL Solid concentration 5% 2% Density of polystyrene 1.055g/cm3 1.055g/cm3 Specific surface area 1.6 × 106cm2/g 1.2 × 105cm2/g charge 3.042meq/g 0.3156meq/g azide no 2mM Excitation/Emission wavelength 505/514 nm 505/514 nm Table 3. Manufacture’s reported details of both particles (Table 1 in Chapter 2)

40nm colloid Experiment pH Ionic strength Deposition Mass Retained Release No. (mM) recovery profiles 1 6.7 0.05 × × 2 6.7 0.1 × × 3 6.7 0.3 × × 4 6.7 1 × × 5 6.7 3 × × 6 6.7 10 × × 7 6.7 30 × × 8 6.7 100 × × × 500nm colloid Experiment pH Ionic strength Deposition Mass Retained Release No. (mM) recovery profiles 1 6.7 0.05 × × × 2 6.7 0.1 × × × 3 9.6 0.1 × × × 4 6.7 0.3 × × × 5 6.7 1 × × × 6 9.6 1 × × × 7 6.7 1 × × × 8 6.7 3 × × × 9 6.7 3 × × × 10 6.7 10 × × × 11 6.7 10 × × × Table 4. A summary of colloid transport experiments performed (Table 2 in Chapter 2)

36nm colloid 490nm colloid pH EPM×108 (m2·V -1·s -1) ψ (mV) pH EPM×108 (m2·V -1·s -1) ψ (mV) 5.08 -1.43±0.20 -30.3±4.2 5.50 -3.46±0.26 -48.8±3.7 6.71 -1.63±0.17 -34.5±3.6 6.70 -3.53±0.02 -49.8±0.3 7.60 -1.95±0.09 -41.3±1.9 7.80 -3.66±0.15 -51.7±2.1 8.31 -2.21±0.10 -46.8±2.1 8.65 -3.73±0.1 -52.6±1.4 9.59 -2.55±0.10 -54.0±2.1 9.40 -3.80±0.1 -53.6±1.4 10.75 -2.80±0.24 -59.3±5.1 10.40 -3.92±0.06 -55.3±0.8 Table 5. Zeta potentials of two colloids as a function of pH (ionic strength is 10mM) (Table 3 in

Chapter 2)

36nm colloid 490nm colloid 8 8 I EPM×10 κap ψ (mV) I EPM×10 κap ψ (mV) (mM) (m2·V -1·s -1) (mM) (m2·V -1·s -1) 0.05 -2.73±0.15 0.42 -57.8±3.2 0.05 -4.18±0.08 5.68 -59.0±1.1 0.1 -2.6±0.27 0.59 -55.0±5.7 0.1 -4.14±0.07 8.04 -58.4±1.0 0.3 -2.28±0.16 1.02 -48.3±3.4 0.3 -4.03±0.05 13.92 -56.9±0.7 1 -2.02±0.39 1.87 -42.8±8.3 1 -3.82±0.14 25.42 -53.9±2.0 3 -1.88±0.23 3.23 -39.8±4.9 3 -3.67±0.17 44.02 -51.8±2.4 10 -1.63±0.17 5.91 -34.5±3.6 10 -3.53±0.02 80.38 -49.8±0.3 30 -1.55±0.17 10.23 -32.8±3.6 30 -3.32±0.04 139.22 -46.9±0.6 100 -1.25±0.37 18.67 -26.5±7.8 100 -2.88±0.17 254.17 -40.6±2.4 Table 6. Zeta potentials of two colloids as a function of ionic strength (pH is 6.7±0.1) (Table 4 in

Chapter 2)

Ionic strength is fixed to be 10mM pH is fixed to be 6.7±0.1 8 2 -1 -1 8 2 -1 -1 pH EPM×10 (m ·V ·s ) ψ (mV) I (mM) κap EPM×10 (m ·V ·s ) ψ (mV) 5.08 -2.21±0.07 -31.2±1.0 0.05 3.83 -3.23±0.12 -45.6±1.7 6.61 -2.45±0.11 -34.6±1.6 0.1 5.41 -3.16±0.24 -44.6±3.4 7.60 -2.57±0.11 -36.3±1.6 0.3 9.38 -2.91±0.14 -41.1±2.0 8.31 -2.67±0.14 -37.7±2.0 1 17.12 -2.75±0.28 -38.8±4.0 9.59 -2.85±0.28 -40.2±4.0 3 29.65 -2.64±0.13 -37.3±1.8 10.75 -2.97±0.24 -41.9±3.4 10 54.13 -2.45±0.11 -34.6±1.6 30 93.76 -2.05±0.22 -28.9±3.1 100 171.18 -1.83±0.18 -25.8±2.5 Table 7. Zeta potentials of quartz sand as a function of ionic strength and pH (Table 5 in Chapter 2)

I ϕ1min Distance to ϕMax Distance to ϕ2min Distance to Energy barrier (mM) (kT) ϕ1min (nm) (kT) ϕMax (nm) (kT) ϕ2min (nm) (kT) 100 -41.531 0.1 3.996 0.7 -0.656 4.3 4.652 30 -31.450 0.1 15.214 0.7 -0.168 11.3 15.382 10 -22.441 0.1 26.379 0.8 -0.047 24.8 26.426 3 -12.256 0.1 39.134 0.9 -0.011 55.0 39.145 1 -6.207 0.1 47.760 1.1 -0.003 111.0 47.763 Table 8. Summary of energy minima and maximum for 36nm colloid (Table 6 in Chapter 2)

I ϕ1min Distance to ϕMax Distance to ϕ2min Distance to Energy barrier (mM) (kT) ϕ1min (nm) (kT) ϕMax (nm) (kT) ϕ2min (nm) (kT) 100 -569.798 0.1 98.803 0.7 -7.606 5 106.409 30 -494.479 0.1 236.597 0.8 -2.251 12.2 238.848 10 -339.809 0.1 404.331 0.9 -0.689 25.9 405.020 3 -264.642 0.1 523.372 1.2 -0.181 55.9 523.553 1 -226.243 0.1 608.719 1.5 -0.052 110.6 608.771 Table 9. Summary of energy minima and maximum for 490nm colloid (Table 7 in Chapter 2)

-1 No. I Total percent of Total percent of Total percent Collision kdep(s ) (mM) effluent colloid retained colloid of mass coefficient concentrations recovery (α) 1 0.05 99.3% 0.1% 99.4% 1.13×10-4 9.27×10-6 2 0.1 97.3% 0.3% 97.6% 4.39×10-4 3.61×10-5 3 0.3 95.9% 0.4% 96.3% 6.71×10-4 5.53×10-5 4 1 95.4% 0.7% 96.1% 7.54×10-4 6.22×10-5 5 3 94.9% 1.2% 96.1% 8.39×10-4 6.91×10-5 6 10 84.9% 6.8% 91.7% 2.62×10-3 2.16×10-4 7 30 53.4% 29.8% 87.0% 1.01×10-2 8.28×10-4 8 100 7.2% 76.6% 83.8% 4.22×10-2 3.47×10-3 Table 10. Characteristic parameters of 36nm colloid mass balance and deposition kinetics (Table 8 in

Chapter 2)

Value Parameter name Symbol 36nm colloid 490nm colloid porosity θ 0.321 Happel sphere-in-cell parameter As 64.47 3 particle density ρp 1.055g/cm approach velocity U 6.37×10-5m/s average pore water velocity v 1.98×10-4m/s fluid dynamic viscosity μ 1.002×10-3 N·s/m2 Boltzmann constant × temperature (293K) kT 4.045×10-21J * -11 2 -13 2 bulk diffusion coefficient D 1.19×10 m /s 8.74×10 m /s

attraction number NAT 11.39 0.0615 van der Waals number NvdW 2.195 2.195 Peclet number NPE 1472.2 20039.6 London number NLo 15.187 0.082 -4 aspect ratio or interception number NR 1.31×10 0.001782 -7 -4 gravity number NG 6.08×10 1.13×10 collector efficiency based on R-T equation η 0.124 0.022 R-T collector efficiency based on T-E equation η 0.112 0.015 T-E Table 11. parameters used to derive Table 8 and 10 in Chapter 2 (Table 9 in Chapter 2)

-1 No. I Total percent of Total percent of Total percent Collision kdep(s ) (mM) effluent colloid retained colloid of mass coefficient concentrations recovery (α) 1 0.05 94.2% 2.0% 96.2% 0.0072 7.89×10-5 2 0.1 93.0% 2.4% 95.4% 0.0087 9.58×10-5 3 0.3 92.4% 8.1% 100.5% 0.0095 1.04×10-4 4 1 86.2% 10.6% 96.8% 0.0178 1.96×10-4 5 3 75.9% 14.9% 90.8% 0.0331 3.64×10-4 6 10 13.1% 82.5% 95.6% 0.2439 2.68×10-3 Table 12. Characteristic parameters of 490nm colloid mass balance and deposition kinetics (Table 10

in Chapter 2)

Initial BTCs Cumulative Cumulative Cumulative Retained Final deposition percentage BTCs BTCs BTCs percentage total condition percentage percentage percentage recovery (release to (release to (release to 3mM) 1mM) 0.1mM) I=0.1mM 93.0% 93.0% 2.4% 95.4% I=1mM 86.2% 86.2% 90.8% 8.2% 99.0% I=3mM 75.9% 75.9% 78.3% 87.5% 8.8% 96.3% I=10mM 13.1% 14.5% 29.6% 72.1% 22.8% 94.9% Table 13. Summary of cumulative colloid recovery based on the release experiments (Table 11 in

Chapter 2)

List of Figures in Chapter 2

Figure 4. Flow chart of the column experiment setup (Figure 1 in Chapter 2)

a b

Figure 5. TEM images for (a) 40nm and (b) 500nm colloids (Figure 2 in Chapter 2)

a b

Figure 6. SEM images of quartz sand at (a) 50x magnification and (b) 1000x magnification

(Figure 3 in Chapter 2)

50 100mM 30mM 10mM 30 3mM 1mM

10 Totalinteraction energy/kT

-10 0 10 20 30 40 Separation Distance/nm

Figure 7. Total interaction potential energy profile of 36nm polystyrene

microspheres and 275μm quartz sand at pH 6.7±0.1 (Figure 4 in Chapter 2)

640 100mM 30mM 510 10mM 3mM 380 1mM

250

120 Total interaction interaction Totalenergy/kT

-10 0 10 20 30 40 Separation Distance/nm

Figure 8. Total interaction potential energy profile of 490nm polystyrene

microspheres and 275μm quartz sand at pH 6.7 (Figure 5 in Chapter 2)

1 100mM 30mM 10mM 0.5 3mM 1mM

-0.5 Total interaction interaction Totalenergy/kT

-1 0 20 40 60 80 Separation Distance/nm

Figure 9. The highlight of the secondary energy minima of 36nm

(Figure 6 in Chapter 2)

0 100mM 30mM 10mM

Total interaction interaction Totalenergy/kT -5 3mM 1mM

-10 0 20 40 60 80 Separation Distance/nm

Figure 10. The highlight of the secondary energy minima of 490nm

(Figure 7 in Chapter 2)

0.8

0.6

0 C/C 0.4

0.2

0 0 2 4 6 8 Pore Volume

Figure 11. Breakthrough curve for the tracer, bromide, y-axis is the

normalized effluent concentration and x-axis is the pore volume

(Figure 8 in Chapter 2)

1 0.05mM 0.1mM 0.8 0.3mM 1mM 0.6 3mM

0 10mM C/C 0.4 30mM 100mM

0.2

0 0 1 2 3 4 5 6 Pore Volume Figure 12. Breakthrough curves for the 36nm colloids as a function of

ionic strength. The pH was constant at 6.7±0.1 and the flow velocity

was 1.98×10-4m/s (Figure 9 in Chapter 2)

0.06

release step 1,I=0.1mM and pH=6.7

release step 2,I=0.1mM and pH=9.6

0.04

0 C/C

0.02

0 6 8 10 12 14 16 18 Pore Volume

Figure 13. Release experiments of 36nm colloid at initial ionic strength

30mM and pH 6.7 (Figure 10 in Chapter 2)

1 0.05mM

0.8 0.1mM 0.3mM 1mM 0.6

0 3mM

C/C 10mM 0.4

0.2

0 0 1 2 3 4 5 6 7 Pore Volume

Figure 14. Breakthrough curves for the 490nm colloids as a function

of ionic strength. The pH was constant at 6.7±0.1 and the flow velocity

was 1.98×10-4m/s (Figure 11 in Chapter 2)

-2

-4

0.05mM 0.1mM 0.3mM -6 1mM 3mM

10mM Modifiedretained colloid concentrations -8 0 0.25 0.5 0.75 1 Modified transport distance

Figure 15. Retained profiles of 490nm colloid. y-axis represents solid (per gram)

concentrations of retained colloids normalized by input concentration, which was

transformed into log scale. x-axis represents the dimensionless transport distance

normalized by the column length (Figure 12 in Chapter 2)

pH=6.7 I=0.1mM 0.8 pH=6.7 I=1mM pH=9.6 I=1mM 0.6

pH=9.6,I=0.1mM

0 C/C 0.4

0.2

0 0 1 2 3 4 5 6 7 Pore Volume

Figure 16. Comparison of 490nm colloid deposition at different pH levels

(Figure 13 in Chapter 2)

0.06

Release stage 1 to 1mM and pH=9.6 Release stage 2 to 0.1mM and

0.04 pH=9.6

0 C/C

0.02

0 6 8 10 12 14 16 Pore Volume

Figure 17. Release experiments evaluating the role of pH at initial

conditions of 1mM NaCl and pH 6.7±0.1 (Figure 14 in Chapter 2)

0.1 Release stage 1 to 1mM

Release stage 2 to 0.1mM 0

0.05 C/C

0 6 8 10 12 14 16 18 20 Pore Volume

Figure 18. Release experiment at initial conditions of 3mM and constant

pH 6.7±0.1 (Figure 15 in Chapter 2)

0.6 Release stage 1 at 3mM Release stage 2 at 1mM Release stage 3 at 0.1mM

0.4

0 C/C

0.2

0 6.5 9.5 12.5 15.5 18.5 21.5 24.5 27.5 Pore Volume

Figure 19. Release experiment at initial deposition conditions of 10mM

and pH 6.7±0.1 (Figure 16 in Chapter 2)

Figure 20. colloid deposition processes and mechanisms known so far

(Figure 17 in Chapter 2)

no secondary dual mode primary particle secondary minimum deposition minimum aggregation minimum dominant dominant dominant zone zone zone zone zone ionic strength

I = 0 I = I1 I = I2 I = I3 I = CCC theoretical first critical second third critical critical minimum ionic critical ionic ionic coagulation value strength strength strength concentration Figure 21. the spectrum of ionic strength for colloid deposition (Figure 18 in Chapter 2)

0.0035

y = 3E-05x - 3E-05 0.0028 R² = 0.9942 y = 0.0003x - 4E-05 R² = 0.9654

) 0.0021

1 -

kdep (s kdep 0.0014 36nm colloid 490nm colloid 0.0007 36nm colloid linear kdep with I 490nm colloid linear kdep with I 0 0 20 40 60 80 100 Ionic Strength (mM)

Figure 22. The relationship between the apparent deposition rate coefficient

and the ionic strength (Figure 19 in Chapter 2)

CHAPTER 3 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK

3.1 Conclusions

In the previous chapter, we evaluated the transport and release of the model polystyrene microspheres in the model quartz sand porous media. Both particles and grain sands were characterized in their size, shape, surface morphology and electrokinetic properties. The classic

DLVO framework was set up based on those parameters measured and the interaction potential energy profiles were used as the main tools explaining colloid transport and release behaviors in porous media.

Tracer breakthrough experiments indicated the flow in the column is uniform and steady.

Colloid deposition displayed apparent ionic strength dependence, and generally the higher ionic strength values were, the more deposition occurred. 36nm colloids were observed to have retarded initial breakthrough at high ionic strength similar to the reversible adsorption of solute species, which may be the evidence of the secondary minimum deposition, while 490nm colloids did not have such delay. Surface roughness might play important roles in the deposition of 36nm colloids at low ionic strength. At high ionic strength, however, both primary and secondary minimum deposition should dominate. Both straining and the secondary minimum contributed to the deposition of 490nm colloids, and both of these two mechanisms are enhanced at greater ionic strength. Along with straining, the 490nm colloids displayed slight size exclusion effects. As the ionic strength increased, the retained profile of 490nm colloids transitioned from hyper- exponential style to non-monotonic style, which was consistent with the literature, and reflected the transition from straining dominated deposition to deposition involving both straining and secondary minimum. 76

Plausible release mechanisms were deduced based on experimental observations. 490nm colloid release experiments revealed the final release step, which involved the transition from the existence of the secondary minimum to no secondary minimum at all, was the most important step. During this transition, no secondary minimum association sites were available for colloid retention, and the only colloid retention sites left should be the straining sites such as grain-grain contact points. The release behavior indicated that global release was the net of local release and subsequent redeposition. All the transport and release breakthrough curves had extended tailing, which was ascribed to the reversible colloid deposition (release from the secondary minimum) under hydrodynamic drag interactions.

3.2 Recommendations for future work

Based on the previous and current studies, it has been proposed that the future research could be toward the following directions based on difficulty from easy to hard.

First, the distributed nature of the interaction energies needs to be solved quantitatively for secondary minimum deposition, or else there will always be a gap between theoretical and measured collision efficiencies (α). Some studies exist in developing approaches to address this problem. One example is the Maxwell approach adopted by Li et al. (2004) and Hahn and

O'Melia (2004). This model considers the Brownian diffusion kinetic energy as distributed values rather than fixed 0.5kT across the range of local colloid velocity (V) for different colloid populations. However, this model does not involve the distributed nature of local hydrodynamic drag interaction and it assumes that particles possessing energy that exceeds the energy barrier will be deposited in the primary energy minimum. As described by Shen et al. (2007), it is possible for those colloids to go back to the bulk solution. Other techniques using moment analysis based on torque or force balance calculations, comparing the relative magnitudes of

DLVO attractive interaction (when secondary energy minimum is dominant) and hydrodynamic

77 drag interaction as a mitigating effect to prevent colloid deposition, also entail improvement for the same reasons (Li et al., 2005).

Second, both local and global colloid release processes lack both qualitative and quantitative understanding. For local release, the relationships relating variation in ionic strength, amount of colloids released, and modification of the secondary well should be modeled. The influence of pH variation on colloid release should be more complicated. It is known that pH change induced surface charge reversal would not necessarily release colloids, and pH change even several orders of magnitude may have a trivial effect on the secondary minimum depth, then it is doubtful how pH change really induces colloid release. Flow velocity does not affect the shape of the secondary well, but its change would influence how much colloids would be trapped in a certain well. Generally, the lower the velocity is, the closer to equilibrium colloid deposition would be. Colloid deposition would be higher under these low velocity conditions considering both mechanisms of straining and secondary minimum. Naturally, increasing flow velocity would enhance colloid release. However, there is no quantitative basis to describe these phenomena. For global release, it is still unclear how the release parameter (e.g., ionic strength) interval impacts release. It is also unknown when release starts to happen, and how the release peak would look like because not every release is instantaneous.

Third, the DLVO framework does not capture system imperfections such as non-uniform colloid or grain size, as well as surface roughness. It is also highly dependent on the accuracy of related measured parameters, like zeta potential and Hamaker constant. The various forms of

DLVO equations proposed for different conditions further increases the complexity and uncertainty in determining DLVO interactions.

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Nomenclature

Notation Interpretation Unit (note: blank means unitless; NA means not applicable) ac radius of collector μm ap radius of colloidal particles nm A Hamaker constant J A131 Hamaker constant for colloid-solution-colloid system J A232 Hamaker constant for collector-solution-collector system J A132 Hamaker constant for colloid-solution-collector system J As Happel sphere-in-cell parameter C aqueous concentration of colloid No. of particles/mL CCC critical coagulation concentration mol/L C0 initial or input aqueous concentration of colloid suspension No. of particles/mL Ceff total effulent aqueous colloid concentration No. of particles/mL D hydrodynamic dispersion coefficient m2/s D* bulk diffusion coefficient m2/s dp diameter of colloidal particles nm dc diameter of collector grains μm d50 median grain diameter μm e electron charge, 1.602 × 10-19C C fϕ fraction of diffusing colloids possessing energy less than ϕ firr fraction of deposited colloids which is irreversibly attached FA net DLVO force N FB Brownian diffusion force N FD hydrodynamic drag force N g acceleration by gravity m/s2 separation distance between colloid and collector, which is h the distance from the center of colloid to the nearest nm collector surface minus colloid radius

h2min separation distance to the secondary energy minimum nm I ionic strength mol/L I1 the first critical ionic strength mol/L I2 the second critical ionic strength mol/L I3 the third critical ionic strength mol/L Kd partitioning coefficient between aqueous and adsorbing phases 9 KE elastic interaction constant, 4.67×10 for polystyrene-quartz Pa sand system KPF a pseudo first order rate constant in IFBL m/s k Boltzmann’s constant, 1.380650424 × 10−23J/K J/K -1 kdep apparent colloid deposition (removal) rate coefficient s -1 krel apparent colloid release rate coefficient s -1 kSec first order rate coefficient for the secondary energy s minimum -1 kStr first order straining rate coefficient s L column length or transport distance at the monitoring point m m number of steps for step-wise colloid release mp mass of individual colloid g N Total number of colloids injected No. of particles 23 -1 -1 NA Avogadro constant, 6.022 × 10 mol mol 92

NAT attraction number Ndep total number of colloids deposited No. of particles NG gravity number NLo London number NPE Peclet number NR aspect ratio or interception number Nsem number of colloids associated with the secondary minimum No. of particles Nstr number of colloids strained and held in grain-grain contacts No. of particles NvdW van der Waals number R hydrodynamic retardation factor S solid concentration of colloid deposited No. of particles/g SMax maximum secondary energy minimum associated solid No. of particles/g concentration of deposited colloids SMaxi maximum straining associated solid concentration of No. of particles/g deposited colloids SSec portion of S due to the secondary energy minimum No. of particles/g SStr portion of S due to straining No. of particles/g S(x) colloid retained profiles No. of particles/g T absolute temperature K TA adhesive or resisting torque J TD applied torque J t time s t0 duration of deposition run s tanh hyperbolic function NA V volume of total colloid suspension injected mL v average pore water velocity, or interstitial flow velocity m/s x transport distance from column inlet m U Darcy velocity, approach velocity or superficial velocity m/s U(t) function that generates dimensionless random numbers between -0.5 and 0.5 z ion valence, for 1:1 electrolyte, z=1 α attachment or collision efficiency, or sticking coefficient αthe theoretical collision efficiency β fitting parameter for straining function μ fluid dynamic viscosity N·s/m2 γ cubic root of (1-θ) λ characteristic decay wavelength of the dielectric, 100nm nm η collector or contact efficiency σB Born collision diameter, 0.5nm nm κ inverse of Debye-Huckel screening length m-1 −12 ε0 vacuum permittivity, 8.854187817 × 10 F/m F/m εr relative permittivity of medium or dielectric constant, which is 80.18 at 20℃ and 78.36 at 25℃ for water θ porosity, or volumetric water content ω parameter used to calculate theoretical collision efficiency ϖ straining capacity parameter ρb bulk density of porous media, or total mass of solid over g/mL total volume of porous media 3 ρp particle density kg/m 3 ρf fluid density kg/m

ψc collector surface potential, approximated by zeta potential mV ψp colloid surface potential, approximated by zeta potential mV ψSec colloid blocking function during the secondary energy minimum deposition ψStr straining function ϕBorn Born short-range repulsive interaction energy ϕBr colloidal Brownian diffusion kinetic energy (thermal energy) ϕEDL potential energy of the electrostatic double layer interaction ϕHyd hydrodynamic interaction energy ϕMax primary energy maximum ϕT total interaction energy ϕvdW potential energy of the van der Waals interaction ϕ1min primary energy minimum ϕ2min secondary energy minimum Γ gamma function NA Γi incomplete gamma function NA Note: all ϕ energy terms above are normalized by kT so they are unitless.