Dynamics of Silica Colloid Deposition and Release in Packed Beds of

The transport and deposition dynamics of colloidal particles in packed porous media ... charged silica particles (0.1 and 0.3 µm in diameter), and th...
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Langmuir 2000, 16, 6906-6912

Dynamics of Silica Colloid Deposition and Release in Packed Beds of Aminosilane-Modified Glass Beads Chun-Han Ko and Jeffrey Y. Chen* Department of Chemical Engineering, Environmental Engineering Program, P.O. Box 208286, Yale University, New Haven, Connecticut 06520-8286 Received March 20, 2000. In Final Form: June 12, 2000 The transport and deposition dynamics of colloidal particles in packed porous media were investigated. The colloids were negatively charged silica particles (0.1 and 0.3 µm in diameter), and the packed-bed columns comprised aminosilane-modified glass beads. The glass beads acquired a positive surface charge by anhydrous chemical reaction with aminoethyl(N-aminopropyl)dimethoxymethylsilane. Maximum attainable surface-coverage (θmax) and excluded-area-parameter (β) values were determined for particle deposition experiments under various physicochemical conditions, namely, solution ionic strength, flow velocity, and particle size. The results demonstrated that excluded-area-parameter values increased with decreasing ionic strength and increasing flow velocity and particle size. Observed excluded-area-parameter values smaller than 1.83, the hard-sphere jamming limit according to random-sequential-adsorption (RSA) mechanics, alluded to the occurrence of multilayer deposition. The release of deposited particles after complete breakthrough was also investigated by reducing the ionic strength of the solution and by reversing the collector surface charge with an anionic surfactant (sodium dodecyl sulfate). Because colloid release was predominantly observed following deposition runs with higher values of surface coverage, which suggested the possible presence of multilayer deposition, it could be inferred that particle-particle repulsion was mainly responsible for the observed colloid release.

* Corresponding author. Phone: (203) 432-4394. Fax: (203) 4322881. E-mail: [email protected].

media packed in laboratory-scale columns,14-18 and field conditions, using natural and force gradient flow.19,20 All of the results of these studies point toward the significance of advection, dispersion, deposition, and mobilization (release) as the primary processes controlling particle transport in porous media. Solution chemistry can also have a profound influence on particle transport and deposition by controlling the electrostatic double-layer interaction and, hence, surface forces between colloids and between colloids and collector grains. Specifically, a rise or decline in the particle deposition rate may occur, depending on whether an electrostatic-energy barrier is present among the particles.2,21 It is of great interest and importance to emulate a chemically equivalent system in laboratory studies, because deposition of negatively charged colloids onto positively charged metal oxide surfaces plays an enormous role in colloid transport in many engineered and natural systems.22,23 Silane agents were long used as a coupling agent in composites, coatings, adhesive joints, and glass fibers; for covalently binding proteins to inorganic surfaces; and as a chromatographic stationary phase.24 Silane

(1) Rajagopalan, R.; Tien, C. AIChE J. 1976, 22, 523. (2) Tien, C. Granular Filtration of Aerosols and Hydrosols; Butterworth: Stoneham, MA, 1989. (3) Ruckenstein, E.; Prieve, D. C. J. Chem. Soc., Faraday Trans. 2 1973, 69, 1522. (4) Kallay, N.; Tomic, M.; Biskup, B.; Kunjasic, I.; Matijevic, E. Colloids Surf. 1987, 28, 185. (5) Mohan, K. K.; Fogler, H. S. Langmuir 1997, 13, 2863. (6) Small, H. J. Colloid Interface Sci. 1974, 48, 147. (7) Ryan, J. N.; Elimelech, M. Colloids Surf. A 1996, 107, 1. (8) Grolimund, D.; Borkovec, M.; Barmettler, K.; Sticher, H. Environ. Sci. Technol. 1996, 30, 3118. (9) McCarthy, J. F.; Zachara, J. M. Environ. Sci. Technol. 1989, 23, 496. (10) Bruck, S. D. J. Biomed. Mater. Res. 1972, 6, 173. (11) Varennes, S.; van de Ven, T. G. M. Colloids Surf. 1988, 33, 63. (12) Elimelech, M.; O’Melia, C. R. Environ. Sci. Technol. 1990, 24, 1528. (13) Adamczyk, Z.; Siwek, B.; Zembala, M.; Belouschek, P. Adv. Colloid Inter. Sci. 1994, 48, 151.

(14) Tobiason, J. E. Colloids Surf. 1989, 39, 53. (15) Elimelech, M.; O’Melia, C. R. Langmuir 1990, 6, 1153. (16) Elimelech, M. J. Colloid Interface Sci. 1991, 146, 337. (17) Fontes, D. E.; Mills, A. L.; Hornberger, G. M.; Herman, J. S. Appl. Environ. Microbiol. 1991, 57, 473. (18) Ryde, N.; Kallay, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1991, 87, 1377. (19) Harvey, R. W.; George, L. H.; Smith, R. L.; LeBlac, D. R. Environ. Sci. Technol. 1989, 23, 51. (20) Higgo, J. W.; Williams, G. M.; Harrison, I.; Warwick, P.; Gardiner, M. P.; Longworth, G. Colloids Surf. A 1993, 73, 179. (21) Adamczyk, Z. Colloids Surf. 1989, 39, 1. (22) Liu, D.; Johnson, P. R.; Elimelech, M. Environ. Sci. Technol. 1995, 29, 2963. (23) Johnson, P. R.; Sun, N.; Elimelech, E. Environ. Sci. Technol. 1996, 30, 3284. (24) Vandenberg, E. T.; Bertilsson L.; Liedberg, B.; Uvdal, K.; Erlandsson, R.; Elwing, H.; Lundstrom, I. J. Colloid Interface Sci. 1991, 147, 103.

1. Introduction Transport and deposition of colloidal particles are important in numerous processes involving engineered and natural systems, including packed-bed filtration,1,2 deposition and release of cells on biological surfaces,3 release and redeposition of corrosion products,4 migration of fine particles in secondary oil recovery,5 chromatographic separation,6 and colloid-facilitated transport of contaminants in the subsurface environment.7,8 The necessity of a broader understanding of the underlying physicochemical aspects of colloid transport and deposition is easily appreciated in environmental,7-9 biological,3,10 and industrial2,4,5,11 fields. Factors affecting particle transport and deposition onto a collector medium consist of particle size, particle velocity, solution chemistry, and the chemical characteristics of the particle and collector surfaces.12,13 Numerous experimental investigations involving the transport of colloidal particles in aqueous porous media were conducted under both controlled laboratory conditions, using granular

10.1021/la000415y CCC: $19.00 © 2000 American Chemical Society Published on Web 07/22/2000

Silica Colloid Deposition and Release

agents can also be applied to chemically modify glass surfaces in order to study favorable (barrierless) colloid deposition.13,25,26 The stability of the resultant covalent bond has been demonstrated for quartz sand grains27 as well as for glass-slide surfaces.13,25 For oppositely charged deposition systems (i.e., negatively charged colloids depositing on positively charged collector grains or vice versa), the long-term deposition behavior is often governed by the repulsive electrostatic interactions between the previously deposited and the suspended particles. Thus, although the initial deposition onto a bare collector surface is favorable, subsequent colloid deposition is inhibited by the particles that are adhering to the collector. A decline in particle deposition rate then takes place. This phenomenon is known as blocking.26,28 In such a scenario, a monolayer particle coverage can be expected, and the maximum fractional surface coverage for monolayer random sequential adsorption (RSA) of charged colloids is found to be lower than the corresponding hard-sphere jamming limit of 0.546,29 depending on the pertinent physicochemical conditions.30 For similarly charged colloids and collector surfaces, the rate and amount of colloid release have been demonstrated to be proportional to the extent of ionic-strength reduction for latex particles deposited on sand, glass beads, or flat glass surfaces.7,31,32 Colloid release for oppositely charged particles and surfaces can be induced by particle or collector surface charge reversal with anionic surfactant4,7 or an increase in solution pH.7 Clay-colloid release from iron-oxide-coated sand, induced by dodecanoic acid,33 and hematite colloid release from stainless steel surfaces, induced by EDTA,4,34 have been demonstrated. At the present time, however, there are no studies investigating colloid release from oppositely charged surfaces by ionicstrength reduction. Present knowledge of physicochemical aspects of colloid deposition and release dynamics in engineered and natural systems is still inadequate for accurate prediction of colloid behavior. Given the need for a better understanding of colloid deposition and release mechanisms, the primary objective of this work was to investigate the effect of key physicochemical factors on the deposition and release dynamics of silica colloids which are interacting with oppositely charged aminosilane-modified glass beads in packed columns. The experiments demonstrated the role of particle size, flow rate, and solution ionic strength in colloid-deposition dynamics. Furthermore, the influence of ionic-strength reduction and addition of an anionic surfactant on silica colloid release from the glass bead surfaces is illustrated and discussed. 2. Materials and Methods 2.1. Colloidal Particles. Silica (SiO2) colloids (MP-1040 and PST-3, Nissan Chemicals, Tarrytown, NY) were selected as the colloidal phase. The MP-1040 and PST-3 silica colloids, as (25) Marston, N.; Vincent, B. Langmuir 1997, 13, 14. (26) Ko, C.-H. Dynamics of Colloid Transport and Deposition in Heterogeneous Granular Porous Media. Ph.D. Dissertation, University of California, Los Angeles, CA, 1999. (27) Elimelech, M.; Nagai, M.; Ko, C.-H.; Ryan, J. N. Environ. Sci. Technol. 2000, 34, 2143. (28) Rajagopalan, R.; Chu, R. Q. J. Colloid Interface Sci. 1982, 86, 299. (29) Schaaf, P.; Talbot, J. J. Chem. Phys. 1989, 91, 4401. (30) Johnson, P. R.; Elimelech, E. Langmuir 1995, 11, 801. (31) Meinders, J. M.; Busscher, H. J. Langmuir 1995, 11, 327. (32) Nocito-Gobel, J.; Tobiason, J. E. Colloids Surf. A 1996, 107, 223. (33) Ryan, J. N.; Gschwend, P. M. Geochim. Cosmochim. Acta 1992, 56, 1507. (34) Lo, C. C.; Matijevic, E.; Kallay, N. J. Phys. Chem. 1984, 88, 420.

Langmuir, Vol. 16, No. 17, 2000 6907 reported by the manufacturer, were monodispersed with mean diameters of 0.1 and 0.3 µm, respectively. The nominal size of the silica particles was verified using dynamic light scattering measurements (Nicomp model 370, Nicomp Particle Sizing Systems, Santa Barbara, CA). Examinations with SEM and TEM also confirmed the sphericity of the silica colloids. Gravimetric measurements revealed a particle density of 2.28 g/cm3 for the colloidal silica. 2.2. Glass Beads and Surface Modification. A granular, porous medium composed of uniform-size (0.46 mm in diameter) soda-lime glass beads (class V, Ferro Corp., Jackson, MS) was used in the particle-deposition experiments. As reported by the manufacturer, the glass beads are 90% true spheres, with less than 2% irregularly shaped beads, and have a chemical composition (by weight) of 72.0% SiO2, 15.0% Na2O, 7.0% CaO, 4.2% MgO, 0.4% Fe2O3, and 0.3% Al2O3. Prior to surface modification, the glass beads were cleaned and prepared by a process based on the procedure reported elsewhere.22 Cleaned glass beads were subjected to anhydrous silylation with aminosilane by a process based on the procedure reported elsewhere,27 transforming the surface charge from negative to positive at the solution pH range relevant to the colloid-transport experiments. Anhydrous silylation was employed to avoid polysilane formation, which can occur in aqueous silylation.35 The silylation agent was (3-aminoethyl-3-aminopropyl)dimethoxymethylsilane (AADM) (United Chemical Technologies, Inc., Bristol, PA), chosen for its enhanced hydrolytic stability as compared to triethoxy derivatives.36 Cleaned grains were first dried at 110 °C under vacuum for 2 h to remove any adsorbed water from the grain surfaces. An acidified AADM solution was prepared by adding 50 mL of AADM to 50 mL of 12 N HCl solution to prevent condensation. The acidified AADM solution was then added to 900 mL of boiling toluene in a reflux condenser at 130 °C to remove any water and methanol that were formed during the silylation reaction. Dried glass beads (500 g) were kept in a reflux condenser for 6 h. The beads were then washed several times with toluene and allowed to cure overnight at 110 °C under vacuum. Finally, before deposition experiments, the aminosilanemodified beads were incubated in deionized water for 24 h. 2.3. Colloid Deposition Experiments. Particle-deposition experiments were performed in laboratory-scale, packed-bed columns. The columns used (Rainin Instruments, Woburn, MA) had a height of 2 cm with an inner diameter of 2.5 cm. The porous medium was “wet-packed” in a solution having the same chemical characteristics as the solution to be used during the subsequent deposition experiment. Standard gravimetric methods were used to determine the column-packing density. The calculated column porosity, based on a grain density of 2.47 g/cm3, was 0.36. Column experiments were conducted by pumping an aqueous particle suspension through the packed column. A constant flow of the solution was delivered to the column by a peristaltic pump (Masterflex, Cole-Palmer, Vernon Hills, IL) driving two parallel pump heads simultaneously. One pump head was used to deliver an appropriate concentration of silica particles suspended in deionized water, and the other head was used to deliver an appropriate dosage of the electrolyte solution. The colloid suspension and the electrolyte solution were mixed in-line just ahead of the column to avoid particle aggregation. Some preliminary calculations of aggregation rates based on Smoluchowski’s approach indicated that the half-times for particle aggregation were higher than the times taken by the suspension to traverse the column. Combined flow rates were set to yield approach velocities of 2 × 10-4 or 1 × 10-3 m/s. By the use of another peristaltic pump, particle deposition was preceded and followed by a particle-free solution having the identical chemical characteristics and flow rate as the colloidal suspension during the deposition experiment. Particle concentrations in the column effluent were monitored at predetermined intervals by using optical density measurements obtained with a UV/vis spectrophotometer (Hewlett-Packard model 8452A) and a 1-cm flowthrough cell. Room temperature was maintained during experi(35) Chaimberg, M.; Cohen, Y. J. Colloid Interface Sci. 1990, 134, 576. (36) Arkles, B.; Steinmetz, J. R.; Zazyczny, J.; Mehta, P. J. Adhes. Sci. Technol. 1992, 6, 193.

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mentation (about 22 °C). The UV/vis detector was calibrated against known concentrations of colloidal suspensions, and the response was linear over the range of colloid concentrations used in the study. The ionic strength of the influent was adjusted from 10-4 M (only HCl) up to 10-1.5 M (10-4 M HCl plus KCl) by adding the appropriate dosages of KCl to the electrolyte solution. HCl was applied to ensure that a positive surface charge of the silanemodified glass beads persisted throughout the experimental runs at pH 4. For the 0.1- and 0.3-µm particles, the initial colloid concentrations used were 60 and 100 mg/L, corresponding to number concentrations of 3.78 × 1010 and 3.00 × 109 cm-3, respectively. 2.4. Colloid-Release Experiments. Colloid release was induced by changing the influent-solution chemistry after a complete particle breakthrough in the deposition stage. Prior to perturbation of solution chemistry, the influent solution was switched to a particle-free solution having a chemical composition identical to that which was used during colloid deposition. The column was subsequently flushed with the new particle-free background electrolyte solution (at an approach velocity identical to that which was used in the deposition step) to investigate the roles which were played by various mechanisms during colloid release. To study the effect of ionic-strength reduction, 10-4 M HCl solution was introduced. Following the injection of 10-4 M HCl solution, the concentration of the released colloids was monitored continuously for several pore volumes until no more colloid release could be observed. The 10-4 M HCl solution was then replaced by a mixture of 10-3 M sodium dodecyl sulfate (SDS) and 10-4 M HCl to examine the effect of an anionic surfactant on colloid release. Again, following the injection of the new background electrolyte solution, the concentration of released colloids was monitored continuously for several pore volumes until no more colloid release could be detected. Identical fluid approach velocities were maintained throughout the colloid deposition and release experiment.

Figure 1. Particle-breakthrough curves of 100 mg/L 0.3-µm silica particles and aminosilane-modified glass beads at different ionic strengths. Approach velocity ) 10-3 m/s, column length ) 2 cm, and pH ) 4. One pore volume (PV) represents 7.2 s.

3. Results and Discussion 3.1. Particle Breakthrough Curves and Deposition Rate. Particle deposition experiments were conducted by passing colloidal suspensions of silica particles through vertical columns which were packed with silane-modified glass beads. Each deposition run was continued until a complete particle breakthrough was attained. The experimental results are displayed as particle breakthrough curves, showing the change in normalized effluent particle concentration (C/C0, where C0 is the influent colloid concentration) as a function of pore volume. Pore volume, which represents dimensionless deposition time, is defined as (Ut)/(L), where U is the fluid approach velocity, t is the deposition time, L is the column length, and  is the porosity. The results for the 0.3-µm silica colloid suspension deposited at an approach velocity of 1 × 10-3 m/s. Various ionic strengths are presented in Figure 1. Figures 2 and 3 show the results of deposition experiments at a flow rate of 2 × 10-4 m/s for the 0.3- and 0.1-µm silica colloid suspensions, respectively. The clean-bed-removal efficiency of the packed bed can be readily identified from the particle-breakthrough curves. Experimental single-collector efficiency (η) values were calculated using37

η)-

( )

4ac C ln 3L(1 - ) C0

(1)

where ac is the grain diameter, L is the column length,  is the porosity, and C/C0 is the value of the normalized (37) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation: Measurement, Modelling and Simulation; Butterworth-Heinemann: Oxford, 1995.

Figure 2. Particle-breakthrough curves of 100 mg/L 0.3-µm silica particles and aminosilane-modified glass beads at different ionic strengths. Approach velocity ) 2 × 10-4 m/s, column length ) 2 cm, and pH ) 4. One pore volume (PV) represents 36.0 s.

Figure 3. Particle-breakthrough curves of 60 mg/L 0.1-µm silica particles and aminosilane-modified glass beads at different ionic strengths. Approach velocity ) 10-3 m/s, column length ) 2 cm, and pH ) 4. One pore volume (PV) represents 7.2 s.

column-effluent concentration at the initial stages of deposition (typically, after one pore volume). Experimental single-collector efficiencies, η, can be used to indirectly assess the effectiveness of the collector surface charge modification by comparison with theoretical η0 values for favorable deposition determined from filtration theory.37 The ratio of the experimental (η) and the

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Table 1. Values of the Collision (Attachment) Efficiency r and Single-Collector Efficiency ηexp at Various Ionic Strengths for Deposition of Two Suspensions of Silica Particles onto Aminosilane-Modified Glass Beads particle size (µm)

0.3

0.3

0.1

approach velocity (m/s)

1.0 × 10-3

2.0 × 10-4

2.0 × 10-4

ionic strength (M) 10-4.5 10-4.0 10-3.5 10-3.0 10-2.5 10-2.0 10-1.5 10-1.0

R 2.054 1.948 1.844 1.742 1.691 1.661

R

ηexp 10-3

6.245 × 5.925 × 10-3 5.609 × 10-3 5.297 × 10-3 5.142 × 10-3 5.050 × 10-3

theoretical favorable (η0) single-collector efficiencies gives the collision (attachment) efficiency R:37

R ) ηexp/η0

(2)

Table 1 presents the experimental single-collector efficiency (ηexp) and collision efficiency (R) values for all of the deposition runs. As is evident from Table 1, all the R values are greater than 1, indicating that surface charge modification was complete (i.e., modified glass beads are positively charged). The obtained range of R values is not unexpected, because enhancement in particle deposition under favorable conditions (i.e., oppositely charged collector and particle surfaces) as a function of solution ionic strength and approach velocities is well-documented in the literature.16,37 For both particle suspensions, collision efficiency increases as ionic strength decreases. Furthermore, collision efficiency also increases as particle size and approach velocity increase. While the experimental R values might deviate slightly from the theoretical values, due to inherent and random experimental errors such as possible nonuniform column packing and nonuniform surface modification, the observed trends are consistent with theoretical predictions for particle deposition onto oppositely charged surfaces.16,38 The effects of solution ionic strength and particle size on colloid-deposition dynamics are reflected by the shapes of the particle-breakthrough curves in Figures 1-3. As can be seen, the slope of the breakthrough curve increases as ionic strength decreases. This observation is directly related to the blocking phenomenon discussed later in this paper. Moreover, a notable sigmoidal shape at the initial stage of particle breakthrough is observed for some of the breakthrough curves. The sigmodial shape becomes more prominent as ionic strength increases, indicating that the effluent concentration rises more slowly for solutions of higher ionic strength. A plausible explanation for the observed sigmodial behavior of the breakthrough curves is a reduction in colloidal stability, which results in an attachment of colloidal particles to previously retained particles. However, it should be noted that the typical values of the half-time for aggregation based on Smoluchowski’s approach were found to be higher than the corresponding times needed for the suspension to traverse the packed column. Hence, destabilization due to aggregation might not have been possible for most of the runs, barring perhaps the runs at the highest electrolyte concentrations. Particle deposition regularly exhibits variable kinetics from process inception to process completion. This was evident from the particle-breakthrough curves in Figures 1-3. As negatively charged silica particles deposit irreversibly onto the positively charged modified-glass (38) Elimelech, M. J. Colloid Interface Sci. 1994, 164, 190.

1.838 1.785 1.680 1.630 1.551 1.531 1.521

ηexp

R

ηexp

1.543 1.501 1.422 1.384 1.307 1.267 1.267

2.629 × 10-2 2.568 × 10-2 2.432 × 10-2 2.367 × 10-2 2.235 × 10-2 2.168 × 10-2 2.168 × 10-2

10-2

1.639 × 1.596 × 10-2 1.503 × 10-2 1.457 × 10-2 1.387 × 10-2 1.369 × 10-2 1.361 × 10-2

beads, a transient deposition rate arises as excluded area effects of the deposited particles cause a reduction in the particle deposition rate. The rate of approach toward a complete particle breakthrough (C/C0 ) 1) is indicative of the relative area blocked by a deposited particle, with steeper breakthrough curves corresponding to larger excluded areas.30,39 A comparison between the breakthrough curves in Figures 1 and 2 demonstrates that a higher approach velocity also leads to more significant blocking. Considering the times taken by the suspension to traverse one pore volume, it immediately becomes evident that a complete breakthrough is attained earlier at the higher flow rate. Further discussions on the possible occurrences of multilayer deposition and the influence of the approach velocity on the blocking dynamics are presented in later sections. 3.2. Maximum Attainable Surface Coverage. For irreversible particle deposition occurring in a packed column, the collector surface coverage θ may be obtained as a function of time from experimental particlebreakthrough data using39

θ)

∫0t(1 - C/C0)dt

πap2UacC0

3L(1 - )

(3)

Here, ap is the particle radius, ac is the collector radius, U is the fluid approach (superficial) velocity, C0 is the column-inlet particle number concentration, C is the column-effluent particle number concentration corresponding to time t, L is the packed bed column length, and  is the bed porosity. The obtained surface-coverage value after a complete breakthrough is reached is defined as the maximum attainable surface coverage (θmax) or jamming limit. The average area excluded by the retained particles is inversely related to the maximum attainable surface coverage (θmax). The excluded-area parameter (β) defines the dimensionless ratio of blocked collector surface area to the projected area of particles and may be obtained as the reciprocal of θmax

β)

1 θmax

(4)

According to eqs 3 and 4, jamming limits and excludedarea-parameter values can be readily determined from the breakthrough curves shown in Figures 1-3. The resultant series of β values are shown in Figures 4 and 5, and the corresponding θmax values are summarized in Table 2. The significance of these results is discussed in the following subsections. 3.3. Influence of Flow Rate on Jamming Limits. Figure 4 illustrates the effect of flow intensity on the extent (39) Song, L.; Elimelech, M. Colloids Surf. A 1993, 73, 49.

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Figure 4. Excluded-area parameter as a function of ionic strength for 0.1-µm silica particles deposited on aminosilanemodified glass beads at approach velocities of 10-3 m/s (filled circles) and 2 × 10-4 m/s (open circles). Values of the excludedarea parameter in the curves were determined from particlebreakthrough curves which approached C/C0 ) 1. Other experimental conditions are described in Materials and Methods. The bottom doted horizontal line, labeled as β∞ ) 1.83, corresponds to the hard-sphere jamming limit, θ∞ ) 0.546.

Figure 5. Excluded-area parameter as a function of ionic strength for two particle suspensions at approach velocities of 2 × 10-4 m/s for 0.1-µm (filled circles) and 0.3-µm (open circles) silica particles. Values of the excluded-area parameter in the curves were determined from particle-breakthrough curves which approached C/C0 ) 1. Other experimental conditions are described in Materials and Methods. The bottom doted horizontal line, labeled as β∞ ) 1.83, corresponds to the hard-sphere jamming limit, θ∞ ) 0.546. Table 2. Values of the Excluded Area Parameter β and Jamming Limits θmax at Various Ionic Strengths for Deposition of Silica Particles onto Aminosilane-Modified Glass Beads particle size (µm) approach velocity (m/s)

0.3 1.0 ×

10-3

0.3 2.0 ×

10-4

ionic strength (M)

β

θmax

β

θmax

10-4.5 10-4.0 10-3.5 10-3.0 10-2.5 10-2.0 10-1.5 10-1.0

9.523 6.250 5.714 4.762 3.802 3.521

0.105 0.160 0.175 0.210 0.263 0.284

6.944 4.762 4.000 3.571 3.268 2.778 2.439

0.144 0.209 0.250 0.280 0.306 0.360 0.410

0.1 2.0 × 10-4 β

θmax

4.566 3.125 2.564 2.083 1.666 1.449 1.163

0.219 0.320 0.390 0.479 0.601 0.689 0.861

of particle blocking. Excluded-area-parameter values are plotted as a function of solution ionic strength for two different approach velocities (2 × 10-4 and 1 × 10-3 m/s)

for the 0.3-µm silica colloid particle suspension. Evidently, the excluded area (β) is larger (or maximum surface coverage θmax is smaller) at higher flow intensity. Higher flow-shear rates generate a larger excluded area downgradient of deposited particles where particle deposition is prevented. Thus, the observed behavior is not entirely unexpected and is generally referred to as the “shadow effect” or “hydrodynamic scattering effect”.27,40,41 Figure 4 also illustrates that the excluded-area parameter decreases (i.e., θmax increases) and gradually approaches the hard-sphere jamming limit as the solution’s ionic strength increases. The decline of β in response to the increase in the ionic strength is in qualitative agreement with the DLVO theory and with previous experimental investigations involving irreversible monolayer deposition of colloids onto various collector surfaces, including flat surfaces and packed-bed columns.42-47 DLVO theory predicts that the electrostatic double layer becomes suppressed as the solution’s ionic strength increases. Consequently, the effective area blocked by the deposited particle becomes smaller as the solution’s ionic strength increases, and the effective area blocked by the deposited particle approaches that of hard sphere in the high-ionic-strength limit. 3.4. Influence of Particle Size on Jamming Limits. Figure 5 shows the effect of increasing particle size on the excluded area parameter. Experimental β values are plotted as a function of the solution’s ionic strength for the 0.1- and 0.3-µm silica colloid particle suspensions at a fixed approach velocity of 2.0 × 10-4 m/s. It can be observed that β values for the 0.3-µm silica colloid particle suspension are significantly larger than those for the 0.1µm particles at a given ionic strength. A possible explanation for the observed phenomenon is that the deposition of larger particles results in larger shadow zones, blocking further deposition by incoming particles. Figure 5 also shows the general dependence of β on the solution’s ionic strength; as the ionic strength increases, the excluded area decreases and gradually approaches the hard-sphere jamming limit of 1.83 for RSA-blocking mechanics for monolayer deposition.33 It should be noted, however, that for the 0.1-µm particles, the values of the excluded-area parameter at ionic strengths higher than 10-2 M are smaller than the 1.83 limit, suggesting the possible occurrence of multilayer deposition under those solution chemistry conditions. 3.5 Particle Release due to Chemical Perturbation. Colloid release can be induced by perturbations in solution chemistry, which, in turn, influences the surface forces between colloids and collector grains. The percentage of particles released due to such perturbations can be determined via mass balance because the area under the release-breakthrough curve represents the amount of released particles. To investigate the effect of ionicstrength reduction on colloid release, the packed-bed column was flushed with a particle-free 10-4 M HCl (40) Ko, C.-H.; Elimelech M. Environ. Sci. Technol., in press. (41) Adamczyk, Z.; Szyk, L.; Warszynski, P. Colloids Surf. A 1993, 75, 185. (42) Adamczyk Z.; Belouschek, P. J. Colloid Interface Sci. 1991, 146, 123 (43) Johnson, C. A.; Lenhoff, A. M. J. Colloid Interface Sci. 1996, 179, 587. (44) Semmler, M.; Mann, E. K.; Ricka, J.; Borkovec, M. Langmuir 1998, 14, 5127. (45) Ryde, N.; Kihira, H.; Matijevic, E. J. Colloid Interface Sci. 1992, 151, 421. (46) Ryde, N.; Kallay, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1991, 87, 1377. (47) Privman, V.; Frisch, H. L.; Ryde, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1991, 87, 1371.

Silica Colloid Deposition and Release

Figure 6. Particle release by ionic-strength reduction with injection of 10-4 M HCl solution (open circles) followed by surface-charge reversal by 10-3 M SDS and 10-4 M HCl solution (open squares) for (a) 0.3-µm and (b) 0.1-µm particles. Total percentage released is shown in open upright triangles. Amount of particle release is expressed as percentage of total particles deposited in the previous deposition run. The horizontal axis displays the ionic strength during the deposition run prior to the colloid-release experiment.

electrolyte solution (at an approach velocity identical to that used in the deposition step) after a complete particle breakthrough was attained. Following the injection of 10-4 M HCl solution, the concentration of the released colloids was monitored and recorded continuously for several pore volumes until no more colloid release could be observed. Finally, to examine the effect of an anionic surfactant on colloid release, following the injection of a 10-4 M HCl solution, a mixture comprising 10-3 M SDS and 10-4 M HCl was injected. Figure 6a,b shows the experimental results for colloid release at a flow rate of 2 × 10-4 m/s for both 0.1- and 0.3-µm silica colloid suspensions. The percentages of particles released by an ionic-strength-reduction mechanism are shown in open circles. For both of the particle sizes, the release due to ionic-strength reduction was negligible (