Effects of Natural Organic Matter and Solution Chemistry on the

Arlington, Virginia 22209, and Department of Geography and. Environmental Engineering, The Johns Hopkins University,. 313 Ames Hall, 3400 North Charle...
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Environ. Sci. Technol. 2003, 37, 1122-1129

Effects of Natural Organic Matter and Solution Chemistry on the Deposition and Reentrainment of Colloids in Porous Media A L E S S A N D R O F R A N C H I * ,† A N D CHARLES R. O’MELIA‡ Malcolm Pirnie Inc., 1101 Wilson Boulevard, Suite 1400, Arlington, Virginia 22209, and Department of Geography and Environmental Engineering, The Johns Hopkins University, 313 Ames Hall, 3400 North Charles Street, Baltimore, Maryland 21218

The role of humic acid in the transport of negatively charged colloids through porous media was examined. Adsorption of humic acid on latex colloids and silica collectors reduced the deposition of suspended particles and enhanced the reentrainment of deposited particles in porous media. These effects are considered to arise from additional electrostatic and steric contributions to the repulsive interaction energy due to the adsorption of negatively charged humic acid on both the suspended particles and the media collectors. At low ionic strength reversible deposition in shallow secondary minima is hypothesized to be the principal attachment mechanism, independent of the presence of humic acid. It is proposed that, under these solution conditions, particle deposition and reentrainment are the result of a dynamic process, in which particles are continuously captured and released from secondary minima. At higher ionic strengths, deposition may be regarded as a combination of two mechanisms: capture in the primary well and capture in the secondary minimum. Theoretical calculations of the attachment efficiency were conducted using two existing mathematical models. The first model is based on deposition in the primary well (interaction force boundary layer, IFBL), and the second model is based on the Maxwell kinetic theory and deposition in the secondary minimum (Maxwell model). Simulations conducted with the Maxwell model provide significantly better fits of the experimental results than those conducted with the IFBL model.

Introduction Particles in natural systems are coated with natural organic macromolecules with the result that electrostatic interactions between surfaces can be, to a large extent, dominated by the presence of an organic adsorbed layer. Some examples of these environments are shallow aquifers, riverbank filtration, septic systems, groundwater recharge with wastewater, and slow sand filters, where large concentrations of natural organic matter (NOM) may be found. Previous research has indicated the importance of the presence of dissolved NOM on the stability of suspended particles (1-4). * Corresponding author phone: 703-351-9100; fax: 703-351-1305; e-mail: [email protected]. † Malcolm Pirnie Inc. ‡ The Johns Hopkins University. 1122

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Colloidal deposition and reentrainment in porous media under conditions in which adsorbed polymers and polyelectrolytes do not play a significant role have been extensively analyzed in several studies (3, 6-11). However, few studies (11-16) have addressed the effect of natural organic matter on deposition only. In particular, this study builds upon the work of McDowell-Boyer (8), who was the first to report on the mobilization of sulfate latex microspheres (1.46 µm) deposited on sand columns, and Hahn (9), who studied the deposition and reentrainment of submicron latex colloids on columns packed with spherical glass beads and conducted an extensive mathematical analysis of the phenomena. This research, in addition to testing a wider variety of solution chemistry conditions, addresses specifically the effects of natural organic matter on particle attachment and detachment. In natural and technological systems, the fraction of the porous media composed of silica (quartz) is often predominant. Often, however, the adsorption of NOM on silica and its effect on colloidal transport has been disregarded (e.g., 5-9). The results presented in this study challenge this assumption because it has been shown that, under chemical conditions of environmental interest, negatively charged humic substances adsorb on negative surfaces such as sodalime glass s which can be considered as analogous to silica sand found in natural and technological systems s and that this occurrence modifies the physicochemical characteristics of the solid-water interface. These effects may be important in subsurface and technological aquatic systems where most particles, porous media, and NOM have negative charges. The first part of this study focused on the physicochemical characterization of the surface properties of suspended particles and porous media (collectors). This characterization included adsorption, electrophoretic mobility, and adsorbed layer thickness measurements. Deposition and reentrainment studies were then conducted in column experiments. Subsequently, mathematical models were used to calculate total interaction energies between particles and collectors and the corresponding theoretical deposition efficiencies. These simulations allowed some speculation regarding the nature of the interactions between colloids and collectors.

Methods The particles used in this study were 98-nm (as given by the manufacturer and as measured by photon correlation spectroscopy) sulfate latex microspheres (Interfacial Dynamics Corporation, Portland, Oregon) with a surface charge density of 1.2 µCoulombs/cm2 (measured by the manufacturer). The submicron size of the particles was selected to avoid the effects of orthokinetic (shear) flocculation and differential sedimentation which affect the transport of particles larger than a micron. The particles were custom cleaned by the manufacturer using an ion-exchange procedure to remove impurities (17). The model collectors (filter media) used in this research were 0.2-mm spherical sodalime glass beads (MO-SCI Corporation, Rolla, MO). The beads were cleaned with 10-2 M NaOH and 1 M HNO3 to remove dirt and other impurities upon receipt from the manufacturer and again after they had been used in column and adsorption experiments (for details see ref 17). Clean glass beads were used for each set of column experiments. For the measurement of electrophoretic mobilities of soda-lime glass beads, microspheres of diameter smaller than 37 µm made of the same material as the collectors were used (MO-SCI). The organic matter used in this study was reference Suwannee River humic acid (SRHA) supplied by the International Humic 10.1021/es015566h CCC: $25.00

 2003 American Chemical Society Published on Web 02/05/2003

TABLE 1. Main Parameters and Results of the Total Interaction Energy Calculationsa (Data from Ref 17)

particle and collector coating

ionic strength (M)

ζ silica (-mV)

ζ latex (-mV)

potential barrier height (kT)

uncoated SRHA-coated uncoated SRHA-coated uncoated SRHA-coated uncoated SRHA-coated uncoated SRHA-coated uncoated SRHA-coated

10-3 10-3 3 × 10-3 3 × 10-3 10-2 10-2 5.5 × 10-2 5.5 × 10-2 10-1 10-1 5 × 10-1 5 × 10-1

47.6 50.3 41.3 44.0 35.0 40.0 22 26 22.7 30.6 16 20

57.8 68.4 54.6 61.3 35.8 43.0 25 33 20.0 23.2 17 26

175 212 133 159 68 100 17 31 8 20 0 7.2

diffuse layer thickness (nm) 9.6 9.6 5.5 5.5 3.0 3.0 1.3 1.3 1.0 1.0 0.4 0.4

secondary minimum depth (kT)

secondary minimum distance from surface (nm)

3.5

0.0011 0.0010 0.0092 0.0087 0.077 0.070 0.94 0.83 1.70 1.49

132 135 63 65 26 27 7 8 4.5 5

n.a.

5.22

1.9

adsorbed ayer thickness (nm) 1 1 2 n.a.

Conditions: ap ) 49 nm, ac ) 0.1 mm, H ) 0.93 × 10-2 J, T ) 296 K, λ (wavelength of dielectric) ) 1 × 10-7 m, Born collision parameter ) 5 × 10-10 m, ζ ) zeta potential, pH ) 7.2, n.a. ) not available. a

Substances Society. SRHA has an estimated molecular weight between 1000 (18) and 10 000 (4) Da, and a charge density of 0.8 Coulombs/mg C (where C stands for carbon) at pH 7 and 10-2 M NaCl (4). Additional characteristics of SRHA can be found in refs 18-20. The methodologies used for adsorption experiments and for measurements (by photon correlation spectroscopy, PCS) of electrophoretic mobility and adsorbed layer thickness are described in detail in the Supporting Information of this paper. For adsorbed amount, adsorbed layer thickness, and electrophoretic mobility experiments the ionic strength (I) was controlled by varying the concentration of NaCl from 0 to 10-1 M, while the concentration of NaCl during column experiments was varied from 0 to 5 × 10-1 M. The pH was maintained constant at 7.2 with 10-4 M NaHCO3 (a significant contribution to the ionic strength only when the concentration of NaCl was 0) as background electrolyte. For the experiments with filter columns the concentration of latex particles and the flow rate were selected such that “clean bed” conditions (only a small fraction of the filter media covered with particles at the end on the deposition step) would be maintained through all column runs. Experiments were conducted both in the absence and in the presence of 1 mg C/L SRHA with flow velocity of 1.27 × 10-3 m/s, column diameter of 25 mm, bed depth of 0.25 m, and a bed porosity of 0.4. A three-step procedure, similar to that adopted by McDowell-Boyer (8) and Hahn (9), was used for deposition/ reentrainment experiments. In phase 1 (deposition step) a suspension of 1 mg/L latex particles was fed continuously to the filter column. The solution ionic strength during this phase was kept constant for each experiment but it was varied for different experiments. In phase 2 (rinse step) the column was rinsed with a particle-free solution of the same ionic strength as the solution used in phase 1. Finally, in phase 3 (reentrainment step), the solution ionic strength was lowered; the column was then flushed with a particle-free solution of low ionic strength (no added NACl). Samples of the effluent were collected directly into a 5-cm quartz spectrophotometer cell, and the latex concentration was monitored using UV220 (ultraviolet light at 220 nm) absorbance measurements. In those experiments where SRHA was used, the column was preconditioned by flushing it with a solution containing SRHA.

Results The adsorption of SRHA on latex (Figure 1) and soda-lime glass (see Supporting Information) followed similar trends,

FIGURE 1. Effects of ionic strength on the adsorption of SRHA on sulfate latex: adsorbed amount versus residual concentration of SRHA. pH ) 7.2, latex surface charge ) 1.2 µCoulomb/cm2, 36 m2 latex/L. Langmuir Fit 10-1 M NaCl: 1/b ) 2.0 mg C/L, R2 ) 0.95, Γmax ) 0.23 mg C/m2; Langmuir Fit 10-2 M NaCl: 1/b ) 5.4 mg C/L, R2 ) 0.75, Γmax ) 0.14 mg C/m2; Langmuir Fit 10-3 M NaCl: 1/b ) 7.1 mg C/L, R2 ) 0.98, Γmax ) 0.09 mg C/m2. but the affinity of SRHA for soda-lime glass was greater. The adsorbed amount of SRHA on both surfaces increased with increasing ionic strength. It also increased with increasing SRHA in solution until a plateau was reached. At 10-1 M NaCl the plateau of adsorbed amount of SRHA on latex and soda-lime glass was approximately at 0.2 mg C/m2. This value is similar to that reported by Au et al. for the adsorption of polygalacturonic acid (an anionic polyelectrolyte) on negatively charged hematite at pH greater than 7 and an ionic strength of 10-2. As reported in Table 1, the thickness of the adsorbed layer, δH, on latex increased with NaCl concentration from approximately 1 nm for 10-3 M to almost 4 nm for 10-1 M (for PCS measurements the standard deviation was 0.5 nm and the coefficient of variation was 5.4%). For both latex and soda-lime glass, mobility measurements (Supporting Information) became more negative with decreasing ionic strength, independent of the presence of SRHA. At all ionic strengths, the mobility measurements were shifted toward more negative values in the presence of 1 mg C/L SRHA. Results of the column experiments are presented in Figure 2 as breakthrough curves s the normalized effluent concentration, C/C0 (C and C0 are the effluent and influent concentrations of latex colloids, respectively), as a function of the number of bed volumes treated. In phase 1, C/C0 rose VOL. 37, NO. 6, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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In phase 3, when the column was rinsed with the low ionic strength solution, a peak in the breakthrough curve was rapidly observed under all chemical conditions. This peak resulted from the detachment of deposited particles from the filter media. The magnitude of the peak increased with increasing ionic strength during phase 1. However, larger peaks did not correspond to a greater fraction of particles recovered because much larger amounts of particles were deposited in runs at high ionic strength. The large peaks in the effluent to influent particle concentration ratio when the columns were rinsed with the low ionic strength solution is consistent with the observations of McDowell-Boyer (8) and Hahn (9). The profiles of these curves obtained in the presence (Figure 2a) and in the absence (Figure 2b) of SRHA are similar. The main difference is that, for the same ionic strength, the value of C/C0 at the plateau was larger in the presence of SRHA than in its absence (this effect was particularly marked for NaCl below 10-2 M). This indicates that fewer particles were deposited when SRHA was adsorbed on the surface. Mathematical expressions were used for a more quantitative characterization of deposition and detachment during the three-step column runs. The deposition data are presented in terms of the experimental attachment efficiency, Rexp, which has been used often to characterize the efficiency of clean bed filtration (6, 11, 22, 23).

Rexp ) -ln

FIGURE 2. Experimental breakthrough curves, effects of ionic strength, and SRHA. Phase 1 ) deposition (10-0.3 to 10-4 M NaCl, pH 7.2, C0 ) 1 mg/L (1.8 × 1012 latex particles/L); Phase 2 ) rinse (10-0.3 to 10-4 M NaCl, pH 7.2); Phase 3 ) reentrainment (0 M NaCl, pH 7.2), 10-4 NaHCO3, T ) 296 K, ap ) 49 nm, ac ) 0.1 mm, U ) 1.27 × 10-3 m/s, L ) 0.25 m, E ) 0.4.

almost vertically from an initial value of zero to a curveshaped region that in turn was followed by an approximately horizontal plateau (with the exception of 5 × 10-1 M NaCl where the curve was too flat to observe the rising limb). The shape of the initial part of the breakthrough curve (vertical rise and curve) was mainly the result of advection and dispersion through the column. The plateau of the curve is where deposition is taking place when a constant concentration of particles is fed to the column. At NaCl concentrations of 10-2 M and below, the breakthrough curves at the plateau approximated unity as phase 1 progressed. In some cases (5.5 × 10-2 and 10-2 M NaCl in the absence of SRHA, and 10-1 and 5.5 × 10-2 M NaCl for 1 mg C/L SRHA), the value of C/C0 at the plateau was not constant but increased over time. Increasing values of C/C0 in the plateau region were observed with decreasing ionic strength. This trend indicates that a smaller fraction of the particles fed through the column was deposited at lower ionic strength. Previous deposition studies have commonly reported this observation (6, 7, 12-16). In phase 2, when the supply of particles to the column was terminated, a quick decrease in C/C0 occurred. This rapid plunge was followed by a gradual decrease until a plateau that approached zero was reached. 1124

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()

4ac C C0 3(1 - )η0L

(1)

Here L is the bed depth, ac is the radius of the collectors,  is porosity of the clean media, and η0 is the single collector efficiency. For submicron particles η0 is defined as the ratio between the number flux of particles which reaches the surface of the collector by convective Brownian diffusion to the upstream particle flux moving toward the collector (22). R(exp) and η0, respectively, describe chemical and physical effects on the deposition of particles on stationary collectors in clean porous media. The fraction of particle recovered, FRC2, during the rinse of phase 2 (conducted at the same ionic strength as the deposition step) was calculated as follows:

FRC2 )

particles recovered phase 2 particles deposited phase 1

(2)

It should be noted that when using this expression those particles remaining in the pore space of the column after that particle supply has been terminated are counted as recovered during phase 2 although they were never deposited. This can lead to overestimating FRC2, particularly at low ionic strength when only a small fraction of the particles flowing through the bed were deposited. Reentrainment was expressed in terms of the fraction of particles recovered (reentrained), FRE3, during phase 3. FRE3 )

particles recovered phase 3 particles deposited phase 1 - particles recovered phase 2

(3)

In practice, FRE3 represents the number of particles that detach from the filter media relative to those that were attached to the filter media after phase 2. A limitation of this expression is that the possible reversibility of deposition under constant chemical conditions can influence the results of the calculations. Specifically, if most deposited colloids are remobilized during phase 2, then the values of FRE3 will be overestimated because of the difficulty of measuring very low latex concentrations. This effect was particularly important at low ionic strength, when the amount of colloids deposited in phase 1 was small.

FIGURE 4. Interaction energy profile (sphere-plate geometry, constant potential interaction case) calculated at the conditions of phase 1 (Figure 2a) of an experiment conducted at 10-1 M ionic strength without SRHA. ap ) 49 nm, Ψparticle ) -0.23 mV, Ψcollector ) -0.30 mV, A ) 0.93 × 10-21 J, T ) 296 K, electrostatic repulsion calculated using Hogg et al. (1966), van der Waals attraction calculated using Gregory (1981) up to 8 nm, and Czarneki (1979) for larger separation distances. increased above 10-2.5 M, the adsorption of SRHA greatly decreased FRE3. At 10-2 M NaCl concentration, FRE3 increased from 0.55 without SRHA to 0.97 with 1 mg C/L SRHA. When the NaCl concentration during deposition was greater than 5.5 × 10-2 M, smaller fractions of deposited particles were recovered without changes of the solution chemistry (phase 2). When the NaCl concentration was 10-1 M, FRC2 was 0.01 in the absence of SRHA and 0.04 in the presence of SRHA. At this ionic strength, FRE3 was 0.26 without SRHA and 0.63 with SRHA. At higher ionic strength (5 × 10-1 M NaCl) no elution was observed during phase 2 both without and with SRHA. The fraction of colloids recovered during phase 3 under these chemical conditions was 0.25 without SRHA and increased to 0.50 with SRHA.

Discussion FIGURE 3. Effects of ionic strength and SRHA on deposition and reentrainment:log r(exp) and fraction of reentrained particles versus log [NaCl] (M). 10-4 NaHCO3, pH 7.2, T ) 296 K, ap ) 49 nm, ac ) 0.1 mm, U ) 1.27 × 10-3 m/s, L ) 0.25 m, E ) 0.4, C0 ) 1 mg/L (1.8 × 1012 latex particles/L). The effects of ionic strength and SRHA on deposition and reentrainment are illustrated in Figure 3. Attachment efficiencies (Rexp) increased with increasing ionic strength both in the absence and in the presence of SRHA (Figure 3a). The addition of SRHA resulted in a significant decrease of particle deposition, as represented by the downward shift in the log Rexp versus log [NaCl] curve. FRC2 was greater than 0.8 for NaCl concentrations of 10-2 M and lower (Figure 3b). When the NaCl concentration was increased above 10-2 M, FRC2 decreased suddenly to a low plateau near zero that was reached for 5.5 × 10-2 M NaCl in the absence of SRHA and for 10-1 M NaCl in the presence of SRHA. FRE3 also decreased as ionic strength was increased (Figure 3c). For NaCl concentrations below 10-2 M without SRHA and below 5.5 × 10-2 M with 1 mg C/L SRHA, FRE3 was near unity, ranging between 0.86 and 1.3 (values exceeding one are due to error resulting from overestimating FRE3, probably due to reentrainment of deposited particles in phase 2 at low ionic strength). This occurred both in the absence and in the presence of SRHA. These large values of FRE3 indicate that nearly all the particles deposited in phase 1were subsequently reentrained. As the NaCl concentration was

Theoretical analysis of the deposition and reentrainment of deposited particles was conducted using DLVO theory (24, 25) and short-range Born interactions (26). DLVO theory describes the balance between van der Waals and electrostatic interactions between two approaching surfaces as a function of their separation distance. For the repulsive case (particle and collector surface charge have the same sign) which describes the system used in this study, three regions characterize the separation distance versus interaction energy curve: the attractive primary well, the repulsive potential energy barrier, and the attractive secondary minimum (Figure 4). The maximum value of the potential energy barrier plus the depth of the secondary minimum represents the energy that a particle must possess to deposit in the primary well. Deposition in the primary well is considered to be irreversible at constant solution conditions, as the energy that a particle must possess to escape from it is equal to the sum of the depth of the primary well and the height of the potential energy barrier. The secondary minimum, in which weak aggregation is possible, can occur at large separation distances. Deposition in the secondary minimum is considered to be reversible when lowering ionic strength under most conditions. Effects of Ionic Strength. In qualitative agreement with DLVO theory, particle deposition increases with increasing ionic strength. For low ionic strengths, thick diffuse layers surround particles and collectors. The screening effect of the salt on the charges on the collectors and the particles is small. VOL. 37, NO. 6, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Deposition and reentrainment of negatively charged colloids to and from negatively charged collectors: deposition step at low ionic strength. (A) Deposition step: particles are simultaneously captured in and released from a shallow secondary minimum (no deposition in the primary minimum). (B) Rinse step: most particles held in a shallow secondary minimum are eluted. (C) Reentrainment step: (change in ionic strength) the few particles still attached to the surface are reentrained. As a result, the electrostatic repulsion between particles and collectors is large. For these conditions (10-2 M NaCl and lower), deposition in the primary well is not likely because a kinetic energy input greater than 70 kT (Table 1) is required to overcome the energy barrier but the average translational kinetic energy of Brownian particles is 0.5 kT for each direction (degree of freedom). It is plausible that, at low ionic strength, the observed deposition takes place in shallow secondary minima located at great distances (more than 20 nm) from the surface. Under these conditions, particle deposition and reentrainment can be considered the result of a dynamic process, in which particles are continuously captured and released from the shallow secondary minima (Figure 5). This speculation is supported by the observation that for low ionic strengths in phase 1, deposited particles were able to detach from collectors without changes in the solution chemistry in phase 2. In fact, most of the particles deposited during phase 1 were recovered during phase 2 (Figure 3b). As proposed by Loveland et al. (27), colloids may collect in the region in front of the energy barrier and then, with time, diffusion and advection may carry them out of the secondary minimum back to the bulk solution. These conclusions are, in part, consistent with those of McDowellBoyer (8) who suggested that the reentrainment of particles larger than 1 µm following deposition at low ionic strength could not be explained on the basis of deposition in the primary minimum of the DLVO-Born interaction energy curve and that this phenomenon might be attributed to deposition and subsequent release from the secondary minimum. However, this explanation of the deposition process does not include the dynamic capture and release of particles from the shallow secondary minima during deposition. This difference is a result of a particle size effect. For the particle size and solution conditions studied by McDowell-Boyer the depth of the secondary minimum was estimated to be 6.7 kT, which is significantly deeper than 1126

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those calculated for the submicron particles used in this study (see Table 1). The larger particles and resultant deep secondary minima allow for “permanent” attachment under constant ionic strength conditions. For the submicron particles used n this research, the secondary minima at low ionic strength are shallow, suggesting a dynamic reversibility. As the salt concentration is increased, the diffuse layers of collectors and particles are progressively compressed and, as a consequence, electrostatic repulsive interactions are reduced. DLVO calculations show that for higher ionic strengths the height of the energy barrier is smaller, whereas the secondary minimum is deeper and located at a closer distance of separation between the surfaces (Table 1). Under these conditions, deposition of particles both in the primary well and in the secondary minimum is theoretically possible. It is the authors’ opinion that, when the energy barrier is small, deposition may be viewed as a combination of the two collection mechanisms. A fraction of the particles collected in the secondary minimum, due to fluctuations in their internal energy, may be able to “jump” into the primary well over the potential barrier, and only those particles still deposited in the secondary minimum may be reentrained during phase 3 (Figure 6). This idea is supported by the observation that only a portion of the particles remaining on the filter after phase 2 are recovered during phase 3 (Figure 3c); a fraction of the deposited particles are irreversibly attached to the media. At 5 × 10-1 M NaCl and in the absence of SRHA, the calculated total interaction energy curve did not show a potential energy barrier (Table 1), and deposition was expected to occur in the primary well. However, contrary to predictions based on DLVO calculations, deposition was partially reversible, and particles were reentrained during phase 3. These observations may be interpreted in terms of the presence of additional repulsive interactions at short distances of separation (e.g., hydration forces) between

FIGURE 6. Deposition and reentrainment of negatively charged colloids to and from negatively charged collectors: deposition step at high ionic strength. (A) Deposition step: particles are captured both in the primary and secondary minima. (B) Rinse step: particles are held in the primary and secondary minima. (C) Reentrainment step: (change in ionic strength) particles held in the primary minimum remain attached, while particles held in the secondary minima are reentrained. particle and collector. These additional repulsive interactions may be related to the presence of hydration layers on amorphous silica surfaces (28). At high salt concentration, the thickness of the hydration layer becomes important relative to the magnitude of the double layer interaction at short separation distance (29); practically, at a separation distance corresponding to its thickness, the hydration layer limits the depth of the primary well. It is speculated here that such short-range repulsive forces may prevent particles from reaching a deep “DLVO” primary well, and that detachment from a primary well of limited depth may be possible. The curves of C/C0 versus bed volume for phase 1 observed during some of the column experiments (Figure 2a and b) actually had small increases in slope in the plateau region. These can be interpreted by considering that, as the number of deposited particles increases during the run, the rate of escape also increases over time (because it is dependent on the number of particles deposited), and the net attachment efficiency decreases with time. When the rate of deposition equals the rate of escape, equilibrium is established between particles collected in the secondary minimum and particles in solution, and C/C0 approaches 1. This progressive increase of C/C0 in the plateau has been related to a blocking effect (26, 30, 31) which describes the reduced surface area available for further deposition due to the increased amount of the collectors’ surface that is covered by latex particles as the experiment progresses. Blocking is an important phenomena in particle deposition in porous media. However, in this study the effect of blocking is expected to be very small, because, even at the highest ionic strength when nearly all particles were deposited, the amount of particles fed through the column was too small to cover a significant part of the collectors’ surface. Effects of SRHA. Under most chemical conditions, the adsorption of humic substances resulted in reduced attachment efficiencies in phase 1 and increased reentrainment (FRE3) in phase 3. The magnitude of these effects was a

function of solution chemistry. It is suggested that these occurrences originated from the increased electrostatic stabilization (increased negative charge) and the steric interactions (32-36) resulting from the adsorption of SRHA on the media grains and on the suspended particles. The adsorption of humic substances at NaCl concentrations at and above 10-2 M corresponded to reduced deposition and increased reentrainment (Figures 2 and 3). Under these solution conditions, the thickness of the diffuse layer was smaller than that of the adsorbed layer (Table 1), and direct interaction between adsorbed SRHA layers on both particles and collectors is probable. Stabilization under these conditions involved some steric interaction (perhaps better described as electrosteric interaction, because the direct interaction between adsorbed layers of similarly charged polyelectrolytes always has an electrostatic component (33). When the deposition step was conducted at less than 10-2 M NaCl, complete or nearly complete particle recovery was obtained independent of the presence of humic substances. For this solution chemistry, the ionic diffuse layer is much larger than the hydrodynamic thickness of the adsorbed layer (Table 1). Particles were, for this reason, stabilized by the electrostatic interaction between diffuse layers surrounding both particles and collectors. The stabilizing effect of SRHA, under these circumstances, can be attributed primarily to the increased negative particle and collector charges and the consequent increased negativity of their electrokinetic potentials (Table 1) caused by SRHA adsorption. Specifically, more negative electrokinetic potentials resulted in greater electrostatic repulsion. In terms of DLVO calculations, the increased electrostatic repulsion between particles and collectors due to the adsorption of SRHA results in higher repulsive energy barriers and in shallower attractive secondary minima located at greater distances of separation (Table 1). Furthermore, the presence of an adsorbed polyelectrolyte such as SRHA produces additional repulsive forces at close distances of VOL. 37, NO. 6, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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separation (37). These modifications of the total interaction energy profile should lead to lower deposition efficiencies and greater detachment rates. The experimental results presented in this paper are in agreement with these considerations. However, it should also be considered that in the interfacial region the charge on the adsorbed SRHA is fixed in space, whereas the charge on the electrolyte is free to diffuse (38, 39). The effects of the presence of this fixed charge are not captured in the DLVO model. For NaCl concentrations above 10-2 M, the significant reduction of Rexp and the increase of the fraction recovered in the presence of SRHA can be related to the larger potential barriers and shallower secondary minima calculated under these conditions. In addition, electrosteric interactions may also have played an important role. For NaCl concentrations of 10-2 M or lower, the energy barriers with or without the addition of SRHA were high (Table 1) and deposition in the primary well is unlikely. Therefore, the decreased Rexp obtained in the presence of SRHA can be the result of the reduced depth of the secondary minimum. Under these ionic strength conditions and independent of the presence of SRHA, both FRE2 and FRE3 were about 1. Because most of the colloids deposited in phase 1 were subsequently recovered in phase 2, the data for FRE2 seem more accurate than those for FRE3 because of the previously mentioned difficulty in accurately measuring low latex concentrations. The reversibility of attachment during phase 2 supports the idea that deposition under these circumstances was controlled by the secondary minimum. Finally, regarding DLVO calculations in the presence of SRHA, it must be noted that, to simulate electric double layer interactions, zeta potentials were used as the electric potential located at 0.6 nm from each surface. This approach does not take into account the change in the location of the slipping plane and steric interactions that may occur due to the adsorption of SRHA. Particularly, at higher ionic strengths the extended thickness of the adsorbed layer may cause the slipping plane to be moved further away from the surface. However, moving the slipping plane within the adsorbed layer thickness range did not significantly affect calculations of the depth of the secondary minimum. Steric or electrosteric interactions were not included in our calculations because there are no reliable expressions to calculate them. Therefore, repulsive interactions in the presence of SRHA may have been underestimated. These additional repulsive forces may have reduced the depth of the primary minimum and allow for reversible deposition at high ionic strength. Comparison of Experimental Data with Theoretical Models for Particle Deposition. Theoretical attachment efficiencies were calculated using two different theoretical approaches: the interaction force boundary layer (IFBL) model (40, 41) based on deposition in the primary well, and the Maxwell model (9) based on deposition in the secondary minimum. The Hamaker constant used in the both models was calculated using the Lifshintz theory for the silica/water/ latex system (26) assuming that the adsorption of SRHA would have a limited effect on this parameter (42). The IFBL approximation has been used often to predict the collection efficiency of particle deposition in packed beds (6, 7, 9, 17) in the presence of repulsive interaction. In general, the quantitative agreement between prediction obtained with this theory and experimental observation has been poor (6, 7, 43). In addition, the lack of sensitivity to particle size of the experimental collection efficiency does not compare well with the model prediction of decreasing collision with increasing particle size (6, 9). Hahn (9, 44) conducted simulations of the deposition of colloids under unfavorable chemical conditions using a combination of Brownian dynamics and Monte Carlo techniques. The results of these simulations indicated that the secondary minimum could play an important role in the 1128

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deposition of colloids. Hahn then proposed a simple secondary minimum deposition model based on the kinetic theory of James Clerk Maxwell. The fraction of particles with sufficient energy to be transported over an energy barrier can be predicted using the distribution of velocities of small particles in a system.

fMax(vp) ) 4π

( ) mp 2πkT

3/2

vp2exp

(

)

-0.5mpvp2 kT

(4)

where

∫f ∞

0

Max(vp)dvp

)1

(5)

Here fMax(vp) is the probability of finding particles with velocity over the interval vp + dvp, and mp is the particle mass. The particle velocity can be used to calculate its one-dimensional thermal kinetic energy, equal to 0.5 mpvp2. The theoretical attachment efficiency can then be described in terms of the activation energy, EACT. In the case of deposition in the secondary minimum, EACT is the energy equal to the depth of this well, Φ2Min. If the kinetic energy of a particle is greater than this activation energy, then the particle has sufficient energy to be transported from the secondary minimum back into solution.

EACT ) Φ2Min ) 0.5 mpvACT2

(6)

Here vACT is the minimum velocity that a particle of mass mp must possess to escape the energy minimum. The theoretical attachment efficiency for deposition in the secondary minimum, R2Min, can be defined as the probability that a particle does not have sufficient energy to escape from the secondary minimum.

RMax2 ) 1 -

∫

∞ f (v )dvP VACT Max p

(7)

Two issues related to the use of the Maxwell model are noted here. First, the “resistance” of the fluid to particle reentrainment caused by viscous drag is not taken into account in the calculations. Second, Maxwell model (and IFBL) predictions are sensitive to the value of the Hamaker constant, which is not an easy parameter to vary experimentally, especially for complex aquatic systems. Calculations of the theoretical attachment efficiency were conducted with the Maxwell (R2Min) and the IFBL models (R1Min) for several of the experimental conditions of this study and compared to the experimental collision efficiency (Rexp). The results are presented in Figure 7. They indicate that predictions based on deposition in the secondary minimum provided a better fit of the experimental data than those obtained with the IFBL approximation. Similar fits between theoretical and experimental attachment efficiencies (not shown in this paper) were also obtained in the absence of SRHA (17). Experimental results for the deposition of NOMcoated hematite particles in quartz porous media reported in the literature (13) were also simulated. For all particles, the Maxwell model provided a significantly better prediction of the experimental data than the IFBL model (17). Hahn (9) used the Maxwell and IFBL models for analogous simulations for the deposition of latex particles of different sizes and surface charge on glass collectors. The predictions of the Maxwell model were in better agreement with the experimental collision efficiency measured by Hahn and those obtained from the literature than those obtained with the IFBL model. Predictions by both the Maxwell and IFBL models are dependent on particle size s the depth of the secondary minimum for the Maxwell model and the height of the potential energy barrier for the IFBL model s but the

FIGURE 7. Comparison of theoretical models with experimental results: log r versus log [NaCl] (M), 1 mg C/L SRHA added. pH ) 7.2, A ) 0.93 × 10-20 J, ap ) 49 nm, ac ) 0.1 mm, E ) 0.4, U ) 1.27 × 10-3 m/s, L ) 0.25 m, T ) 296 K. calculations of R2Min with the Maxwell model are significantly less sensitive to this parameter. As a result, the Maxwell approach closely predicts experimental deposition results that have been shown to be relatively insensitive to particle size (6). In summary, the modeling effort supports the importance of the secondary minimum in particle deposition.

Acknowledgments We gratefully acknowledge the support of U.S. Environmental Protection Agency and the National Science Foundation, and the suggestions of Dr. E. Shchukin of the Moscow State and Johns Hopkins Universities, and anonymous reviewers.

Supporting Information Available Details on adsorption, electrophoretic mobility, and hydrodynamic layer thickness experiments. Information on the calculation of the total interaction energy profiles (pdf). These materials are available free of charge via the Internet at http://pubs.acs.org.

Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

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Received for review June 15, 2001. Revised manuscript received October 30, 2002. Accepted November 13, 2002. ES015566H

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