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Jeremy A. Redman a, Mary K. Estes b, Stanley B. Grant a,* a Department of ...... [9] M.V. Yates, C.P. Gerba, L.M. Kelley, Appl. Environ. Microbiol. 49 (1985) 778.

Colloids and Surfaces A: Physicochemical and Engineering Aspects 191 (2001) 57 – 70

Resolving macroscale and microscale heterogeneity in virus filtration Jeremy A. Redman a, Mary K. Estes b, Stanley B. Grant a,* a

Department of Chemical and Biochemical Engineering and Materials Science, Uni6ersity of California, Ir6ine, CA 92697, USA b Di6ision of Molecular Virology, Baylor College of Medicine, Houston, TX 77030, USA

Abstract In this paper, we characterize the filtration and deposition profiles of a recombinant analog of Norwalk virus, an important waterborne pathogen, in packed beds of saturated quartz sand under both ‘clean-bed’ and ‘dirty-bed’ conditions. Under clean-bed conditions with NaCl as the electrolyte, the retained Norwalk virus particles decline like a power-law with depth. The power-law decay in retained particle concentration is consistent with the predictions of a recently proposed filtration model which assumes that microscale heterogeneity leads to particle filtration length scales of all sizes; i.e. the filtration is fractal in nature. However, under dirty-bed conditions with either ground water or wastewater as the pore fluid, the deposited Norwalk virus particles profiles are considerably more complex. Analysis of these data using both the traditional filtration model and the fractal filtration model suggests that, under dirty-bed conditions, macroscale heterogeneity dominates virus removal rates. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Norwalk virus; Virus filtration; Heterogeneity; Water reuse; Ground water recharge

1. Introduction In the United States, greater than 50% of the population relies on ground water as the principal source of drinking water [1]. To reduce the risk of waterborne diseases, Federal and State rules often mandate the disinfection of water used for irrigation and/or municipal supply. Despite the fact that, historically, greater than 50% of all waterborne disease outbreaks in the US are attributed * Corresponding author. Tel.: + 1-949-824-7320; fax: +1949-824-3672. E-mail address: [email protected] (S.B. Grant).

to ground water [2–5], these mandates have not traditionally extended to water obtained from ground water sources, primarily because such water was thought to be ‘naturally disinfected’ by percolation through the subsurface matrix. However, mounting evidence that ground water may serve as a pathway for the transmission of viral pathogens [6–11] has led to a rethinking of this policy. In 2000, for example, the US Environmental Protection Agency proposed the Ground Water Rule, that would require routine monitoring and specific levels of virus treatment [12]. Because of their small size, resistance to disinfection, and potential mobility in subsurface environments, vi-

0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 1 ) 0 0 7 6 4 - 6


J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

ral pathogens are generally considered the target organisms in both existing and proposed ground water regulations. The dominant processes influencing the fate and transport of viruses in the subsurface include advection, dispersion, inactivation, and filtration. While advection, dispersion [13], and inactivation [9] are fairly well understood, the factors controlling virus filtration are not. Because of their small size (B 1 mm), viruses are considered colloidal particles. The standard deep-bed filtration model for colloidal particles is premised on a simple first-order expression for the decline of the interstitial particle concentration C with distance z: dC/dz = −C/l. In this formulation, the filtration length scale l is the reciprocal of the commonly used filter coefficient u [14]. The value of l varies in magnitude depending on the properties of both the filter media and the contaminant particles as well as the mechanism of filtration [15]. Traditionally, filter performance has been assessed by monitoring the effluent particle concentration and this breakthrough concentration is often used to calculate a dimensionless parameter, the overall single collector removal efficiency, ph [16]. The single collector collision efficiency p represents the frequency of particle/collector collisions, and the attachment efficiency h represents the number of collisions that result in sticking. The value of p can be determined from geometric and hydrodynamic considerations [15,17]. While h is known to depend on solution and surface chemistry, attempts at predicting h values from first principles have not been successful [16,18]. It has been proposed that microscale heterogeneity of both particles and collectors — including surface roughness and spatial distribution of charge — accounts for the large discrepancy between model and data [19– 23]. The parameter ph is often assumed to be constant in the initial or clean-bed state of filtration — corresponding to conditions when the fractional surface coverage of the collectors is small. However, as particles accumulate on the collectors, ph can decrease due to blocking or the ‘shadow’ effect [24– 26] or increase due to filter ripening [27– 29].

In a recent review of virus filtration literature, Schijven and Hassanizadeh [30] point to number of studies in which measurements of h over different length scales were shown to differ by up to an order of magnitude [31–36]. Additionally, a number of filtration experiments involving parasites, bacteria, and viruses suggest that non-exponential decline in the retained particle concentration results from physical and/or surface-chemical particle heterogeneity [37– 40]. In this report, we examine the impact water quality has on the filtration and deposition patterns of radiolabeled recombinant Norwalk virus (rNV) particles in packed beds of ultra-cleaned quartz grains. In particular, we compare initially ‘clean-bed’ filtration in the presence of an indifferent electrolyte with ‘dirty-bed’ filtration for two different pore fluids: a tertiary treated wastewater and a ground water. The results of these experiments are examined using a recently-proposed model for particle filtration that incorporates heterogeneity at all length scales [41]. Differences between this fractal model and the standard deepbed filtration model are presented.

2. Fractal filtration model The development of the fractal filtration model was presented in detail by Redman et al. [41], and is briefly reviewed here. This derivation applies only for the steady-state portion of the breakthrough curve, and it assumes that hydrodynamic dispersion can be neglected; the influences of unsteadiness and dispersion are the subject of ongoing investigations. Instead of assuming a constant filtration length scale — corresponding to constant a l or ph value — Redman et al. assumed that a range of filtration length scales are represented among the particle population. A particle filtration distribution (PFD) function n(l, z) was defined such that n(l, z)dl represents the number of particles per unit pore volume at depth z in a filter that have filtration length scales in the range l to l+ dl. If each differential slice of the particle population obeys first-order kinetics, then (n(l, z)/#z = − n(l, z)/l, which after integration becomes n(l, z)= n(l, 0)e − z/l.

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Two limiting cases can be identified. If the filter media and particles are perfectly homogeneous, then a single filtration length scale l applies to all of the particles and the initial PFD is given by n(x, 0) =C0l(x −l), where l(x) is Dirac’s delta function, C0 is the influent particle concentration, and x is the integration variable. For this choice of an initial PFD, the standard deep-bed filtration equations are recovered: C(z)= C0e − z/l S(z)=

t0uC0m − z/l e lzb

(1a) (1b)

The variables in Eqs. (1a) and (1b) represent the particle concentration in the pore fluid C(z) and retained on the filter media S(z) at depth z, the operation time t0 of the filter, the interstitial velocity u of the pore fluid, and the filter’s porosity m and bulk density zb. Under clean-bed conditions, the filtration length scale in the standard deep-bed filtration equation is typically defined as follows [15,17]: l=

2dc 3(1− m)ph


where dc is the collector diameter. The opposite of a perfectly homogeneous filter is one for which no single filtration length scale characterizes the filtration dynamics. In this case, the initial PFD may be considered fractal in nature and n(l,0) =Al − a, where the premultiplier A and power-law exponent a are constants [42]. In addition to heterogeneity at the particle/collector scale (microscale heterogeneity), heterogeneity can also occur at the filter scale (macroscale heterogeneity). This macroscale heterogeneity can be modeled by dividing each differential slice of the PFD distribution by a macroscale heterogeneity function h(z) that varies with distance z in the filter. In this way, the filtration length scale l is replaced with an effective filtration length scale l eff, where l eff =l/h(z). The effective PFD for a system with micro- and macroscale heterogeneity is n(l, z)= n(l, 0)e − zh(z)/l and after integration, the fractal filtration model can be written as follows:


C(z)= C0z − (a − 1)B(a− 1,z,l*min,l*max,a) S(z)=

t0uC0m zh(z) − a z B(a,z,l*min,l*max,a) zb H0 (z)


(3a) (3b)

where, B(m,z,l*min,l*max,a)=

G(m,z/l*max,z/l*min )(1−a) −a 1 − a l 1 max − l min (3c)

lminz H0 (z) l z l*max = max H0 (z)


l*min =

H0 (z)=




(3f )



In these equations lmin and lmax are the minimum and maximum filtration length scales represented in the particle population, respectively, and Y(r, b0, b1) is the incomplete Gamma function, which is G(r,b0,b1)= bb10t r − 1e − tdt. The function B(m,z,l*min,l*max,a) in Eqs. (3a–3f) is a weak function of z if l*min z l*max and m\ 0. In clean-bed filters (i.e. h(z) is constant), when lmin  z lmax, the fractal filtration model predicts that (i) the concentration of particles in the pore fluid decays like a power-law of depth, C(z) z − (a − 1) when a\ 1; and (ii) the concentration of particles retained in the filter decays like a power-law of depth S(z) z − a when a\0. The macroscale heterogeneity function h(z) in Eqs. (3a–3f) can be calculated from experimental measurements of the retained particle concentration as follows. Letting wi and S(zi ) represent, respectively, the dry weight of the i-th segment of the filter and the measured concentration of retained particles in the i-th segment, then the macroscale heterogeneity function h(zi ) for the i-th segment can be estimated by solving for the root of Eqs. (4a) and (4b):

l z l z (a − 1) z− B a− 1,zi, min i , max i ,a i H0 (zi ) H0 (zi )


S(zj )wj j = 1CoumActo

= 1− %



H0 (zi )= % h(zj )Dj j=1



J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

Here, Ac represents the cross-sectional area of the filter, Zj represents the length of the j-th segment and all other variables have been previously defined.

3. Materials and methods

3.1. Preparation of Norwalk 6irus particles Radiolabeled recombinant Norwalk Virus particles used in the filtration experiments were prepared by infection of Spodoptera frugiperda insect cells with the rNV-baculovirus at a multiplicity of infection of 10 in Hink’s medium (GibcoBRL, Gaithersburg, MD), followed by the addition of 10 mCi ml − 1 of 35S-trans label (ICN, Irvine, CA). Thirty-three hours postinfection, cold methionine was added, and the infection was allowed to continue for 4 days. rNV particles released into the medium were harvested by pelleting for 2 h at 26 000 rpm in an SW28.1 rotor (Beckman, Fullerton, CA), followed by isopycnic centrifugation on a cesium chloride gradient, diluted into water and pelleted. The pelleted rNV particles were then suspended in 500 ml of sterile Milli-Q water (18.2 MV cm, Millipore, Inc., Bedford, MA) and characterized by electron microscopy and BSA protein assay (Pierce, Rockford, IL). The procedure for generating unlabeled rNV particles used for the electrophoretic mobility measurements was the same as described above, except that no radioactive precursors were added during the infection step that was carried out in Grace’s media supplemented with 0.5% fetal calf serum.

3.2. Water sampling Wastewater samples were collected from the final effluent of the San Jose Creek Water Reclamation Plant, located in Los Angeles County, California. Ground water samples were collected from a 15.2-m deep well located in United States Geologic Survey’s research basin at the San Gabriel Spreading Grounds in Los Angeles County. The well was screened between 13.4 and 14.9 m. Water was collected from a depth of 7.9 m below ground surface, and at the time of

sampling, the depth to ground water was 6.6 m below ground surface. The samples were pumped (Fultz Pumps, Inc., Lewiston, PA) into autoclaved polypropylene 5- and 10-l carboys at a rate of 0.7 l min − 1. The pump and tubing were purged for approximately 15 min (wastewater sampling) and 1 h (ground water sampling) prior to sample collection. After collection, the wastewater and ground water samples were capped, placed on ice, and transported to a 4 °C cold room, where they were stored in the dark until use. Deionized water (Milli-Q) and analytical-grade NaCl, HCl, and NaOH were used to prepare a 0.01 M NaCl solution, which was equilibrated to approximately pH 7.

3.3. Physical, chemical and microbiological analyses of water samples Inline measurements of several physical and chemical parameters were conducted while collecting the water samples, using a Surveyor 4 Minisonde (Hydrolab Corp, Austin, TX). These measurements included temperature, dissolved oxygen, specific conductivity, pH, and oxidation/ reduction potential. Several additional chemical analyses were conducted in the laboratory. UV absorbance was measured using a Hewlett Packard spectrophotometer model 8452A (Palo Alto, CA). The total dissolved solids concentration was determined gravimetrically. Total organic carbon (TOC) was measured using an O-I-Analytical 1010 Total Organic Carbon Analyzer. The electrophoretic mobility of rNV particles in the various waters was determined using a Rank Brothers Mark II apparatus (Cambridge, UK) equipped with a 0.5-mW green (544 nm) He–Ne laser (Melles Griot Model 05 SGR 851, Melles Griot, Carlsbad, CA) as described in previous reports [43,44]. The microbiological quality of the water was determined by heterotrophic plate count.

3.4. Filtration experiments The quartz sand used in the filtration experiments was purchased from Unimin (New Canaan, CT), size fractionated by a wet sedimentation/ flotation technique and then cleaned to remove

J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

metal and organic contaminants [45,46]. The cleaning steps included soaking the sand in 12 N HCl for at least 24 h, washing with deionized water (Milli-Q) and baking the sand overnight at 800°C. Cleaned sand was stored under a vacuum. Before conducting filtration experiments, the sand was rehydrated by boiling for at least 1 h in deionized water. The filtration experiments were carried out in 1.6-cm inner diameter, adjustable bed-height glass columns (Pharmacia LKB C16, Piscataway, NJ) by allowing the quartz sand to settle in deionized water. The packed columns were equilibrated by pumping (Pharmacia LKB P1 peristaltic pump) approximately 60 pore volumes of the sample water through the column prior to each filtration experiment. Filtration experiments were conducted by pumping a pulse of virus-laden solution (either wastewater, ground water or 0.01 M NaCl solution) through the column for 30 min, followed by a pulse of virusfree solution for at least 30 min. In addition, during select experiments an additional pulse of virus-free solution was applied for 30 min. The pulses were controlled by a three-way valve. At the culmination of a pulse, the pump was stopped for a short period (B10 s), while the valve was switched. Influent solutions were prepared by diluting radioactively-labeled rNV particles directly into 250 ml of sample solution. The stock rNV solution was filtered (0.22 mm, Whatman, Clifton, NJ) prior to dilution into 0.01 M NaCl for the experiment labeled high C0, to remove large clumps of coagulated particles. Samples were collected from the influent solution at both the beginning and end of the experiment. Column effluent was collected in 3-min increments using an automatic fraction collector (Pharmacia LKB FRAC-200). Blank samples were collected from the column effluent prior to applying the initial virus-laden pulse, as well as from all non-viruscontaining solutions. All samples were mixed with scintillation cocktail and analyzed for radioactivity with a Beckman LS6000IC scintillation counter (Beckman, Fullerton, CA). In select experiments, the pore fluid (either ground water or wastewater) was filtered (0.45 mm) prior to the equilibration step. All filtration experiments were conducted in a 4 °C cold room.


3.5. Analysis of quartz fractions Upon completion of each filtration experiment, the glass columns were partially disassembled and the free fluid at the top of the packed sand bed was siphoned away. Compressed air was used to force the packed bed out of the column assembly as an intact core, whereupon it was sectioned and dried overnight in a 40 °C oven. The sections were weighed, and approximately 1 g of quartz from each section was transferred to a scintillation vial, mixed with 10 ml of scintillation cocktail and analyzed for radioactivity as described previously. The coefficient of variance between the weights of the analyzed subsections was less than 3%. The presence of quartz and wastewater/ ground water organics did not interfere with the scintillation detection of the radiolabled particles, as was demonstrated by a control experiment in which a known quantity of radiolabeled rNV particles was added to quartz sections from a filter bed that had been previously equilibrated with either wastewater or ground water (data not shown).

3.6. Estimating model parameters To compare the fractal filtration model with experimental data, values for the parameters in Eqs. (3a–3f) must be estimated. Some of these parameters (C0, t0, u, m, zb, wi, S(zi ), Ac, Di ) are either known or are readily measurable. The remaining parameters (a, lmin, lmax) were estimated as follows. The power-law exponent a was estimated from the slope of a log–log plot of the retained particles S(z) against depth z for the filtration experiment involving 0.01 M NaCl with a ‘high C0’. The minimum filtration length scale lmin was assumed to be equal to the diffusion limited deposition rate for the smallest particles (dp = 2 nm, the approximate diameter of a single rNV capsid protein) and calculated from Eq. (2) [47,48]. Because lmin was chosen to have a value equal to the diffusion limited deposition rate, and Brownian particles cannot be removed from the pore fluid faster than they can be transported to the collector surface, the effective filtration length

J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70


scale l eff can never be smaller than lmin: l eff ] lmin. Recalling that l eff =l/h(z), this inequality leads to the following constraint on the value of h(z): h(z)51. A single value of lmax was arbitrarily chosen such that this constraint on the value of h(z) was satisfied throughout the length of each filter for all of the experiments presented here.

4. Results

4.1. Virus filtration In this study we examined the filtration of rNV particles in columns packed with uniformly sized quartz grains. Filtration experiments were carried out with three different pore fluids: a 0.01 M NaCl solution equilibrated at pH 7 representing clean-bed filtration, and treated wastewater and ground water samples representing dirty-bed filtration. Physical and chemical parameters of the three pore fluids are presented in Table 1 and the relevant experimental conditions are presented in Table 2. The rNV particles are negatively charged in all three pore fluids, as measured by capillary microelectrophoresis (see Table 1) as are the bare quartz grains [45]; thus particle filtration occurs against a repulsive electrostatic barrier. In the experiments, a pulse of virus-laden solution was applied to a pre-equilibrated column for

approximately five pore volumes. This pulse was followed by a virus free pulse of identical chemical composition for approximately three pore volumes. In the experiments involving the 1- and 3-day-old ground water and the 2-day-old wastewater, a final pulse of different composition was applied to the columns (as described later). The breakthrough curves (BTCs) for the filtration experiments are plotted in Fig. 1. Two separate filtration experiments were conducted in the presence of 0.01 M NaCl [Fig. 1 (A)]: one with C0 = 1.6× 109 particles ml − 1 (‘low C0’, represented as circles) and C0 = 6.5× 1010 particles ml − 1 (‘high C0’, represented as squares). For the high C0 experiment, the stock rNV solution was filtered (0.22 mm) prior to dilution into the influent NaCl solution; the stock was not filtered prior to dilution for the low C0 experiment. The average normalized steady-state breakthrough concentrations of rNV particles for both experiments is 0.8590.07 (9 1 SD). The scatter in the steadystate portion of the BTC for the low C0 experiment (between pore volumes 2–7) may be an artifact of analysis, as the measured levels of radiation were close to the detection limit of the scintillation counter. In the presence of unfiltered ground water [Fig. 1 (B)], the normalized steadystate breakthrough concentration of rNV particles is 0.389 0.02. Within experimental error, filtration experiments conducted with 1-, 3-, and 5-

Table 1 Physical and chemical characteristics of pore fluids used to equilibrate the packed beds Parameter

Ground water


0.01 M NaCl

Temperature (°C)a Dissolved oxygen (mg l−1)a Specific conductivity (mS cm−1)a pHa Oxidation/reduction potential (mV)a TOC (mg −l–C−1)c UV254 absorbance Heterotrophic plate count (CFU ml−1)c Total dissolved solids (mg l−1)c Electrophoretic mobility of rNV particles (mm s−1)/(V cm−1)

23.0 9 0.4 0.12 9 0.05 917 93 7.11 90.01 329 97 2.5 90.1 0.0439 110 616 −0.6190.09

27.6 9 0.4 4.23 9 0.08 1109 9 11 6.96 9 0.03 663 915 8.5 90.1 0.1167 23 632 −0.7490.10

NDb ND 1124 6.93 ND ND ND 0 586 −0.709 0.16


Determined at time of collection with YSI sonde. Not determined. c Determined within 24 h of collection. b

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Table 2 Experimental and model parameters for packed-bed filtration studies Source

Age (days)

Column length (cm)

Superficial velocity (cm s−1)

Influent concentration (particles ml−1)


Ground water Ground water Ground water Filtered ground water Wastewater Wastewater Filtered wastewater NaCl (low C0) NaCl (high C0)

1 3 5 10 2 7 9

30.4 29.5 29.3 30.2 30.3 29.1 29.7 29.0 29.4

0.025 0.025 0.025 0.025 0.025 0.025 0.026 0.024 0.025

2.8×1010 4.6×1010 1.2×1010 5.8×109 2.4×1010 1.5×1010 5.0×109 1.6×109 6.5×1010

NDb 0.81 0.77 1.02 0.79 0.83 0.89 1.23 0.93

The bulk density of the quartz was determined to be zb =1.33 g cm−3. The packed bed porosity was estimated to be m =0.49 9 0.02 and the average grain diameter, determined by sieve analysis, was dc =222 932 mm [52,53]. As described in Section 3, the value of lmin, determined from Eq. (2), is 10−2.88 m; the power-law exponent a is 0.8; and lmax was chosen to be 10−1 m. a Recovery is defined as the fraction of radiation in the filter effluent and deposited on the quartz compared to the total radiation applied at the influent. b Not determined; column was not segmented.

day-old ground water had near-identical results. After 10 days, the ground water was filtered (0.45 mm), and a packed bed was equilibrated with this water. The steady-state breakthrough concentration of virus particles decreased to 0.2490.03. In contrast, the virus BTCs in the presence of unfiltered wastewater showed a pronounced temporal dependence [Fig. 1 (C)]. Two days after the wastewater was collected, the steady-state breakthrough concentration of rNV particles was 0.229 0.01 (circles). After the wastewater was aged 7 days (triangles), the steady-state breakthrough concentration increased to 0.799 0.06. After 9 days, the wastewater was filtered (0.45 mm) and a packed bed was equilibrated with the filtered wastewater (diamonds). The steady-state breakthrough concentration of the rNV particles in filtered wastewater was 0.3290.03. The high C0 clean-bed (NaCl) experiment and the 7-day wastewater experiment have been published previously [41].

4.2. Spatial deposition of attached particles As described in Section 3, a virus-free solution was pumped through the filter after the passage of the virus-laden pore fluid. The purpose of this pulse was to minimize the amount of fluid-phase

radiation remaining in the column prior to removing the sediment from the column apparatus for sectioning. This step ensured that the radiation measured in the dried segments was from attached particles, not fluid-phase particles. The spatial distributions of retained particles are presented in Fig. 2. When the pore fluid consists of 0.01 M NaCl [Fig. 2 (A)], the retained particle concentration decreased as a power-law with distance (i.e. the data fall along a straight line when plotted in a log –log format). Apart from a few sections near the top of the filter, the concentration of retained particles generally declined monotonically with distance in the presence of ground water [Fig. 2 (B)]. Furthermore, the three different ground water profiles — corresponding to ground water that had been aged 3, 5, and 10 days — are quite similar. Although breakthrough data were collected for the ground water aged 1 day, that particular filter bed was not dissected and analyzed for radiation. In contrast to the ground water and NaCl experiments, the concentration of retained particles in the presence of wastewater [Fig. 2 (C)] reached a maximum at a depth of approximately 10 cm in the filter bed. Note also that there are significant differences in the deposition patterns for the three different wastewater conditions.


J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

4.3. Particle detachment In select experiments, a final pulse was applied to the column to measure potential virus detachment caused by changes in the chemical composition of the pore fluid. A virus-free wastewater solution was applied to filters that had been previously exposed to the 1- and 3-day-old ground

Fig. 2. The concentration of rNV particles retained on filter beds equilibrated with NaCl (panel A), ground water (panel B), and wastewater (panel C). The amount of radiation, as determined by scintillation counting, per unit weight of column segment is plotted against the midpoint of each column segment.

Fig. 1. rNV particle breakthrough curves for filtration experiments conducted with NaCl (panel A), ground water (panel B), and wastewater (panel C). The breakthrough curves were generated by dividing the concentration of rNV particles in the filter effluent C(L) by the concentration in the influent C0 and then plotting this ratio against the number of pore volumes passed through the filter. Relevant physical and chemical characteristics of the experimental system are summarized in Tables 1 and 2.

water, and a virus-free ground water solution was applied to a filter that had been previously exposed to the 2-day-old wastewater. The final pulse in these experiments was the same age as the equilibrating pulse; i.e. a 1-day-old wastewater pulse was applied to a column equilibrated with 1-day-old ground water, etc. The goal of these studies was to determine how wastewater exposure, as might occur during a ground water recharge operation, affected the mobilization of


J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

previously deposited viruses. This final pulse was initiated between pore volume 9– 10. Referring to Fig. 1 (B, C), approximately one pore volume after changing the influent pore water, the effluent virus concentration increased slightly. The fraction of viruses eluted by wastewater from the 1- and 3-day ground water columns were estimated to be 0.0005 and 0.004, respectively [Fig. 1 (B)]. The fraction of viruses eluted by ground water from the 2-day wastewater column was estimated to be 0.003 [Fig. 1 (C)]. However, in all three experiments, the concentration of viruses eluted was low and very close to the detection limit of the scintillation counter. In this set of experiments, perturbation of the pore fluid chemistry by switching from ground water to wastewater (or vice versa) was minimally effective at mobilizing previously deposited rNV particles.

5. Discussion

5.1. Comparison between standard deep-bed filtration model and fractal filtration model The standard deep-bed filtration model predicts an exponential decline in retained particle concentration with distance in clean filter beds Eqs. (1a) and (1b). The deposition patterns of rNV particles retained in the presence of 0.01 M NaCl indicate a power-law decline in S(z) with distance z Fig. 2 (A). Whether this non-exponential pattern is the result of spatial variability in collection rates within the filter (macroscale heterogeneity), or results from an intrinsic range of collection rates within the particle population (microscale heterogeneity) is not obvious. In order to assess the source of heterogeneity, both the deep-bed filtration model and the fractal filtration model were applied to the data set. The standard deep-bed filtration model Eqs. (1a), (1b) and (2) can be used to calculate values of the overall single collector efficiency for each column segment using a modified formulation presented by Martin et al. [49]:

(ph)i = −

2 dc ln 1− 3 (1-m)Di





N0 − %Ni − 1

where (hh)i, N0 and Ni represent the overall single collector removal efficiency for the i-th column segment, the number of particles added to the column, and number of particles retained on the i-th segment, respectively. The parameter ph is used as the experimental variable, rather than the more conventionally used h, because in dirty-bed filters, hydraulic and geometric conditions could vary with depth and hence p would not be constant throughout the length of the filter. Results of applying Eq. (5) to the retained particle concentration data are presented in Fig. 3. The ph values calculated using Eq. (5) for the clean-bed NaCl experiment are not constant throughout the filter bed (Fig. 3 (A)). Rather, ph decreases like a power-law with distance. While blocking or ripening phenomena have been invoked to explain non-exponential behavior in filtration experiments, it is unlikely that either of these phenomena are responsible for the patterns observed in the presence of NaCl. The S and ph profiles (Fig. 2 (A) and Fig. 3 (A), respectively) are inconsistent with a blocking mechanism, because there is no region at the top of the filter where the amount of deposition does not vary with distance (i.e. a saturation front). Ripening, in which deposition is accelerated by the presence of previously deposited particles, might be consistent with the high concentration of particles observed near the entrance of the filter. However, if ripening were occurring, greater ph values would be expected in the experiment utilizing the highest influent concentration, which is not supported by the results presented in Fig. 3 (A). Instead, the ph values in the high C0 experiment are consistently lower than comparable segments in the low C0 experiment (compare squares and circles in Fig. 3 (A)). Microscale heterogeneity in the collection rates of contaminant particles may contribute to the spatial variability of ph. This hypothesis is in agreement with one of the well-documented fail-


J.A. Redman et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 191 (2001) 57–70

ings of DLVO theory in predicting collection rates under repulsive electrostatic conditions — namely that both particles and collectors are assumed to have homogeneous surfaces and surface potentials [16,18]. Microscale heterogeneity can arise from a number of sources, including variations in the surface potentials of both the particles and collectors, non-uniform size distributions, surface roughness, and the non-spherical nature of the collectors, as well as others [16]. The fractal model for particle filtration presented here accounts for this microscale heterogeneity by assuming that there is no single filtration length scale l, but

Fig. 4. The spatial variability of the heterogeneity function h(z) (left axis) and l eff max (right axis) for filters equilibrated with NaCl (panel A), ground water (panel B) and wastewater (panel C). Note that the scale on the right axis is reversed; l eff max values plotted higher on this axis correspond to a greater degree of filtration. Relevant parameters used in the calculations are presented in Table 2.

Fig. 3. Experimental ph values calculated by Eq. (5) for segmented filters equilibrated with NaCl (panel A), ground water (panel B) and wastewater (panel C).

rather a range from lmin to lmax. In addition, this model quantifies the degree of spatial variability (i.e. macroscale heterogeneity) in filter properties by calculating values for a heterogeneity function h(z) for each column segment. Regions that are unfavorable for filtration will have a smaller h(z) value and correspondingly larger maximum and minimum effective filtration length scales, l eff max = lmax/h(z) and l eff = l /h(z). When the fractal min min

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filtration model is applied to the NaCl data, the resulting h(z) and l eff max curves (Fig. 4(A)) are essentially constant over the length of the column, indicating that there is no appreciable macroscale heterogeneity in the filter beds and that the range of filtration length scales in each section of the column are identical. This suggests that although no single filtration length scale can be used to describe the rNV filtration in this particular system, there exists a fixed range of length scales, lmin to lmax, that applies throughout the length of the filter. Indeed, despite the fact that the BTCs for the two NaCl experiments are nearly identical (implying that ph values calculated from the BTCs should be near identical, see Fig. 1(A)), the ph profiles are notably different (Fig. 3(A)). The values of l eff max calculated from the fractal filtration model, on the other hand, compare favorably between the two NaCl experiments (Fig. 4(A)). The fact that the fractal model parameters are not sensitive to the influent virus concentration is further evidence that this model is correctly capturing the physics of clean-bed filtration. The retained particle concentration in the ground water equilibrated columns generally decreased with distance (Fig. 2(B)), although the S(z) profiles do not exhibit the power-law behavior observed in the presence of NaCl. The calculated values of ph (Fig. 3(B)) also decline with distance. The ground water experiments show an approximate two order of magnitude decrease in ph from the filter entrance to exit compared to a 5 1 order of magnitude decrease in ph for the NaCl experiments. When the fractal filtration model is applied to the data (Fig. 4(B)), the h(z) and l eff max values show significant spatial variability. The effective maximum filtration length scale is lowest near the column entrance and increases with distance, suggesting that filtration occurs preferentially at the column entrance. This behavior is consistent with a ripening phenomena. As the packed beds were being equilibrated with the ground water, the top several centimeters became visibly discolored, presumably due to deposition or adsorption of suspended solids and/or natural organic matter in the ground water. These constituents likely altered the electrostatic potential of the collectors, created more surface area, and/


or altered the hydrodynamic conditions, which could be responsible for the enhanced deposition rates near the top of the filters. In contrast to the ripening observed in filter beds equilibrated with ground water, the wastewater equilibrated filters showed a minimum in retained particle concentration near the column entrance (Fig. 2(C)). The retained particle concentration achieves a maximum at a depth of approximately 10 cm. When ph and l eff max values are calculated, the results confirm that the initial several centimeters of the column are much less favorable for particle deposition than deeper depths (Fig. 3(C) and Fig. 4(C)). The S(z) patterns observed here are similar to patterns observed in other systems where blocking of deposition sites by previously deposited particles occurs [24]. During the equilibration step that preceded the filtration experiment, wastewater organics or suspended solids probably deposited near the top of the filter. Organic surface coatings have been implicated in blocking deposition by forming steric and/or electrosteric barriers [34,50], which is consistent with the decreased deposition of rNV particles observed here. Indeed measurements of the rNV electrophoretic mobility show that the particles are most negatively charged in the wastewater, and least negatively charged in the ground water, although the observed difference in mobilities is not great (Table 1). In general, the shape of the ph and l eff max distributions calculated for the dirty-bed experiments are quite similar. In the case of the ground water experiments, both ph and l eff max show a decrease in the collection efficiency with distance (Fig. 3(B) and Fig. 4(B)). For the wastewater equilibrated filters, both models indicate that filtration in the initial region of the filter is less favorable (Fig. 3(C) and Fig. 4(C)). The differences between experiments are also preserved by both filtration models. For example, there was very little filtration in the 7-day-old wastewater compared to the other two wastewater filtration experiments (Fig. 1(C)) and this fact is reflected in the values of ph and l eff max. Furthermore, in experiments with similar BTCs (e.g. the 2- and 9-day-old wastewater and the 3- and 5-day-old ground water) the ph and l eff max values are similar. Taken as a whole,


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these results suggest that in filter beds containing significant spatial variability in collector properties, the macroscale heterogeneity of the filter has a much greater influence on particle filtration compared to microscale heterogeneity. Hence, understanding the spatial and temporal nature of the macroscale heterogeneity is critical to predicting virus filtration in natural systems. Furthermore, these results suggest that clean-bed filters may be a poor model system for characterizing the factors most likely to dominate virus filtration in the field. As mentioned previously, the observed powerlaw decay in S(z) with distance for the NaCl experiments is predicted by the fractal filtration model. Although the normalized steady-state breakthrough rNV concentrations for the two NaCl experiments are quite similar, the S(z) profiles have different slopes: 0.8 for the high C0 and 0.5 for the low C0. As a first-approximation, we assumed that the parameter a in Eqs. (3a–3f) Eqs. (4a) and (4b) had the same value in all of the experiments presented here. Whether or not a is a universal constant is not clear. Aside from the differences in influent concentration, the rNV stock solution was passed through a 0.22-mm filter prior to being diluted into the NaCl solution during the high C0 experiment. Potentially large clusters of coagulated virus particles and protein debris may have been applied to the filter bed during the low C0 experiment. The difference in slopes could therefore be due to differences in the initial rNV particle concentration (in which case, a clearly is not universal), differences in the nature of the rNV particle preparation, or simply within the margin of error of our experimental system.

5.2. Implication for potable reuse Using reclaimed wastewater to augment or recharge existing ground water supplies is becoming an increasingly attractive and necessary endeavor as water suppliers struggle to keep up with increasing population demands. Typically recharge water is ponded in specially designed basins and allowed to infiltrate into the subsurface. Over time, organic matter, suspended solids and biofilms accumulate on basin sediments. A number of studies have shown that wastewater components, such as

organic matter, that deposit on sediment grains can reduce the effectiveness of packed beds in filtering colloidal particles [34,51]. The experiments presented in this study support this conclusion. After being exposed to a wastewater for approximately 18 h (corresponding to approx. 60 pore volumes) substantial spatial variations in deposition patterns and corresponding h(z) and l eff max values are observed (Fig. 2 (C) and Fig. 4(C), respectively) in the filters. Particle deposition is lowest near the entrance, presumably due to increased repulsive forces resulting from the presence of a previously filtered/deposited wastewater component, such as organic matter or bacteria. The increased repulsive forces at the filter entrance effectively reduces the length over which substantive particle filtration can occur. It would be reasonable to assume that as the exposure time of the filter bed to the wastewater is extended, this ‘contamination front’ would progress deeper into the packed bed, further reducing the effective length of the filter available for the removal of viruses. As the wastewater is aged, the degree of repulsive forces increases. This is clearly demonstrated by comparing the breakthrough curves for the wastewater aged for 2 and 7 days (Fig. 1(C)). An almost fourfold increase in the effluent virus concentration is observed after the wastewater has been aged 5 days. This can also be seen in the order of magnitude differences in l eff max values calculated from the deposited virus concentration for each experiment (Fig. 4(C)). Clearly, some component of the wastewater is evolving over time to create a much more unfavorable environment for virus filtration. Furthermore, this wastewater component is most likely particulate in nature. After passing the 9-day aged wastewater through a 0.45-mm filter, the l eff max profiles returned to the pre-aged state (the 2-day wastewater), and the corresponding normalized effluent particle concentration also dropped to a value similar to the earlier experiment. Bacteria growing in the wastewater are an obvious potential source of particulates that would increase in concentration as the wastewater was allowed to age. The presence of deposited bacteria on the surface of the collectors could stabilize the rNV particles by a blocking process; e.g. by creating an electrosteric barrier to deposition. Alternatively, rNV par-

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ticles may be transported in the pore fluid adsorbed to a stable colloidal or bacterial phase, so-called colloid-facilitated transport [16]. The initial concentration of heterotrophic bacteria was lower in the wastewater (23 CFU ml − 1) compared to the ground water (110 CFU ml − 1), although the higher concentration of organics present in the wastewater (Table 1) could serve as a substrate for the growth of heterotrophic bacteria and lead to an increase in the concentration of particles over time. Further studies aimed at clarifying the relationship between the concentration of bacteria and virus filtration seem warranted. These results have important implications for the use of wastewater in ground water recharge operations. As wastewater is applied to a recharge basin, wastewater components will deposit on near-field sediment grains reducing the effectiveness of the packed bed to act as a barrier to pathogen transmission. Over time, the extent of this blocking zone will increase reducing the filter’s ability to remove pathogens.

6. Conclusion Traditional methods for predicting particle filtration involve calculating h values from measured breakthrough concentrations of laboratory- and short field-scale experiments. The results presented in this study, coupled with the work of other researchers, suggest that deep-bed filtration theory oversimplifies a complex natural phenomena. By analyzing the retained particle profiles, rather than breakthrough concentrations, we find that S(z) follows a power-law distribution for the clean-bed filtration of rNV particles in packed beds composed of quartz grains. This non-exponential behavior implies that predictions of filtration based on h will overestimate the degree of removal. The situation is further complicated by the spatial variability in collector properties due to the deposition or sorption of components of natural water, such as suspended particles, organic material, and bacteria.


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