Article pubs.acs.org/est
Surface Roughness Impacts on Granular Media Filtration at Favorable Deposition Conditions: Experiments and Modeling Chao Jin,† Stefano D. Normani,† and Monica B. Emelko*,† †
Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada S Supporting Information *
ABSTRACT: Column tests were conducted to investigate media roughness impacts on particle deposition in absence of an energy barrier (i.e., high ionic strength). Media/collector surface roughness consistently influenced colloid deposition in a nonlinear, nonmonotonic manner such that a critical roughness size associated with minimum particle deposition could be identified; this was confirmed using a convection-diffusion model. The results demonstrate that media surface roughness size alone is inadequate for predicting media roughness impacts on particle deposition; rather, the relative size relationship between the particles and media/collectors must also be considered. A model that quantitatively considers media surface roughness was developed that described experimental outcomes well and consistently with classic colloid filtration theory (CFT) for smooth surfaces. Dimensionless-scaling factors f roughness and f PCIF were introduced and used to develop a model describing particle deposition rate (kd) and colloid attachment efficiency (α). The model includes fitting parameters that reflect the impact of critical system characteristics such as ionic strength, loading rate, hydrophobicity. Excellent agreement was found not only between the modeled outcomes for colloid attachment efficiency (α) and experimental results from the column tests, but also with experimental outcomes reported elsewhere. The model developed herein provides a framework for describing media surface roughness impacts on colloid deposition.
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considerably higher than on uncoated, smooth beads.18 Similarly, Shellenberger and Logan (2002) investigated the deposition of latex microspheres and two strains of bacteria (E. coli and Dechlorosoma sp KJ.) suspended in a high ionic strength solution and observed 50% higher deposition on rough glass beads as compared to smooth beads.19 Several others have also concluded that (bio)colloids preferentially deposit on rough surfaces as compared to smooth ones.20−22 In contrast, several studies have also reported that surface roughness does not enhance particle or bacterial deposition in packed columns or on flat plate surfaces. For example, Morales et al. (2009) reported that surface roughness resulted in a 20% increase in particle removal by small media with an effective size of 0.3−0.4 mm, but not by larger media with 0.8−1.2 mm effective size.16 Similarly, Shellenberger and Logan (2002) did not observe any differences in particle removal when high ionic strength suspensions of latex microspheres were passed through rough and smooth media.19 In further contrast, Chen et al. (2010) investigated nanoscale roughness on stainless steel/ aluminum plates and reported less particle deposition on rough
INTRODUCTION A thorough understanding of the physical and chemical mechanisms of particle removal by granular media filtration is required for better evaluation and optimization of particle and microorganism removal by filtration in engineered and natural (e.g., subsurface) systems.1−4 In the past few decades, numerous experimental and theoretical studies have been conducted to investigate the effects of multiple factors affecting particle deposition. These include particle and filtration media properties,5,6 physicochemical (or biological) interactions between particles and media,7−9 and system operational conditions.10,11 Among these, the morphology of media/ collector surfaces (i.e., roughness) is an important factor that has been recognized for decades; however, literature on this topic has been, for the most part, contradictory, nonmechanistic, and nonquantitative.12−16 It is widely believed that media surface roughness can enhance colloidal particle deposition on surfaces; numerous examples of this effect have been reported. Tamai (1983) examined the deposition behavior of polystyrene latex particles on polyamide and polyacrylonitrile fibers and found that colloidal particles preferably attached along rough surface grooves rather than on open smooth planes.17 Bai and Zhang (2001) coated glass beads with polypyrrole and observed that particle deposition on the relatively rough, coated surfaces was © 2015 American Chemical Society
Received: Revised: Accepted: Published: 7879
April 20, 2015 June 6, 2015 June 8, 2015 June 8, 2015 DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology
Figure 1. Representative 2-D and 3-D SEM images of Media A and Media B (U.S. standard, Mesh 20−25 and Mesh 30−35) with no treatment, smooth (T0); Treatment 1, moderate roughness (T1); and Treatment 2, roughest (T2).
successfully described particle deposition on smooth and rough surfaces. While it is widely believed that media surface roughness can enhance particle deposition on surfaces; this effect has not been consistently observed nor rigorously described. The objectives of this investigation were to evaluate media roughness impacts on particle deposition in absence of an energy barrier and to develop a model framework that is consistent with and builds on classic colloid filtration theory by describing them.
surfaces relative to smooth ones in some cases. Several other studies have reported similar outcomes.23,24 Accordingly, while a potential impact of surface roughness on particle deposition is generally expected, the nature of that impact and the factors that govern it are not well described. Consequently, the approach to incorporate media surface roughness within mathematical frameworks describing colloid deposition on surfaces such as granular media is currently unclear. Particle attachment on surfaces is partly governed by DLVO forces, which are the sum of Lifshitz-van der Waals attraction forces and electrostatic double layer repulsive forces.25 It is believed that only a few nanometers of surface roughness can reduce the magnitude of interaction energy substantially, thereby enhancing particle deposition on surfaces.15,26,27 Surface charge heterogeneity, attachment within the secondary energy minimum, hydration, and hydrophobicity have also been used to explain contributions of surface roughness to particle deposition.8,28,29 Additional factors that may help to interpret contributions of surface roughness to particle deposition include straining,30 grain to grain contact,31 the “shadow effect”32 and others.33 While all of these factors may be able to qualitatively explain surface roughness impacts on particle deposition in specific situations, none have been proven broadly relevant or applicable. Here, column tests were conducted using two colloidal particles (1.0 and 4.5 μm diameter), two sizes of glass beads (Medium A: 0.707 to 0.841 mm and Medium B: 0.5 to 0.595 mm) and three levels of surface roughness (smooth, moderately rough, and roughest). All of the experiments were conducted at a loading rate of 1.5 m/h with the microspheres suspended in a background electrolyte solution of 100 mM KCl. A finite element model was developed, which enabled simultaneous evaluation of colloid concentrations deposited on the media and in the pore fluid. Based on the calculated deposition rate, which was confirmed by the finite element model, dimensionless models that describe the deposition rate (kd) and attachment efficiency (α) were developed and
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MATERIALS AND METHODS Colloidal Particles. Two sizes of carboxylated, fluorescentdyed polystyrene microspheres (Fluoresbrite YG microspheres, Polysciences Inc., Warrington, PA) were used: 1.0 and 4.5 μm diameter. These sizes were verified by dynamic light scattering (Zetasizer NanoZS Malvern, UK). The stock suspensions of 1.0 and 4.5 μm microspheres contained 4.99 × 1010 and 4.99 × 108 microspheres/mL, respectively. The density of the microspheres was 1.045 g/cm3. Prior to introducing the microspheres into the filtration column, the 1.0 and 4.5 μm microsphere stock suspensions were diluted to achieve influent concentrations (C0) of 5.7 × 107 and 1.0 × 106 particles/mL, respectively, with a pH of 6.5− 6.7. The microspheres were suspended in 100 mM KCl, thereby creating favorable conditions for particle deposition. The colloid suspensions were sonicated in a water bath for 30 min prior to and throughout the experiment to ensure no particle aggregation. This was confirmed using epifluorescence microscopy before and after the experiments. Granular Porous Media and Surface Modification. Two sizes of spherical soda-lime glass beads (Class V, MO-SCI Corporation, Rolla, MO) were used as model collectors. The beads were size-fractioned with nylon sieves (U.S standard size of 20−25 and 30−35) and had diameters of 0.707 to 0.841 mm (Medium A) and 0.5 to 0.595 mm (Medium B). Prior to modification, the glass beads had smooth surfaces. All glass beads were soaked in 2% Extran (VWR, Canada) for 30 min 7880
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology
introduction in the column influent. Then, six pore volumes of the colloidal particle suspension were passed through the column. The seed suspension was continuously sonicated to prevent particle aggregation and maintain a constant influent concentration. All experiments were conducted in duplicate. Column effluent samples were collected every minute in 5 mL glass tubes using a fraction collector (Spectra/Chrom CF-1, Houston, TX). The microsphere concentrations in the effluent samples were determined by measuring UV absorbance (HP model 8453 UV-spectrophotometer, Agilent, Canada) at 280 and 220 nm for the 4.5 and 1.0 μm particles, respectively. Column effluent samples were sonicated for 3 min and then vortexed for 15 s prior to measuring absorbance. The particle concentrations were then calculated using a calibration curve (Supporting Information Figure S-1). Destructive sampling of the packed bed was conducted after every experiment to determine the spatial distribution of microspheres within the porous media and to perform a mass balance to evaluate any microsphere loss within the system (Supporting Information Figure S-2). After each experiment, the packed media were removed from the column in seven discrete segments (six 2 cm segments and one 3 cm segment). Each segment was placed in a glass tube (20 mL) containing 10 mL of Milli-Q water and the mass of the medium was recorded. The glass tubes were sonicated for 15 min and then vortexed for 30 s at 2000 rpm to release attached microspheres and obtain a homogeneous supernatant. A 1 mL sample of supernatant was collected from each tube and the microsphere concentration was enumerated using the previously described spectrophotometric method.39 Samples were diluted with background electrolyte solution as necessary. Model Development. Colloid transport in a saturated homogeneous porous medium with first-order attachment and inactivation was defined by Sim and Chrysikopoulos (1995) as
and then sonicated for 15 min to remove metal and organic impurities. They were extensively rinsed with deionized (DI) water and then soaked in 12 N HCl (Fisher Scientific, Canada) for 12 h, after which they were washed with Milli-Q water and baked at 550 °C overnight. Hydrofluoric (HF) acid (BDH, Canada) was used to etch the glass surfaces to achieve varying levels of surface roughness.34 The etching rate and extent is related to the HF acid concentration and reaction time.35 Two different acid concentrations and etching durations were employed to generate the two desired scales of roughness. Moderate roughness was achieved by soaking the glass beads in 8% HF acid for 30 min (Treatment 1, moderately rough), whereas the “roughest” surface was achieved by soaking the beads in 36% HF acid for 12 h (Treatment 2, roughest). During the etching process, a magnetic stir bar was used to continuously mix the acid to maintain uniform etching conditions. After etching, the modified glass beads were extensively rinsed with Milli-Q water until the rinsewater reached a pH of 6.52−6.92. The rinsed beads were then baked at 550 °C for 12 h to remove any residuals or impurities. Characterization of Media Surface Properties. The surface topography of the etched glass beads was assessed using scanning electron microscopy (SEM) (JEOL 6380LV, Peabody, MA) with 3-Dimensional fractographic analysis. The beads were coated with 10 nm of pure gold and then 3D SEM images were obtained by merging the paired topographic images using stereophotogrammetry software, which can provide detailed information regarding surface roughness features, as shown in Figure 1. Mercury intrusion porosimetry (MIP) (Porous Materials, Inc. Ithaca, NY) was used to evaluate the pore volume distribution and total surface area of the glass bead surfaces.36 Electrokinetic Characterization of Colloidal Particles and Collectors. Microelectrophoresis (ZetaSizer Nano ZS, Malvern, UK) was used to characterize the electrokinetic properties of the polystyrene microspheres suspended in the background electrolyte solution (100 mM KCl) used during the column experiments. Microsphere electrophoretic mobility was measured in triplicate at 22 ± 1 °C using particle suspensions of 1.0 × 106 and 2.3 × 108 particles/mL, of 4.5 and 1.0 μm microspheres, respectively. seven grams of clean glass beads were wet back, extensively rinsed with DI water and equilibrated in 100 mM KCl solution at pH 5.8.37 After 20 min of sonication, the electrophoretic mobility of the background electrolyte was measured. The corresponding zeta-potentials of colloids and glass beads were calculated from the measured electrophoretic mobilities using Smoluchowski’s equation.8 Column Experiments. Bench-scale column tests were conducted by pumping the colloidal particle suspensions through an adjustable-height glass chromatography column (GE health care, C16/20) with 1.6 cm inner diameter. The glass beads were wet-packed to a height of 15.0 ± 0.1 cm with vibration to maximize compaction and minimize air entrapment and formation of preferential pathways for fluid flow and associated particle transport. Using a gravimetric method,38 the porosities of the packed media A and B were determined to be 0.39 and 0.38, respectively. To ensure that the packed media were saturated with the background electrolyte solution, 30 pore volumes of particlefree background electrolyte were pumped through the packed bed at a constant loading rate (1.5m/h) prior to microsphere
ρ ∂C* ρ ∂ 2C ∂C ∂C + =D 2 −v − λC − λ* C * ∂t θ ∂t ∂x θ ∂x
(1)
where C is the colloid concentration in the pore fluid [M/L3], C* is the colloid concentration on the medium [M/M], t is time [T], ρ is the bulk density of the porous medium [M/L3], θ is the porosity of the porous medium [−], D is the dispersion coefficient [L2/T], v is the interstitial pore fluid velocity [L/T], λ is the decay rate for colloids in the pore fluid, and λ* is the decay rate for colloids on the porous medium [1/T].40 The units are defined as M = mass, T = time, and L = length. The dispersion coefficient is further defined as D = αLv where αL is the longitudinal dispersivity [L/T], which is defined as α = 1.75dm where dm is the mean grain size.41 Colloid deposition on the porous medium is defined as ρ ∂C* ρ = kdAC − (kdD + λ*)C* θ ∂t θ
(2)
where is the first-order attachment coefficient and is the first-order detachment coefficient [1/T].40 Microspheres do not degrade, so λ = λ* = 0 in this study. For a semi-infinite domain, the initial and boundary conditions are specified as kAd
C(x , 0) = 0, C*(x , 0) = 0
(3a)
C(0, t ) = C0
(3b)
−D 7881
kDd
∂C(0, t ) + vC(0, t ) = vC0 ∂x
(3c)
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology Table 1. Characterization of Physical and Chemical Properties of Glass Beads media type- treatment
media size (μm)
roughness (Rq) (nm)
cumulative pore volume (mL/g)
total surface area (m2/g)
zeta potential (mV)
media A-T0 media A-T1 media A-T2
710−840
12.1 ± 7.6 165.9 ± 37.8 649.6 ± 76.5
0.0184 0.0206 0.0303
0.0016 0.0019 0.003
−20.3 ± 6.6 −17.9 ± 8.3 −19.6 ± 7.3
media B-T0 media B-T1 media B-T2
500−550
9.0 ± 3.9 280.3 ± 48.3 694.2 ± 89.9
0.0329 0.0433 0.0547
0.0022 0.0028 0.0034
−23.9 ± 5.3 −19.4 ± 7.8 −21.2 ± 6.3
where eq 3a represents the initial conditions, eq 3b represents a Dirichlet boundary condition at the column inlet, eq 3b represents a Cauchy boundary condition at the column inlet, tp is the time to stop the seeding of stock solution, and C0 = 0 for t > tp. A Cauchy boundary condition was used for model calibration. The system of differential equations was solved using the Galerkin finite element method. Specifically, a two-dimensional transient triangular finite element model was developed in which both equations (eqs 1 and 2) were solved simultaneously yielding the concentrations C and C* at each node. Fully implicit time stepping was used for the transient simulations and the LAPACK matrix library was used to solve the resulting system of coupled matrix equations.42 The model domain was 1 cm wide and 45 cm in length, a factor 3× greater in length than the experimental column to avoid boundary effects. Concentration breakthrough curves were determined at 15 cm from the column inlet. A total of 182 nodes and 180 elements comprised the model domain, with nodes at 5 mm spacing along the length. Although the model was two-dimensional, it was constructed to model a one-dimensional process with the same inlet concentration being applied to both inlet nodes of the model domain. The calculated colloid deposition rate depositionkdwhere kd = kAd − kDd , attachment, and detachment rates (kAd and kDd , respectively) were evaluated for each column experiment through an inverse modeling process. A total of 24 experiments were calibrated. Each calibration consisted of 30 trials in which initial values of kAd and kDd were selected by uniform random sampling. For each trial, the simplex method was used to minimize the sum of the absolute value to the 1.5th power of the difference between the simulated and observed effluent concentrations.43 The corresponding values of kAd and kDd that yielded the least error or residual for each of the 24 conducted experiments were used. To validate the implemented model, the numerical results from eq 1-3 were compared to analytical solutions (Supporting Information Figure S-3).
scale asperities and only minimal microscale roughness−this definition of “smooth” surfaces is consistent with other experimental works that have been integral in developing classic CFT.2,3,6,19 The root-mean-square height (Rq) of unmodified smooth beads of Media A and B was 12.1 ± 7.6 nm and 9.0 ± 3.9 nm (mean ± standard deviation), respectively. Treatment 1 resulted in surface roughness (Rq) of 165.9 ± 37.8 nm and 280.3 ± 48.3 nm on Media A and B, and Treatment 2 resulted in surface roughness (Rq) of 649.6 ± 76.5 nm and 694.2 ± 89.9 nm on Media A and B, respectively. Media Cumulative Surface Area (CSA) and Cumulative Pore Volume (CPV). Surface roughness modifications can also impact packed bed “bulk properties,” such as cumulative surface area (CSA) and cumulative pore volume (CPV). Determined by mercury intrusion porosimetry, the CPV of each type of collector is plotted against pore diameter in Figure 2; the embedded figure depicts maximum CPV and
RESULTS AND DISCUSSION Media Surface Roughness. Surface characteristics determined from 10 replicate images each for all of the media used during this investigation are summarized in Table 1. Representative images depicting modifications in surface roughness on Media A and B are presented in Figure 1. These images demonstrate that beads with both sizes had the roughest surfaces after Treatment 2 (the longest period of etching). The surface asperities on the modified glass beads covered the entire media surfaces and included both macro-and microscale roughness. In contrast, Treatment 1 (the shorter etching period) created “moderate roughness” comprised of microscale roughness features with relatively few macro-scale asperities. Untreated, smooth glass beads did not have macro-
Figure 2. CPV and CSA of selected filtration media with different surface treatments.
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CSA. These results indicate that while micro- and macro-scale roughness were generated during the chemical etching process, CPV and CSA also increased, regardless of media size. As roughness size increased, CPV and CSA also increased. CPV is the pore space on the media surfaces and should be distinguished from “porosity”, which refers to void spaces in the packed bed and is more dependent on physical size of the media and packing method. Here, packed bed porosity was identical in all of the filter columns containing the same size of medium, regardless of its roughness. In contrast, the CPV of smooth Media A and B increased by 11.9% and 31.6% 7882
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
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Environmental Science & Technology
Table 2. Column Experiment Conditions, Mass Balances, Simulated Deposition Rate and Model Parameters Using Eqs 8 and 9 experiments
C/C0 (%)
mass recovery (%)
α
kAd (10−4)
kDd (10−4)
media A-T0-1.0
87.5 87.7
91.4 89.2
0.67 0.66
10.8 10.3
5.7 2.3
media A-T1-1.0
86.9 87.6
89.1 88.5
0.71 0.67
10.9 9.8
media A-T2-1.0
95.6 96.1
95.6 95.4
0.23 0.20
media B-T0-1.0
78.8 76.7
84.7 79.4
media B-T1-1.0
95.8 95.5
media B-T2-1.0
kd (10−4)
rroughness
rparticle
rmedia
rcritical
FSystem (10−5)
αSim
6.5 ± 2.0
0.012
0.98
390
0.50
2.51
0.665
1.7 5.0
7.0 ± 3.1
0.165
1.77
0.468
3.8 2.5
3.1 0.0
1.6 ± 1.3
0.650
1.01
0.266
0.62 0.69
29.6 29.8
13.7 7.6
19.0 ± 4.5
0.009
4.14
0.653
101.8 101.3
0.11 0.12
4.8 4.3
1.1 2.7
2.7 ± 1.5
0.28
1.54
0.144
73.0 74.2
75.7 80.2
0.82 0.77
25.1 25.8
1.8 4.8
22.1 ± 1.7
0.70
3.57
0.929
media A-T0-4.5
65.8 66.6
94.4 80.9
1.09 1.06
28.0 35.6
0.3 3.9
29.7 ± 2.8
0.012
5.63
1.072
media A-T1-4.5
78.5 79.9
133.5 108.5
0.63 0.58
17.2 40.6
0.6 19.3
18.9 ± 3.3
0.165
2.49
0.494
media A-T2-4.5
48.3 48.7
62.6 103.7
1.89 1.87
49.9 52.1
0.8 0.1
50.5 ± 2.0
0.650
10.26
1.795
media B-T0-4.5
40.0 41.0
115.0 83.0
1.07 1.04
97.3 104.8
26.9 43.6
65.8 ± 6.5
0.009
12.34
1.052
media B-T1-4.5
74.1 76.0
114.1 111.0
0.35 0.32
33.5 52.0
9.8 25.1
25.3 ± 2.3
0.28
3.29
0.243
media B-T2-4.5
16.0 17.6
88.0 97.6
2.13 2.02
130.9 142.9
1.0 2.0
135.4 ± 7.8
0.70
26.08
2.039
0.30
4.5
265
0.26
0.26
and 21% removal, respectively. Destructive sampling of the filter beds supports these observations (Figure 3(b)). Here, the medium with the roughest surface (T2) retained the most particles within the packed column, followed by the medium with the smooth surface (T0). The medium with the moderately rough surface (T1) had the fewest retained colloids and therefore the highest normalized effluent colloid concentration, as shown in Figure 3(a). Collectively, the colloid breakthrough curves and retained colloid concentration profiles demonstrated that when an adequate range of roughness sizes was investigated, surface roughness on media/collector surfaces consistently influenced colloid deposition in a nonlinear, nonmonotonic manner such that a critical roughness size associated with minimum particle deposition could be identified (Table 2; Figure 3). The exact mechanism(s) causing that effect (e.g., DLVO effects, hydrodynamics, etc.) must be further elucidated; however that analysis is beyond the scope of this investigation. Representative simulated effluent concentration curves (lines) are plotted as compared to the experimental data (symbols) in Figure 3(a). It can be seen that the simulated data successfully represented the breakthrough curves regardless of surface roughness. The residual error surface contours for the calibration of one experiment (4.5 μm particles on Medium A
respectively, after Treatment 1; and by 64.7% and 66.3% respectively, after Treatment 2 (Table 1). Column Experiments. All of the normalized colloid removals, mass recoveries from the packed beds, particle deposition, attachment, and detachment rates (kd, kAd and kDd , respectively), and attachment efficiencies (α) obtained during the investigation are summarized in Table 2. Representative microsphere breakthrough curves are presented in Figure 3(a) and depict the normalized effluent particle concentration (C/ C0) over time since the suspension was introduced to the filter column. The associated retained particle concentration profiles within the columns are provided in Figure 3(b). The determined C/C0 and retained particle profile were added to obtain total mass recovery during all the experiments (Supporting Information Figure S-4). The mass recoveries of the 4.5 and 1.0 μm microspheres were consistently good; mean recovery ± standard deviation was 93.6 ± 2.7% and 89.4 ± 8.4%, respectively (Table 2). The presence of surface roughness on media/collector surfaces significantly influenced colloid deposition (Table 2; Figure 3). For example, the mean removal of 4.5 μm microspheres by the roughest medium (Treatment 2) was 51%, whereas the smooth medium (Treatment 0) and the moderately rough medium (Treatment 1) only achieved 34% 7883
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology
Figure 3. (a) Representative observed (symbol) and simulated (line) colloid breakthrough curves; and (b) the corresponding retained particle concentration profiles within the column: 4.5 μm colloids on Media A with treatments T0 (Smooth), T1 (Moderately Rough), and T2 (Roughest); (c) Representative error or residual surface contours for calibration (kAd vs kDd in log scale): 4.5 μm colloids on Media A with treatment T0; and (d) Particle deposition rates kd (s−1) for 1.0 and 4.5 μm colloids in Media A and B with treatments T0, T1, and T2.
with T0 treatment) is plotted in Figure 3(c) in terms of kAd and kDd . The minimum residual is clearly visible as a v-shaped trough for low values of the detachment rate (kDd ). The calibrated particle attachment rate (kAd ) has a distinct minimum for the residual error surface, whereas the residual error surface for the detachment rate (kDd ) was relatively flat. Relative to kDd , the values of kAd contributed most to the global minimum. The values of kAd and kDd that yielded the least error or residual between observed and simulated effluent concentrations for all 24 experiments are presented in Table 2. The absolute values of the best fitted kAd for all experiments are ∼100 times higher than those for kDd (Table 2), suggesting that attachment dominated the particle deposition behavior observed during the present experimental investigation. This observation was expected, as it is consistent with CFT, which would predict that colloid deposition is dominated by attachment processes during the initial period of filter column operation (i.e., clean bed period) at favorable conditions for deposition. The particle deposition rate (kd) determined for 1.0 and 4.5 μm colloids in Medium A (0.707 to 0.841 mm in diameter) and B (0.5 to 0.595 mm in diameter) with surface treatments T0 (smooth), T1 (moderately rough), and T2 (roughest) are also presented in Figure 3(d), which demonstrates that the particle deposition rate was lower in the larger sized medium (A) than in the smaller sized medium (B) (Figure 3(d)). Higher particle deposition rates (kd) were also observed for the larger (4.5 μm) colloids than for the smaller (1.0 μm) one (Table 2). For example, the 4.5 μm colloid deposition rate on the smooth media was 457% and 346% higher in Media A and B respectively, when compared to that for 1.0 μm colloids.
(Table 2; Figure 3(d)). These observations are also consistent with CFT, which would suggest that, at the same operational conditions, (1) a lower particle deposition rate would be expected for larger media/collectors than for smaller ones and (2) a lower particle deposition rate would be expected for 1.0 μm particles as compared to 4.5 μm particles because particles near 1.0 μm in size would be near a minimum contact efficiency with collectors due to the cumulative contributions of diffusion, convection and sedimentation.2,3 As would be expected, observed trends in particle attachment efficiency (α) data are consistent with the particle deposition rates (kd) (Table 2). For example, the particle attachment efficiencies (α) calculated for the smooth medium (Treatment 0) ranged from 0.66 to 1.07 (Supporting Information Figure S5) and were close to 1.0, which would be expected at favorable conditions for particle deposition, according to CFT. The observed agreement between the experimental results obtained herein with smooth media and the theoretical outcomes expected based on CFT underscore the applicability of CFT for such experimental conditions (i.e., smooth collector surfaces) and demonstrate the efficacy of the developed model at describing particle deposition in a manner that is consistent with and builds upon classic CFT. Roughness Impacts on Particle Deposition. In general, the highest rate of colloid deposition occurred on the roughest medium (T2), followed by the smooth medium (T0); with the lowest rate of microsphere deposition occurring on the moderately rough medium (T1) (Table 2; Figure 3(d)). The exception to this trend was the scenario in which 1.0 μm microspheres deposited on Medium A. In this case, colloid 7884
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology
Figure 4. (a) Linear relationship between the observed particle deposition rate, kexp(s−1) and the proposed dimensionless factor, F system[−]; (b) Comparison of normalized experimental21 and simulated total deposited P. aeruginosa 848/25 and 803/4 cells on 316L-stainless steel surfaces with various roughness; and (c) comparison of the observed αexp[−] and simulated αsim[−] particle attachment efficiency.
Modeling Particle Deposition in Response to Variable Media Surface Roughness. A dimensionless model describing the particle deposition rate for variable levels of media surface roughness is proposed, such that
deposition rates on the smooth and moderately rough media were similar, while less microsphere deposition was observed on the roughest medium; this result was confirmed by microsphere retention within the beds, the mass recovery assessment, and replicated experiments (Table 2). Although shifted in that experiment, the existence of a critical roughness size associated with a minimum particle deposition rate was generally demonstrated (e.g., Figure 3(d)), such that when the roughness size was less than a critical value, particle deposition decreased with increased roughness size; and, when the roughness size was greater than the critical size, particle deposition increased with increased roughness size. These results also highlight that the interrelationships between the multiple system factors (e.g., particle size, media size, loading rate, roughness size, etc.) that govern particle deposition on surfaces must be appropriately considered when attributing experimental outcomes to specific system factors or mechanisms; elucidation of these mechanisms was not the focus of this investigation, however. Most importantly, these results underscore that consideration of media surface roughness size in isolation is inadequate for describing or predicting roughness impacts on particle deposition; rather, additional system factors such as the relative relationship between the sizes of the particles being deposited and the media collectors must also be considered when describing these effects.
kd ∝ F system
(4)
where kd = kAd − kDd is the calculated colloid deposition rate and Fsystem is a dimensionless system factor that quantitatively describes roughness effects on particle deposition as F system = froughness *fPCIF
(5)
Here, f roughness is the media roughness factor, which is a dimensionless scaling factor accounting for media surface roughness impacts on particle deposition as froughness = C1
rroughness | r − 1| critical
(6)
and f PCIF is a dimensionless particle-collector interaction factor (PCIF) representing the relative relationship between particle, critical roughness, and collector sizes as fPCIF =
rparticle*rcritical 2 rmedia
(7)
where rroughness is the mean measured roughness size and rcritical is the critical roughness size; rparticle and rmedia are the average 7885
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology particle and media collector radii, respectively. C1 is a system specific fitting constant that reflects other operational factors such as ionic strength, hydrophobicity, etc. which affect particle deposition on surfaces. Equations 4−7 represent a framework that describes particle deposition on surfaces in response to variable media surface roughness. The framework can be adjusted to reflect various operational conditions (e.g., ionic strength, loading rate, hydrophobicity, etc.) using the following general model
That study was selected because it involved investigation of four levels of media surface roughness, whereas most reported investigations only assess two levels of roughness. Cell deposition data from that study were normalized by the maximum observed deposition for a given cell type so that the two cell types investigated (i.e., the deposited particle types) could be quantitatively compared. Details regarding the application of the framework to these data are available in Supporting Information Table S-1. The observed normalized cell deposition data were then compared to simulated normalized deposition data obtained using the developed framework (eqs 4−7) (Figure 4(b)). This analysis demonstrates that the developed framework could also successfully describe (R2 = 0.972) the effects of surface roughness on cell deposition as reported by Vanhaecke et al. (1990),21 thereby suggesting the potential for broader application. Of course, in this case C1 and C2 have different values than those that were used to describe the present study system; many operational factors would have likely contributed to this (e.g., data obtained in a parallel plate chamber rather than a filter, cell hydrophobicity, hydrodynamics, etc.). Elucidation of those factors or mechanisms was not the objective of the present investigation, which focused exclusively on describing media surface roughness effects on particle deposition. It is important to note that the framework that is developed in eqs 4−7 to describe particle deposition on surfaces in response to variable media surface roughness is consistent with and builds upon classic CFT for particle deposition on smooth surfaces. Specifically, at favorable conditions for particle deposition, bigger particles (e.g., 4.5 μm here) and smaller media collectors (e.g., Medium B here) should have higher deposition rates as compared to those obtained using smaller particles (e.g., 1.0 μm here) and bigger media collectors (e.g., Medium A here).3 The developed framework was consistent with CFT for smooth media and successfully described (R2 = 0.956) the experimental observations obtained with the smooth media regardless of particle and media size (Supporting Information Figure S-7). Modeling Attachment Efficiency (α) in Response to Variable Media Surface Roughness. The developed dimensionless factor Fsystem (eq 6) can be utilized to predict particle attachment efficiency (α). During physicochemical filtration, the attachment efficiency (α) is calculated from experimental data by
kd = C2*froughness *fPCIF = C2*C1
rroughness r *r | r − 1| particle critical critical * 2 rmedia
(8)
where C1 and C2 are the system specific fitting constants that account for various other operational factors that affect particle deposition on surfaces. This framework enables calculation of best fit values of rcritical (Table 2). The model presented in eq 8 was used to describe the present study system; here, C1 and C2 are 8 and 54, respectively (Figure 4 (a)). The observed particle deposition rates obtained for the various roughness, media, and particle size combinations used in this investigation are successfully described by the model, with a coefficient of determination (R2) of 0.981. The residual plot for the best-fit model is provided in the upper left corner of Figure (4a). It does not show heteroscedasticity or systematic trends and the residuals are centered around zero; therefore, the model is valid. Using this model, particle deposition rates can be described by simply multiplying Fsystem by the slope of the best fit regression line (54 for the present study system). Following the tradition of plotting the observed particle deposition rates against the modeled ones in a 1:1 plot yields a slope of 0.981 (as would be expected in a linear transformation) and an intercept of 1.4× 10−4 (Supporting Information Figure S-6). Perfect agreement between observed and modeled deposition rates would yield a slope of 1.0 and intercept of 0. Following this rationale, the model described by eq 8 successfully describes particle deposition in the study system. In the framework developed in eqs 4−7 to describe particle deposition on surfaces in response to variable media surface roughness, the particle-collector interaction factor ( f PCIF) increases as particle size increases and/or collector size decreases. The media roughness factor (f roughness) contributes to mimicking the observed minima in particle deposition or “sag effect”. When rroughness approaches rcritical, the f roughness approaches unity and the determined deposition rate approaches the minimum deposition rate at rcritical; otherwise, the deposition rates vary proportionally as observed in the conducted experiments. Not surprisingly, when rroughness > rcritical, media surface roughness enhances particle deposition, as has been widely reported.19,22,44,45 In contrast, when rroughness < rcritical, media surface roughness contributes to decreased particle deposition, relative to smooth surfaces; this may explain some reported outcomes as well.19,21,22 To explore the applicability and validate the efficacy of the proposed framework for describing particle deposition on surfaces in response to variable media surface roughness, the framework was applied to data reported by Vanhaecke et al. (1990) (upper left inset in Figure 4(b)), who systemically investigated the kinetics of Pseudomonas aeruginosa attachment on stainless steel with several levels of surface roughness.21
α=−
2dc ln(C /C0) 3(1 − ε)Lη0
(9)
where the ε is the porosity of the medium, dc is the collector diameter, η0 is the single collector contact efficiency, C/C0 is the normalized effluent concentration at the plateau of breakthrough curves, and L is the bed depth.2 Here, attachment efficiency on rough media surfaces (αroughness) was described by αroughness =
F system|rroughness F system rsmooth
*αsmooth
(10)
The experimental (αexp) and simulated particle attachment efficiencies (αsim) were calculated using eqs 9 and 10, respectively and compared in Figure 4(c), in which the error bars represent the range between duplicate experiments. Least squares linear regression of the data yields a slope of 0.998, an intercept of 0.0283 (close to the ideal slope of 1.0 and intercept 7886
DOI: 10.1021/acs.est.5b01998 Environ. Sci. Technol. 2015, 49, 7879−7888
Article
Environmental Science & Technology of 0), and a coefficient of determination (R2) of 0.978, thereby suggesting that αsim successfully described αexp regardless of the utilized combinations of particle, roughness, and media sizes. As this traditional representation of data and associated analysis represents further transformation of the particle deposition rate data (Table 2; Figure 4(a)), this outcome was expected because with each such transformation, detail regarding the original variance in simulation of data is lost, resulting in an artificially inflated coefficient of determination (R2). Accordingly, simulation of kd (as presented above), rather than α provides the more accurate indication of a model’s ability to successfully describe particle deposition data. Using bothapproaches, the presented experimental data as well as data reported by others demonstrated that the framework presented herein can successfully describe particle deposition in response to variable media surface roughness.
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ASSOCIATED CONTENT
S Supporting Information *
Supporting Information (Figure S1−S7 and Table S-1). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.5b01998.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +1-519-888-4567×32208; e-mail: mbemelko@ uwaterloo.ca. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Water Network for financial support.
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ABBREVIATIONS CFT classic colloid filtration theory DI deionized water MIP mercury intrusion porosimetry SEM scanning Electron Microscopy CPV cumulative pore volume DLVO theory Derjaguin−Landau−Verwey−Overbeek theory PCIF particle-collector interaction factor
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