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Deviation from the Classical Colloid Filtration Theory in the Presence of Repulsive DLVO Interactions Nathalie Tufenkji*,† and Menachem Elimelech‡ Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 2B2, Canada, and Department of Chemical Engineering, Environmental Engineering Program, P.O. Box 208286, Yale University, New Haven, Connecticut 06520-8286 Received May 31, 2004. In Final Form: September 8, 2004 A growing body of experimental evidence suggests that the deposition behavior of microbial particles (e.g., bacteria and viruses) is inconsistent with the classical colloid filtration theory (CFT). Well-controlled laboratory-scale column deposition experiments were conducted with uniform model particles and collectors to obtain insight into the mechanisms that give rise to the diverging deposition behavior of microorganisms. Both the fluid-phase effluent particle concentration and the profile of retained particles were systematically measured over a broad range of physicochemical conditions. The results indicate that, in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions, the concurrent existence of both favorable and unfavorable colloidal interactions causes significant deviation from the CFT. A dual deposition mode model is presented which considers the combined influence of “fast” and “slow” particle deposition. This model is shown to adequately describe both the spatial distribution of particles in the packed bed and the suspended particle concentration at the column effluent.
Introduction The classical colloid filtration theory (CFT) is the most commonly used approach for predicting particle deposition behavior in saturated porous media. Originally developed by Yao et al.,1 this conceptual model is of practical interest in chromatographic separation,2 granular (deep-bed) filtration in water and wastewater treatment,3,4 transport and fate of colloids and colloid-associated pollutants in the subsurface environment,5-7 and natural filtration of microorganisms such as bacteria, viruses, and protozoa.8-10 In this classic “clean-bed” filtration model, the removal of suspended particles is described by first-order kinetics, resulting in concentrations of suspended and retained particles that decay exponentially with distance. However, a growing body of experimental evidence suggests that the deposition of microbial particles (e.g., bacteria and viruses) is inconsistent with the classical CFT.11-17 In most * Corresponding author. Phone: (514) 398-4494. Fax: (514) 3986678. E-mail:
[email protected]. † McGill University. ‡ Yale University. (1) Yao, K. M.; Habibian, M. T.; O’Melia, C. R. Environ. Sci. Technol. 1971, 5, 1105-1112. (2) Prieve, D. C.; Hoysan, P. M. J. Colloid Interface Sci. 1978, 64, 201-213. (3) Tobiason, J. E.; O’Melia, C. R. J.sAm. Water Works Assoc. 1988, 80, 54-64. (4) Tien, C.; Payatakes, A. C. AIChE J. 1979, 25, 737-759. (5) McDowell-Boyer, L. M.; Hunt, J. R.; Sitar, N. Water Resour. Res. 1986, 22, 1901-1921. (6) McCarthy, J. F.; Zachara, J. M. Environ. Sci. Technol. 1989, 23, 496-502. (7) Ryan, J. N.; Elimelech, M. Colloids Surf., A 1996, 107, 1-56. (8) Harvey, R. W.; Garabedian, S. P. Environ. Sci. Technol. 1991, 25, 178-185. (9) Schijven, J.; de Bruin, H. A. M.; Hassanizadeh, S. M.; Husman, A. M. D. Water Res. 2003, 37, 2186-2194. (10) Tufenkji, N.; Ryan, J. N.; Elimelech, M. Environ. Sci. Technol. 2002, 36, 422a-428a. (11) Albinger, O.; Biesemeyer, B. K.; Arnold, R. G.; Logan, B. E. FEMS Microbiol. Lett. 1994, 124, 321-326. (12) Baygents, J. C.; Glynn, J. R.; Albinger, O.; Biesemeyer, B. K.; Ogden, K. L.; Arnold, R. G. Environ. Sci. Technol. 1998, 32, 1596-1603. (13) Bolster, C. H.; Mills, A. L.; Hornberger, G. M.; Herman, J. S. Water Resour. Res. 1999, 35, 1797-1807.
experiments presented, particle deposition rates decline monotonically with distance. Such observations of microbial deposition which diverge significantly from predictions based on the CFT have important implications for numerous processes in natural and engineered systems. Particularly, these results suggest that predictions of particle removal in saturated porous media are considerably overestimated by the classical CFT. Several explanations have been proposed to account for this observed deviation from the CFT, including heterogeneity in microbial surface properties,12,17 distributions in the interaction energies between microorganisms and collector grains,18 and particle deposition dynamics.18 Although the causes of deviation from the CFT with respect to filtration of microbial particles have been hypothesized, the mechanisms controlling this behavior have not been elucidated. Laboratory-scale column experiments conducted with model uniform particles and collector grains under welldefined physicochemical conditions can provide insight into the mechanisms that give rise to the diverging deposition behavior of microorganisms. However, such controlled studies where the profiles of retained particles are quantified are scarce.19-22 Fitzpatrick and Spielman22 measured the fluid-phase concentration profiles of uniform latex particles in columns packed with spherical glass (14) Camesano, T. A.; Logan, B. E. Environ. Sci. Technol. 1998, 32, 1699-1708. (15) Martin, M. J.; Logan, B. E.; Johnson, W. P.; Jewett, D. G.; Arnold, R. G. J. Environ. Eng. Div. (Am. Soc. Civ. Eng.) 1996, 122, 407-415. (16) Redman, J. A.; Estes, M. K.; Grant, S. B. Colloids Surf., A 2001, 191, 57-70. (17) Simoni, S. F.; Harms, H.; Bosma, T. N. P.; Zehnder, A. J. B. Environ. Sci. Technol. 1998, 32, 2100-2105. (18) Tufenkji, N.; Redman, J. A.; Elimelech, M. Environ. Sci. Technol. 2003, 37, 616-623. (19) Li, X.; Scheibe, T. D.; Johnson, W. P. Environ. Sci. Technol., in press. (20) Bradford, S. A.; Simunek, J.; Bettahar, M.; van Genuchten, M. T.; Yates, S. R. Environ. Sci. Technol. 2003, 37, 2242-2250. (21) Bradford, S. A.; Yates, S. R.; Bettahar, M.; Simunek, J. Water Resour. Res. 2002, 38, 1327-1338. (22) Fitzpatrick, J. A.; Spielman, L. A. J. Colloid Interface Sci. 1973, 43, 350-369.
10.1021/la0486638 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/03/2004
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beads by sampling at successive depths of the packed bed using hypodermic needle probes. Under conditions where electrostatic double-layer repulsion is not important, deposition rates determined from the slope of the particle concentration profile were in good agreement with theoretical predictions.22,23 Bradford et al.20,21 observed that the spatial distributions of latex colloids in columns packed with glass beads and Ottawa sand were not well described by the classical CFT. In their studies, however, physical straining was believed to be a significant particle removal mechanism. Since the contribution of straining to particle removal is not considered in the CFT, the work of Bradford et al. is not appropriate in determining the causes of deviation from the CFT. In this paper, we present well-controlled laboratoryscale column deposition experiments to investigate the mechanisms and causes of deviation from the CFT. Emphasis was placed on conditions where repulsive electrostatic double-layer interactions predominate. Uniform polystyrene latex colloids and spherical soda-lime glass beads were selected as model particles and collectors, respectively. To examine the validity of the classical CFT, we systematically measured both the fluid-phase effluent particle concentration and the profile of retained particles over a broad range of physicochemical conditions. We demonstrate that the CFT breaks down in the presence of repulsive electrostatic interactions. A dual deposition mode model is applied which considers the simultaneous “fast” and “slow” deposition of colloids. This model is shown to adequately describe both the spatial distribution of particles in the packed bed and the suspended particle concentration at the column effluent. Theory Classical Colloid Filtration Theory. The transport of colloidal particles through saturated homogeneous porous media can be described by accounting for particle advection, hydrodynamic dispersion, and deposition (filtration). For relatively low particle concentration and moderate ionic strength, blocking and ripening effects are not significant and particle release is typically negligible. Under these conditions, the concentrations of fluid-phase particles, C(x, t), and retained particles, S(x, t), at column depth x and time t can be described by a one-dimensional advection-dispersion equation with a first-order kinetic deposition term:24,25
∂2C ∂C Fb ∂S ∂C + )D 2 -v ∂t ∂t ∂x ∂x
(1)
Fb ∂S ) kC ∂t
(2)
Here, v is the interstitial particle velocity, D is the hydrodynamic dispersion coefficient, is the bed porosity, Fb is the porous medium bulk density, and k is the particle deposition rate coefficient. The latter is related to the commonly used single-collector removal efficiency, η,1,24,26 via (23) Spielman, L. A.; Fitzpatrick, J. A. J. Colloid Interface Sci. 1973, 42, 607-623. (24) Grolimund, D.; Elimelech, M.; Borkovec, M.; Barmettler, K.; Kretzschmar, R.; Sticher, H. Environ. Sci. Technol. 1998, 32, 35623569. (25) Kretzschmar, R.; Barmettler, K.; Grolimund, D.; Yan, Y. D.; Borkovec, M.; Sticher, H. Water Resour. Res. 1997, 33, 1129-1137. (26) Tufenkji, N.; Elimelech, M. Environ. Sci. Technol. 2004, 38, 529536.
k)
3(1 - )v η 2dc
(3)
where dc is the diameter of the collector grains. For most applications of practical interest (e.g., chromatographic separation and granular filtration), the system is considered at steady state and the influence of hydrodynamic dispersion is negligible. It is also typically assumed that the rate of particle deposition is both spatially and temporally invariant; that is, a single value of k is specified. Under these conditions, for a continuous particle injection at concentration C0 (at x ) 0) and time period t0, the solutions to eqs 1 and 2 for a column initially free of particles are
k C(x) ) C0 exp - x v
[ ]
S(x) )
(4)
t0kC0 t0k k C(x) ) exp - x Fb Fb v
[ ]
(5)
Equation 4 is commonly referred to as the classical colloid filtration model and has been used extensively in modeling the transport of model colloids and microorganisms in saturated porous media.8,11,16,25,27,28 Dual Deposition Mode Model. As discussed previously, the classical CFT is based on the assumption that the particle deposition rate coefficient, k, is constant. However, variability in the colloidal interactions between particles and collector grains can give rise to a distribution in the deposition rate. Particularly, in the presence of repulsive electrostatic double-layer interactions, particles may exhibit a dual deposition mode whereby a fraction of the particle population experiences a fast deposition rate and the remaining particles deposit at a slow rate. The causes of this variation in the particle deposition rate will be discussed in more detail later in the paper. In brief, these fast and slow deposition rates can be attributed to the concurrent existence of both favorable and unfavorable chemical-colloidal interactions, respectively. Particle deposition is termed favorable in the absence of repulsive interaction energies, whereas unfavorable deposition refers to the case where repulsive colloidal interactions predominate.28 The occurrence of both favorable and unfavorable conditions in an otherwise homogeneous system can be considered by including a bimodal distribution of k in the classical colloid filtration theory:18
∫0∞exp[- kvx]p(k) dk
C(x) ) C0 S(x) )
(6)
t0C0 Fb
∫0∞k exp[- kvx]p(k) dk
(7)
where p(k) is the linear combination of two normal (Gaussian) distributions:
[ (
)] [ (
h slow 1 1 k-k exp p(k) ) fslow 2 σslow σslowx2π
2
+
)]
h fast 1 1 k-k exp ffast 2 σfast σfastx2π
2
(8)
(27) Martin, R. E.; Bouwer, E. J.; Hanna, L. M. Environ. Sci. Technol. 1992, 26, 1053-1058. (28) Elimelech, M.; O’Melia, C. R. Environ. Sci. Technol. 1990, 24, 1528-1536.
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Here, k h slow and k h fast are the mean deposition rate coefficients, σslow and σfast are the corresponding standard deviations, and fslow and ffast are the fractions of the total population associated with each mode.
Tufenkji and Elimelech
Colloidal Particles. Surfactant-free fluorescent polystyrene latex colloids (EX 490 nm, EM 515 nm, Interfacial Dynamics Corporation, Portland, OR) with carboxyl-modified functional groups were used as model particles. The monodispersed particles have a mean diameter of 3.0 µm and a titrated surface charge density of 119.8 µC/cm2. The density of the particles, as reported by the manufacturer, is 1.055 g/cm3. Porous Media. Spherical soda-lime glass beads (Class V, MO-SCI Corporation, Rolla, MO) were utilized as model collector grains. The manufacturer reported the average diameter of the glass beads as 0.328 mm. The chemical composition (by weight) of the beads is as follows: ∼70% SiO2, ∼3% Al2O3, ∼10% CaO, ∼3% MgO, ∼15% Na2O, and
