Environ. Sci. Technoi. 1992, 26, 400-401
CORRESPONDENCE Comment on "Use of Colloid Filtration Theory in Modeling Movement of Bacteria through a Contaminated Sandy Aquifer" SIR Harvey and Garabedian (1) are among the first to apply filtration theory to quantify bacterial transport in the subsurface. Although this quantification is a major breakthrough, three components of the work require clarification and correction: (1)the reaction terms in the transport equation, (2) the evaluation of the single collector efficiency ( q ) ,and (3) the specific gravities for bacteria. The authors used a filtration-sink term (-I& c) and an adsorption retardation term [ p b ( d s / d t ) ] in t6e one-dimensional transport equation for bacteria (eq 1 from the referenced article). Filtration was modeled as an irreversible, kinetically controlled process, and sorption was modeled as a reversible, equilibrium process. Consequently, two mechanisms remove bacteria from the bulk liquid (filtration and sorption), but only one mechanism provides the reverse reaction (desorption). This approach "double counts" removal and is conceptually inconsistent. The correct approach to modeling the bacterial interactions with the solid surfaces is to have a deposition term and a detachment term according to the formulation
Here, Rd is the kinetically controlled rate at which bacteria are deposited on the solid phase due to filtration (v%k,c), and Rs is the kinetically controlled rate at which bacteria detach from the solid phase of the porous media. Rittmann (2) gave the detachment rate as
Rs = bSPf where b, is a specific detachment loss coefficient and pf is the biomass density in the porous media. Taylor and Jaffe (3)discussed additional relationships for Rd and R,. In the correct formulation, the same bacteria are filtered and detached by one mechanism each, and those mechanisms are consistent with each other. Harvey and Garabedian (1) evaluated the single collector efficiency ( q ) utilizing the approach of Yao et al. ( 4 ) for deposition on isolated spheres. However, the collector grains in an aquifer do not exist as isolated spheres, because they are surrounded by other grains. Rajagopalan and Tien (5) presented a superior filtration model that includes the influence of neighboring collectors (Happel flow) and hydrodynamic retardation. The neighboring collectors that exist in porous media increase q by confining the flow around each collector. Hydrodynamic retardation causes a resistance to particle transport near the collector surface. This resistance comes from water having to be squeezed out as the particle approaches the collector surface. Hydrodynamic retardation is important for collisions caused by gravity and interception, but plays a negligible role in Brownian diffusion. A comparison of the isolated-sphere model used by Harvey and Garabedian with the more appropriate Rajagopalan and Tien model for computation of q as a function of cell diameter appears in Figure 1. The input param400
Environ. Sci. Technol.. Vol. 26, No. 2, 1992
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M a t e d Sphere (Yao et al.) Porous Media (Ra). and Tien) Porous Media (Raj. and Tien) Porous Media (Raj. and Tien)
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Cell Diameter, (pin)
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Flgure 1. Single collector efficiency ( q )as a function of cell diameter and specific gravity for the Yao et al. ( 4 ) and Rajagopalan and Tien (5)filtration models.
eters are those reported in the Harvey and Garabedian article, and a Hamaker constant of J is used for the Rajagopalan and Tien model calculations. The bacteria ranged from 0.2 to 1.4 pm in diameter. The Rajagopalan and Tien q values are -4 times larger over this cell diameter range and specific gravity (1.002), because the presence of neighboring collectors yields a substantially higher value of q in the Brownian diffusion region (
