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7.1 Introduction
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aws common line is also consistent with the batch experiments of Thompson
and Yates [1999] and Thompson et al. [1998].
7.1.3 Mathematical models
Mathematical and conceptual models of adsorptive transport were initially developed
for saturated porous media [Van der Lee et al., 1992, Corapcioglu and
Jiang, 1993, Song and Elimelech, 1994, Swanton, 1995, Grindrod and Lee, 1997,
Sun and Walz, 2001, Elimelech et al., 2003] and were later adapted to unsaturated
media [Darnault et al., 2004, Saiers, 2002, Lenhart and Saiers, 2002,
Corapcioglu and Choi, 1996, Wan and Tokunaga, 1997]. These models usually
assume that the convective dispersive equation is valid; some models also accounted
for preferential (or bypass) flow. Colloid deposition was included as
a sink-source term. The sink term for colloid retention, in some models, was
described as the product of two factors: (1) the collision efficiency, which is
the probability of a mobile particle contacting a collector surface, comprising
the effects of interception, sedimentation, and Brownian motion; and (2) the
sticking efficiency, which is the probability that such a collision will result in
attachment [Elimelech and O’Melia, 1990, Yao et al., 1971]. Descriptions of
colloid retention in partially saturated media are complicated by the existence
of the two AW and SW interfaces that can each serve as collector surfaces,
albeit with distinct electrostatic and surface tension properties. The water film
thickness can vary under partial saturation, depending not only on the water
content, but also by the position of the film relative to the pendular rings of water
between grains. In addition, some studies suggested attachment of colloids
to the aws line.
Kinetic effects in the transport of adsorptive solutes could be due to physical
and/or chemical kinetic processes. The physical kinetic (two-region) models
explain nonideality based on the presence of both mobile regions, where solute
is transported by advection and dispersion, and immobile regions, where only
solute diffusion takes place [van Genuchtan and Wieranga, 1976, van Genuchten
and Cleary, 1979, Rao et al., 1980a,b, Nkedi-Kizza et al., 1982]. Because these
models attribute nonideality to the physical makeup of the soil, nonideal BTCs
would be expected not only for reactive solutes but also for nonreactive solutes.
Among chemical kinetic models, the two-site model, in which the porous medium
is considered to contain two types of sites having different adsorption kinetic
characteristics, is the most common; one site is considered to be in equilibrium,
while the other site is assumed to undergo time-dependent kinetic adsorption
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