Effect of Entrained Colloidal Particles in Enhancing the Transport of Adsorbable Chemical Contaminants

Abstract

The role of entrained colloidal particles in enhancing the combined convective and diffusive transport of an adsorbable chemical contaminant otherwise dissolved in a solvent flowing through the interstices of a porous medium (and adsorbed onto the surfaces of this medium) is theoretically studied. The contaminant partitions between the mobile solvent, the surface(s) of the immobile porous matrix, and the surfaces of the mobile colloidal particles entrained in the interstitial fluid. The suspended colloids are assumed to be of uniform size, and to form a stable (i.e., noncoagulating) homogeneous suspension, uniformly distributed throughout the interstitial fluid. A detailed set of three-dimensional microtransport equations governing the local contaminant concentration field P( x, y, z, t) at each point ( x, y, z) of the interstices and each instant of time t is formulated for an initial instantaneous contaminant point-source input. (This serves as the Green's function for a more general initial contaminant spatial distribution.) A generalized Taylor-Aris dispersion scheme is then employed to reduce this complex formulation to a single, one-dimensional macrotransport equation governing the mean, i.e., area-averaged, contaminant concentration field P̄ ( z, t) along the direction z of the mean interstitial flow. The two phenomenological coefficients Ū* and D̄* appearing in this macroscale description, respectively representing the mean velocity vector and dispersivity dyadic of the contaminant, are expressed in terms of microscale geometric, kinematic, and physicochemical parameters and phenomenological functions quantifying the original microscale problem. By way of example, the generic problem solved above is applied to a simple model of a porous medium, consisting of a two-dimensional Poiseuille flow between flat plates. Detailed numerical results for this model are given for Ū* and D̄ *. These numerical values are used to demonstrate that the presence of entrained colloidal particles, even in relatively small amounts, can greatly enhance the contaminant transport rate accompanying groundwater flow through a porous medium.