Effective medium approximation and deposition of colloidal particles in fibrous and granular media

Abstract

Laminar flow of fluids through fibrous and granular media and deposition of colloidal particles from a liquid suspension are two fundamental phenomena encountered in many industrial applications. An Effective Medium Approximation (EMA) is used to determine the fluid flow permeability and particle capture efficiency of random arrays of cylindrical and spherical collectors. The EMA assumes a model system in which a packing element (a single fiber in the fibrous medium and a single sphere in the granular medium) is surrounded by a fluid envelope and an effective-medium beyond the envelope. It integrates the important features of both the cell models and Brinkman's model. The Stokes equation and Brinkman equation are solved for the fluid envelope and effective medium regions, respectively, to obtain the permeability and close-to-surface velocity field around the collectors. The convective diffusion equation is then solved to determine the particle deposition rate. The analytical expressions for the permeability and particle deposition rate are derived for all possible cases of random packing of uniform and non-uniform cylinders and spheres. Effects of various system properties and operating conditions on deposition of colloidal particles are investigated. The physical or chemical conditions include the properties which affect the magnitude of double layer interaction: the electrolyte concentration and surface potentials, and the property which affects the van der Waals interaction: the Hamaker constant. It was found that the effects of the above properties is much more significant when the surface interactions play more important roles in the particle deposition process, or when the height of the total interaction energy barrier is higher than 5 k B T. Particle deposition becomes virtually impossible when the height of the repulsive energy barrier increases beyond 20 k B T.