Solute dispersion between two parallel plates containing porous and fluid layers

Abstract

This paper presents an analytical solution for the dispersion of a solute between two parallel plates consisting of two regions, one region filled with porous matrix and another region filled with purely viscous fluid. The Brinkman model is used to define the flow through the porous matrix. The fluids in both regions of the parallel-plate channel are incompressible, and their transport properties are assumed to be constant. The closed-form solutions are obtained in both fluids regions of the channel. The results are tabulated for various values of porous parameter, viscosity ratio, and pressure gradient on the effective dispersion coefficient and volumetric flow rate. It is found that the effective Taylor dispersion coefficient decreases as the porous parameter increases. The validity of the results obtained for a two-fluid model is compared with the available one-fluid model in the presence of porous matrix, and the values agree very well. The effective dispersion coefficient and volumetric flow rate are also found for a two-fluid model in the absence of porous matrix and are verified with the available one-fluid model, and the results are in good agreement. © 2012 by Begell House, Inc.