Marcio A. Murad
LNCC-MCT, Brasil

A Two-Scale Computational Model for Swelling Porous Media

Electrochemical interaction between colloidal particles and an aqueous solution is a central subject in colloid science.This phenomenon is typical of expansive porous media including clays, shales, polymers gels (for application to drug delivery substrates), corneal endothelium and connective biological tissues. Expansive materials have in common a structure that can be loosely identified as a mixture of macromolecules or colloidal particles (polymers, clay particles, proteglycanns) and solvent (water, hydrocarbons). In this talk we propose a two-scale model for a swelling medium composed of a charged solid phase saturated by a binary monovalent aqueous electrolyte solution. The homogenization technique is applied to propagate information available in the pore-scale model to the macroscale. Macroscopic electrokinetic phenomena such as electro-osmotic flow driven by streaming potential gradients, electrophoretic motion of mobile charges and osmotically induced swelling are derived by homogenizing the microscopic electro-hydrodynamics coupled with the Nernst-Planck and Poisson-Boltzmann equations governing the flow of the electrolyte solution, ion movement and electric potential distribution. A notable consequence of the upscaling procedure proposed herein are the micromechanical representations for the electrokinetic coefficients and swelling pressure. The two-scale model is discretized by the finite element method and applied to numerically simulate contaminant migration and electrokinetic attenuation through a compacted clay liner underneath a sanitary landfill.