In this article we present a precise correlation between macroscopic electro-chemical properties of swelling clays such as permeabilities (chemico-osmotic and electro-osmotic), partition coefficient and the nanoscale distribution of the electrical double layer potential satisfying the Poisson-Boltzmann problem in the nano-pore domain occupied by an electrolyte solution. This is accomplished within the framework of a dual porosity model which is derived by a formal homogenization asymptotic analysis applied to two levels of averaging to include nano and macro-pores of the swelling medium. When applied to reactive contaminant transport in montmorillonite this framework combined with the threescale picture of the swelling medium allows to build-up numerically a generalized adsorption isotherm of Freundlich type and to provide nanoscopic representations for the partition coefficient in terms of the solution of the Poisson-Boltzmann problem. In addition, by solving this local closure problems posed on a unit periodic cell at the nanoscale we develop accurate constitutive laws for the chemico-osmotic and electro-osmotic permeabilities of the clay. The up-scaling technique proposed herein along with the correlations between properties at different scales allow to bridge the fields of macroscopic Soil Mechanics and nanoscopic Colloid Science.
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- Macroscopic Behavior of Smectitic Clays Derived From Nanostructure
Márcio A. Murad
- Springer Netherlands
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