A Three-Scale Model of pH-Dependent Flows and Ion Transport with Equilibrium Adsorption in Kaolinite Clays: II Effective-Medium Behavior

Abstract

In part I (Lima et al., Transp Porous Media, 2009), a three-scale model governing the movement of an aqueous saline solution containing four monovalent species (Na+, H+, Cl−, OH−) in kaolinite clays was derived. Unlike purely macroscopic approaches, the novelty of the formulation relied on the double averaging of the nanoscopic electro- chemistry of particle/electrolyte solution interface ruled by the electrical double layer coupled with protonation/deprotonation reactions. The passage from the nano to the micro (pore)-scale gave rise to ion-sorbed concentrations and slip velocity at the solid/fluid interface which are coupled with the microscopic Stokes problem and Nernst–Planck equations governing the hydrodynamics and ion transport in the micropores. Application of a formal homogenization procedure led to macroscopic governing equations with effective electro-chemical parameters, such as retardation coefficients, electro-osmotic permeability, and electric conductivity. In this study, we reconstruct the constitutive laws of the macroscopic coefficients by solving the nano and microscopic closure problems. New generalized isotherms for Na+ and H+ − OH− sorption are build-up based on a perturbation approach and the limitations of classical Freundlich isotherm for modeling ion sorption at the solid/fluid interface are discussed. The macroscopic governing equations are discretized by the finite volume method and numerical simulations of a transient electroosmosis experiment for desalination of a clay sample by electrokinetics are presented.