Clay micromechanics: Numerical modelling of electrical double-layer interactions to develop particle-based models for clay

Abstract

Discrete element modelling of clays requires defining the interaction energy between two particles. The Derjaguin, Landau, Verwey and Overbeek (DLVO) theory combining the effect of the van der Waals forces and the Coulombic forces due to the double layer of counterions provides a widely accepted framework to characterise the pair potential energy. Solutions of the Poisson-Boltzmann (PB) equation to quantify the Coulombic forces are only available for the case of infinitely extended and uniformly charged facing plates (1D conditions). However, these assumptions are not representative of a clay particle system. Particles should be represented by platelets of finite size and finite thickness, with different charges between the edge and the basal planes. This paper addresses the problem of deriving the Coulombic interaction forces for plates of finite size and thickness in 3D configuration by solving the Poisson-Boltzmann equation numerically via the Finite Element Method (FEM). It is shown that 2D particles (plates of infinitesimal thickness) provide an adequate representation of Coulombic interaction as long as the particles are uniformly charged. The advantage of 2D particles is to reconcile numerical modelling with analytical solutions available in the literature. The use of 2D particles is questionable when considering different charges between basal planes and edges.