Revisiting DLVO theory to inform particle-scale modelling of clays

Particle-scale modelling of clays requires defining an energy-separation function for a pair of platy particles. The Derjaguin, Landau, Verwey and Overbeek (DLVO) theory provides a convenient framework for developing such a function as it embeds the combined effect of pore-fluid temperature, dielectric permittivity, and electrolyte concentration. Therefore, it can underpin the modelling of clay mechanical behaviour associated with thermal and environmental loading. The DLVO theory assumes particle interactions to be controlled by the van der Waals forces and the Coulombic forces via the Electrical Double-Layer (EDL). This paper first explores the 1D EDL interactions via the thermodynamics-based Grand Potential for the case of parallel sheets (with infinitesimal and infinite thickness). For infinitesimal thickness sheets, it is shown that i) the approximate analytical solutions of the Poisson-Boltzmann equation provide a qualitatively robust representation of EDL interactions, ii) the EDL interaction is qualitatively similar regardless of whether the interaction is modelled assuming constant surface charge or surface potential thus eliminating the uncertainty about the most appropriate electrical boundary condition to model EDL interactions; iii) the mechanical pressure required to ‘aggregate’ two sheets interacting via the EDL is finite and not infinite as often assumed in the literature (i.e. van der Waals forces do not need to be invoked to generate the energy barrier that triggers face-to-face aggregation but it remains fundamental for the quantitative definition of the potential energy barrier responsible for particle aggregation). Finally, the paper compares the 1D solutions for infinitely extended particles with the numerical solutions derived for face-to-face finite cuboidal particles with different aspect ratios to investigate the 1D analytical solutions that can conveniently be used as a benchmark in particle-scale modelling.