A theoretical model for the hydraulic conductivity of montmorillonite in relation to the concentration and valence of electrolyte cations in solution

Abstract

This study is among the first to report on a theoretical relationship linking the hydraulic conductivity of soil and aquifer with environmental solution conditions. A mathematical model is developed for predicting the hydraulic conductivity of montmorillonite from the concentration and valence of electrolyte cations in solution. The model relies on the diffuse double layer and DLVO theories, the aggregation kinetics, and the Hazen equation, with a few plausible assumptions, for establishing three individual relationships, with each corresponding to one of three steps in the cation-to-particle-to-grain-to-hydraulic conductivity pathway. It is based on a mechanistic understanding that the concentration and valence of electrolyte cations controls the size of montmorillonite primary particles by influencing the electrical double layer, subsequently regulates the grain-size distribution of montmorillonite via inter-particle collision, and finally determines the hydraulic conductivity of montmorillonite. The model is validated by direct measurements of the surface charge density, the grain-size distribution and the hydraulic conductivity of montmorillonite in NaCl and CaCl2 solutions of various concentrations. The theoretical model of predicting hydraulic conductivity developed here is novel for implementing more accurate modeling of contaminant transport in the environment with advantage of cost-savings.