Non-linear Poisson-Boltzmann Theory for Swollen Clays

TL;DR

This paper develops a semi-analytical method to solve the non-linear Poisson-Boltzmann equation for charged clay particles, providing insights into their osmotic behavior and matching experimental data.

Contribution

It introduces an efficient iterative integral equation approach for solving non-linear PB equations applicable to clay suspensions.

Findings

Method accurately predicts osmotic pressure in clay gels

Solution aligns well with experimental data

Approach is adaptable to other cell model problems

Abstract

The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient, robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in fair agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.