Numerical model supplemented by thin-layer analysis for diffusiophoresis of a particle incorporating finite ion size effects

Abstract

The impact of finite-sized ions on the diffusiophoresis of a charged colloid subjected to a concentration gradient of electrolyte solution consisting monovalent or multivalent ionic species, is studied. In diffusiophoresis, the ion concentration is of O(1M). In this non-dilute electrolyte solutions, the ion–ion steric interaction is important. We have adopted the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model to account for the ion steric interactions and the Batchelor–Green expression for the relative viscosity of suspension. We have solved the standard model numerically considering ions as point charge (PNP-model), the modified Nernst–Planck equations incorporating the ion steric interaction with constant viscosity (MNP-model), and modification of the MNP-model by incorporating the viscosity variation with the ionic volume fraction (MNPV-model). Semi-analytical expressions for mobility based on a linear perturbation technique under a thinner Debye length is presented for PNP- and MNP-models. In the MNP-model, counterion saturation in the Debye layer due to the ion steric interaction enhances the surface potential by attenuating the shielding effect, diminishes the surface conduction, and magnifies the induced electric field. These in combination create a larger mobility at a thinner Debye length compared with the PNP-model. This increment in mobility attenuates when the MNPV-model is considered. The MNPV-model is more appropriate to analyze the finite ion size effects, and it is found to yield the mobility values more close to the experimental data compared with the MNP- and PNP-model. The semi-analytical expressions for mobility based on the PNP- and MNP-models agree with the corresponding exact numerical solutions when the surface potential is in the order of thermal potential. However, a large discrepancy between the simplified expression and the exact numerical results is found for a concentrated electrolyte in which the induced electric field is large.