Electrohydrodynamic lubrication theory

TL;DR

This paper develops a comprehensive electrohydrodynamic lubrication model for charged colloids near rigid boundaries, integrating electrostatics, electrokinetics, and hydrodynamics to analyze their motion.

Contribution

It introduces a novel theoretical framework combining multiple physics to describe colloid motion near boundaries, extending classical mobility models with surface charge and ion effects.

Findings

Reveals complex behaviors beyond existing electroviscous-lift models.

Extends classical mobility matrices to include surface charges and ions.

Provides numerical and asymptotic analysis of colloid dynamics.

Abstract

The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication theoretical framework, in order to characterize such a motion in the case of an infinite rigid cylinder near a rigid wall. Combining hydrodynamic lubrication theory, Debye-H\''uckel electrostatics, and Nernst-Planck electrokinetics, we derive the three coupled equations of motion for the normal, longitudinal and rotational degrees of freedom of the cylinder, which are then investigated numerically and through asymptotic analysis. Our results reveal complex behaviours, beyond existing asymptotic electroviscous-lift expressions, and extend the classical Faxen-Brenner-like mobility matrix when surface charges and dissolved ions are incorporated.