Electrohydrodynamic lubrication theory for an immersed cylinder moving near wall

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-Hückel 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 behaviors, beyond existing asymptotic electroviscous-lift expressions, and extend the classical Faxen-Brenner-like mobility matrix when surface charges and dissolved ions are incorporated.