Molecular Hydrodynamics: From Kubo To Smoluchowski Example of a Montmorillonite Clay

Abstract

Electro‐osmosis is an electro‐kinetic phenomenon corresponding to the motion of a liquid phase adjacent to a charged surface under an applied electric field. The classical theory of electro‐osmosis was initially proposed by Smoluchowski. In this mesoscopic approach, the macroscopic law of Navier‐Stokes is solved taking into account the geometry of the pores. The electro‐osmotic flow is induced by the force of the external electric field on the ions in the liquid phase of the system and the flow is controlled by the concentration profile of the ions. Ionic concentration profiles in the interlayer of a montmorillonite clay have been obtained using microscopic and mesoscopic models. Further, the profile of electro‐osmotic velocities was calculated from the microscopic model (Kubo relation) and compared to the solution of the Poisson‐Boltzmann and Navier‐Stokes equations. It was concluded that Smoluchowski theory can be applied only if slipping hydrodynamic boundary conditions are introduced.