Achieving large zeta-potentials with charged porous surfaces

We discuss an electro-osmotic flow near charged porous coatings of a finite hydrodynamic permeability, impregnated with an outer electrolyte solution. It is shown that their electrokinetic (zeta) potential is generally augmented compared to the surface electrostatic potential, thanks to a large liquid slip at their surface emerging due to an electro-osmotic flow in the enriched by counter-ion porous films. The inner flow shows a very rich behavior controlled by the volume charge density of the coating, its Brinkman length, and the concentration of added salt. Interestingly, even for a relatively small Brinkman length, the zeta-potential can, in some cases, become huge, providing a very fast outer flow in the bulk electrolyte. When the Brinkman length is large enough, the zeta-potential could be extremely high, even at practically vanishing surface potential. To describe the slip velocity in a simple manner, we introduce a concept of an electro-osmotic slip length and demonstrate that the latter is always defined by the hydrodynamic permeability of the porous film and also, depending on the regime, either by its volume charge density or by the salt concentration. These results provide a framework for the rational design of porous coatings to enhance electrokinetic phenomena, and for tuning their properties by adjusting bulk electrolyte concentrations, with direct applications in microfluidics.