  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-ions porous films. The inner flow shows a very rich behavior controlled
by the volume charge density of the coating, its Brinkman length, and
concentration of added salt. Interestingly, even for 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
  the salt concentration. These results provide a framework for the rational
design of porous coatings to enhance electrokineic phenomena, and for tuning
their properties by adjusting bulk electrolyte concentrations, with direct
applications in microfluidics.
