Electro-osmotic flow over a charged superhydrophobic surface.

Bubbles can be trapped inside textured structures such as grooves, forming a superhydrophobic surface. A superhydrophobic surface has a large effective hydrodynamic slip length compared to a smooth hydrophobic surface and holds the promise of enhancing electrokinetic flows that find many interesting applications in microfluidics. However, recent theoretical studies suggested that electro-osmotic flows over a weakly charged superhydrophobic surface [the zeta potential of the surface is smaller than the thermal potential (25 mV)] can only be enhanced when liquid-gas interfaces are charged [T. M. Squires, Phys. Fluids 20, 092105 (2008); Bahga, J. Fluid Mech. 644, 245 (2010)]. So far there is little work reported when the zeta potential of the surface is comparable or even larger than the thermal potential. In this paper we numerically investigate electro-osmotic flows over a periodically striped slip-stick surface by solving the standard Poisson-Nernst-Planck equations. Our results indicate that at large zeta potentials, even if liquid-gas interfaces are charged, the nonuniform surface conduction due to the mismatch between surface conductions over no-shear and no-slip regions leads to electric field lines penetrating the double layer and thus the nonuniform surface conduction weakens the tangential component of the electric field which primarily drives electro-osmotic flows. Our results imply that, in the presence of strong nonuniform surface conduction, enhanced electro-osmotic flows over a superhydrophobic surface are possible only in certain conditions. In particular, the enhancement due to the slip can potentially be lost at large zeta potentials. Similar loss of the enhancement of a charged particle's electrophoretic mobility due to the slip was reported by Khair and Squires [Phys. Fluids 21, 042001 (2009)].