  The influence of the texture of a hydrophobic surface on the electro-osmotic
slip of the second kind and the electrokinetic instability near
charge-selective surfaces (permselective membranes, electrodes, or systems of
micro- and nanochannels) is investigated theoretically using a simple model
based on the Rubinstein-Zaltzman approach. A simple formula is derived to
evaluate the decrease in the instability threshold due to hydrophobicity. The
study is complemented by numerical investigations both of linear and nonlinear
instabilities near a hydrophobic membrane surface. Theory predicts a
significant enhancement of the ion flux to the surface and shows a good
qualitative agreement with the available experimental data.
