Electrokinetic flows through a parallel-plate channel with slipping stripes on walls

Longitudinal and transverse electrohydrodynamic flows through a plane channel, of which the walls are micropatterned with a periodic array of stripes, are considered. One unit of wall pattern consists of a slipping stripe and a non-slipping stripe, each with a distinct zeta potential. The problems are solved by a semi-analytical method, where the basic solutions satisfying the electrohydrodynamic equations are expressed by eigenfunction expansions, and the coefficients are determined numerically by point collocation satisfying the mixed stick-slip boundary conditions. In the regime of linear response, the Onsager relations for the fluid and current fluxes are deduced as linear functions of the hydrodynamic and electric forcings. The phenomenological coefficients are explicitly expressed as functions of the channel height, the Debye parameter, the slipping area fraction of the wall, the intrinsic slip length, and the zeta potentials. Attention is paid to some particular kinds of patterns, with a view to revisit and to generalize the theoretical limits made in previous studies on electrokinetic flow over an inhomogeneously slipping surface. One should be cautious when applying the theoretical limits. We show that when a surface is not 100% uniformly slipping but has a small fraction of area being covered by no-slip slots, the electro-osmotic enhancement can be appreciably reduced. We also show that when the electric double layer is only moderately thin, slipping-uncharged regions on a surface will have finite inhibition effect on the electro-osmotic flow. (C) 2011 American Institute of Physics. [doi:10.1063/1.3647582]