Two-fluid Electrokinetic Flow in a Circular Microchannel

The two-fluid flow is produced by the combined effects of electroosmotic force in a conducting liquidand pressure gradient force in a non-conducting liquid. The Poisson-Boltzmann and Navier-Stokesequations are solved analytically; and the effects of governing parameters are examined. Poiseuillenumber increases with increasing the parameters involved. In the absence of pressure gradient, the twofluids demonstrate plug-like velocity profiles. The results reveal that the two-fluid electroosmoticpumping flow rate is feasible for a relatively small interface zeta potential; or large wall zeta potentialand electrokinetic radius. For particular values of the governing parameters, the flow rate approaches aspecific value as the electrokinetic radius tends to infinity. A back flow (a negative value of theresultant flow rate) occurs for sufficiently small values of the wall zeta potential or sufficiently largevalues of the interface zeta potential (even in the case of pressure-assisted flow). Zero-value flow ratesmay also be attained.