Numerical solution of two-fluid electroosmotic flow

Two-fluid flows in microchannel are often found in biological analysis, such as during ion exchange or solvent extraction from one phase to another. In this article, a numerical scheme is presented to describe a two-fluid flow in microchannel with electroosmotic (EO) effects. In this two-fluid system, the interfacial viscous force of a high EO mobility fluid drags a low EO mobility fluid; the high EO mobility fluid is driven by electroosmosis. We particularly analyze the electric double layer (EDL) regions close to the wall and the interface in the high EO mobility fluid. As the governing equation of the electrical potential is singularly perturbed, finer meshes are adopted to capture these EDL regions. In simulation, the interface between the two fluids evolves along the flow direction as the flow develops. Level set method is used to capture the interface implicitly. A localized mass preservation scheme is used to ensure mass conservation. A finite-volume method is used to solve the coupled electric potential equation, level set equations and Navier-Stokes equation. The validity of the numerical scheme is evaluated by comparing its predictions with the results of the analytical solutions in the fully developed regions. The interface positions; pressure gradients; mass flow rates and velocity profiles of the two fluids along the channels are obtained numerically.