Semi-Analytical Model of Mixed Electroosmotic/Pressure Driven Two Immiscible Fluids with Curved Interface

Abstract

This study is motivated by the need to develop a semi analytical model for predicting the stratified two-fluid flow with a curved interface in a rectangular microchannel under the combined effect of pressure and electroosmosis. With the non-slip boundary conditions at the wall and the matching condition at the curved interface, the fully developed Navier-Stokes equation and Poisson-Boltzmann equation are solved using separate variable method. Part of parameters in the distributions of velocity and electric potential is calculated using the least-square method. Details of the analytical treatment of the two-fluid flow with curved interface are presented. The results show that the analysis can be employed for concave, convex and planar interface. The validity of the two-fluid model with curved interface is evaluated by comparing its prediction with available numerical data and with the results of exact analytical solutions for laminar flows with planar interface, comparison of the electric potential distribution and velocity distributions shows excellent agreement with data in the literature. Finally, the effects of interface shape on the electric potential distribution, electroosmotic velocity distribution, and flow rates are discussed, the results show that the interface shape influences the two-fluid flow in microchannel significantly. Keywords: Curved interface, microchannel, electroosmotic flow, two - fluid stratified flow, Lab-on-a-chip devices, EDLs, Electric Potential Distributions, Velocity, Pressure Gradient, Electroosmotic Force