Semi-analytical model of mixed electroosmotic/pressure driven two immiscible fluids with curved interface

This study is motivated by the need to develop a semi analytical model for predicting the stratified two-fluidćflow with a curved interface in a rectangular microchannel under the combined effect of pressure and electroosmosis.ćWith the non-slip boundary conditions at the wall and the matching condition at the curved interface, the fully developedćNavier-Stokes equation and Poisson-Boltzmann equation are solved using separate variable method. Part of parameters inćthe distributions of velocity and electric potential is calculated using the least-square method. Details of the analyticalćtreatment of the two-fluid flow with curved interface are presented. The results show that the analysis can be employed forćconcave, convex and planar interface. The validity of the two-fluid model with curved interface is evaluated by comparingćits prediction with available numerical data and with the results of exact analytical solutions for laminar flows with planarćinterface, comparison of the electric potential distribution and velocity distributions shows excellent agreement with dataćin the literature. Finally, the effects of interface shape on the electric potential distribution, electroosmotic velocityćdistribution, and flow rates are discussed, the results show that the interface shape influences the two-fluid flow inćmicrochannel significantly.