Computational and theoretical model of electro-osmotic flow pumping in a microchannel with squeezing walls

Abstract

Numerical simulation and theoretical solution for the electro-osmotic pumping flow of electrolyte solution in a microchannel with squeezing and charged walls are developed in this study. The mathematical model is derived based on using a strong coupling between the nonlinear Poisson–Boltzmann equation and the flow lubrication theory. The governing equations are integrated numerically using the finite difference method. Moreover, an analytical solution to the problem is also obtained using the lubrication theory and is used to solve the Poisson–Boltzmann equation without any approximation technique. The effects of various parameters such as the wall zeta potential, Debye length, and electric field on the fluid pressure distribution, velocity field, and the net flow rate are investigated in detail. The results show that the induced pumping rate depends strongly on the combined effects of the Helmholtz–Smoluchowski, zeta potential, and electrical double layer. Moreover, the produced net flow directionality can be controlled efficiently by manipulating the Helmholtz–Smoluchowski and/or the wall zeta potential. The results obtained from the numerical simulation are then compared with the theoretical analysis and have shown to be in agreement with the proposed mathematical model.