Computational modeling of electro-osmotic multi-membrane pumping of casson fluid in microchannels

This study investigates a bioinspired multi-membrane pumping mechanism for Casson fluid flow in a microchannel, modulated by electro-osmotic effects. A theoretical model is developed for two membranes, positioned along the channel walls with varying amplitudes, diameters, and phase lags, creating pressure gradients to drive fluid flow in both directions. The mathematical formulation is based on mass and momentum principles, with the low Reynolds number assumption and lubrication theory used to linearize the equations. These linearized equations are solved analytically through complementary functions and particular integrals. Numerical computations are implemented in MATLAB using the Finite Difference Method (FDM), to validate the model by showing excellent agreement with the analytical solutions for axial velocity. The study focuses on the interaction of various parameters, such as pressure gradients, pressure distribution, velocity distributions, flow rates, shear stress and streamlines. It is found that the pressure gradient is nearly constant along the channel, with fluctuations at membrane locations (X∈[0.25,0.35] and X∈[0.65,0.75]). The geometry of the membranes and fluid rheology significantly affect the flow and pumping performance in this multi-membrane micro-pump configuration.