Bingham plastic fluids flow analysis in multimembranes fitted porous medium

Abstract

A mathematical analysis is presented for the flow of a Bingham plastic fluid propelled by the multi-membranes pumping mechanism through porous media. Two successive membranes with different amplitude, diameter, and phase lag, are fitted at the upper wall of the channel, and the lower wall is stationary. Due to the simultaneous propagation of both membranes, the pressure is generated at the membrane's position, which helps in propelling the fluids in forward and backward directions depending upon the compression and expansion cycles of the membranes. The low Reynolds number assumption and lubrication theory are utilized to linearize the governing equations, which are further analytically derived, and then employing MATLAB codes to compute the illustrations for the interpretation of the results. The effects of key parameters like plug flow region, pore size and diameter of membranes on the velocity field, wall shear stress, pressure gradient, fanning friction factor, head loss and particle trajectories, are analysed in the microchannel. Results of the present model conclude that the geometrical properties of membranes, rheological properties of fluids and porosity of the medium significantly alter the flow and pumping characteristics which give valuable insights for the design of micro-valve less pumping actuators to be aimed at controlling microscale transport processes in various medical diagnoses and treatments.