Transient flow of electrolyte solution in porous media with membranes fitted at the upper wall surface and lower charged surface

The flow analysis of electrolyte solution in microchannel/capillary is essential in various applications of health care such as dialysis and diagnosis processes of biological fluids/samples. To investigate the flow analysis in a homogeneous and isotropic porous microchannel with two membranes fitted at the upper wall surface, a novel biophysical model is presented mathematically. The lower wall surface is kept stationary and negatively charged to analyse the influence of the electroosmosis mechanism. The membranes have a self-propagating pumping process with varying amplitude and phase lag. The continuity and momentum equations are considered to describe the fluid flow and the Poisson–Boltzmann equation is taken to analyse the distribution of the electric potential for the electrolyte solution in the normal direction to a charged surface. To derive the governing equations, we have considered the approximation of low Reynolds number and Debye-Hückel linearization. Using MATLAB coding, key results like velocity, pressure difference, skin friction, volumetric flow rate, and stream function are computed under the influence of significant parameters. Present study finds that the movement of the electrolyte solution can be driven by membrane-based pumping at a small scale and further regulated by electroosmosis. The resistance due to the porous medium impacts the velocity and volumetric flow rate but this resistance can be mitigated by increasing the strength of the external electric field. This analysis is potentially useful for developing membrane-based microfluidic devices to analyse the biological flow at the micro-scale.