Electrokinetic effects on Brinkman micropolar flow through stationary randomly corrugated microchannels

An analytical investigation is conducted into the electrokinetic phenomena within a porous medium saturated with a microstructured fluid, modeled by micropolar theory, in a stationary, randomly corrugated microchannel. The flow is driven by a pressure gradient and an electric field. A stationary random model is employed to simulate the surface roughness of the channel. The corrugation amplitude, oriented perpendicular to the flow, is assumed to be small relative to the average length of the channel walls. Consequently, a domain perturbation technique is utilized. The electrokinetic analysis is based on the linearized Poisson–Boltzmann equation. In this analysis, it is assumed that the surface zeta potential is small, as accounted for by employing the Debye–Hückel approximation. The solution obtained is used to assess the impact of the corrugations on the pressure gradient, flow rate, microrotation strength, and electric current density. These physical quantities are illustrated through graphs for various parameter values and are compared with existing data from the literature. The primary motivation for studying Brinkman micropolar electrolyte flow within corrugated channels lies in its potential applications for microfiltration and ultrafiltration.