Oscillatory Brinkman-micropolar electroosmosis in cylindrical microannuli

Abstract

This study presents an analytical investigation of unsteady, time-periodic flow in a hydrogel medium confined within a cylindrical microannulus, driven by both a pressure gradient and an externally applied electric field. The hydrogel is modeled as a Brinkman porous matrix saturated with a micropolar fluid. By coupling the linearized Poisson-Boltzmann equation (Debye-Hückel approximation) with the Brinkman-micropolar momentum equations, closed-form expressions are derived for the axial velocity and microrotation as functions of radial position, time, and key dimensionless parameters. The flow is shown to comprise two independent contributions: a pressure-driven component and an electroosmotic component, each influenced by specific physical mechanisms. Quantitatively, increasing the permeability resistance parameter ($\lambda$) from 0 to 10 reduces the volume flow rate by 89.64 %, the streaming function by 83.63 %, while increasing microrotation strength by 62.05 %. Raising the micropolar coupling number ($c$) from 0.1 to 0.9 leads to a 38.20 % decrease in flow rate, a 165.55 % increase in the streaming function, and a 28.43 % rise in microrotation. Frequency effects are especially pronounced: increasing the forcing frequency parameter ($\alpha$) from 0.5 to 50 results in a 99.98 % drop in flow rate, a 100 % increase in the streaming function, and a 99.9997 % rise in microrotation. The electrokinetic width ($k$) is a dominant tuning parameter-doubling $k$ from 10 to 20 leads to a 581.94 % increase in flow rate, and 315.86 % in the streaming function. The analysis also reveals how zeta potential asymmetry ($\beta \ne 1$) enables precise flow control, including reversal. All classical limiting cases-Newtonian, purely pressure-driven, and steady electroosmotic-are exactly recovered, validating the model. These findings provide quantitative guidelines for the design of hydrogel-based microfluidic systems where electrokinetic and microstructural effects critically influence transport.