Electrokinetic energy conversion of unsteady couple stress fluids with Caputo–Fabrizio time-fractional derivative

Abstract

This study investigates the unsteady electrokinetic flow of couple stress Newtonian fluids between parallel plates. The time-fractional Caputo–Fabrizio derivative is introduced to characterize the relaxation memory effect throughout the fluid flow evolution. Analytical solutions for velocity, streaming potential, and energy conversion efficiency are derived by virtue of the separation of variables and fractional Laplace transform. Graphical examinations are conducted to clarify the influences of temporal evolution, fractional-order, couple stress and electrokinetic parameters, and identified the key parameters governing the energy conversion process Results show that a lower fractional order aggravates the fluid flow response delay and enhances historical dependence, while couple stress induce inherent dissipation, thereby regulating energy transport. The energy conversion efficiency is jointly governed by both the fractional-order and couple stress parameters. This work provides a theoretical basis for coupling time memory and scale effects in electrokinetic microchannel flows.