Electro-osmosis modulated periodic membrane pumping flow and particle motion with magnetic field effects

Abstract

Theoretical studies of micro-electro-mechanical systems provide important insight into the mechanisms and optimization of such devices for a range of applications, including biomedical and chemical engineering. Inspired by emerging applications of microfluidics, unsteady viscous flow in a microchannel with periodic membrane pumping modulated by electro-magnetohydrodynamics is analyzed in a mathematical framework. The membrane kinematics induces the pressure inside the microchannel, where an electric field enhances the capability of the pumping flow rate. This model is formulated based on the Navier–Stokes equations, the Poisson equation, and the Maxwell electromagnetic equations and is further simplified using the lubrication approximations and Debye–Hückel linearization. The transformed dimensionless conservation equations under appropriate boundary conditions are analytically solved and the graphical results are illustrated through MATLAB (2019b) software. From the computational results, it is found that the Hartmann number enhances the fluid pressure uniformly throughout the microchannel, while the electric field parameter enforces the direction of the pressure-driven flow. The time-averaged flow rate exhibits a linear decay with axial pressure gradient, and it is strongly elevated with electric field parameter whereas it is weakly increased with electric double layer thickness parameter. It is further observed that the fluid is driven unidirectionally by the membrane contractions via a particle tracking simulation method. This study is relevant to provide the parametric estimation in designing the magnetic field-based microfluidics devices for microlevel transport phenomena.