Magnetohydrodynamics-based pumping flow model with propagative rhythmic membrane contraction

Abstract

A novel magnetohydrodynamics (MHD)-based pumping flow model is proposed to study the magnetic property in transient flow of viscous fluids through finite length channel where the upper channel wall is derived to describe the propagative membrane mode of rhythmic contractions. The flow is generated by the pressure difference due to propagative membrane contraction. Inlet and outlet pumping flow mechanisms are applied during the compression and expansion phases. This model is developed based on low Reynolds number flow to considering the microscale transport phenomena in biomedical sciences. Closed-form solutions for velocity fields, pressure, volumetric flow rate, wall shear stress and stream functions are derived under the lubrication analysis. Salient features of the flow analysis and pumping performances are illustrated with the aid of graphical results under the effects of time variation, membrane shape parameter and Hartmann number. Contour plots for velocity fields, stream function and shear stress are prepared for better visualization and analysis. It is inferred that the pressure along the channel length is more with increasing the magnetic field property in both phases (expansion and compression) of membrane contractions. Maximum pressure difference occurs at the membrane contractions, which represents the pumping mechanism. This pumping model can be utilized to design the novel biomedical MHD micropumps for wide-ranging biomedical applications.