Darcy–Forchheimer flow driven by membrane pumping and magnetohydrodynamics: perturbation solution

Membrane based pumping addresses the critical need for precise fluid control in biomedical applications, particularly in targeted drug delivery, dialysis, and biofluid circulation, by investigating magnetohydrodynamic (MHD) fluid flow in porous microchannels. The aim of this study is to develop a Darcy–Forchheimer-based MHD pumping model to analyze transient viscous fluid flow through a finite-length microchannel. The methodology involves modelling the upper wall of the channel as undergoing rhythmic, propagative membrane contractions to replicate physiological transport mechanisms and lower wall is stationary. A perturbation technique is employed to derive the analytical series solution, using lubrication theory and assuming a low Reynolds number. The effects of key parameters including the membrane shape parameter, Hartmann number, inverse Darcy number and Forchheimer number are examined on flow and pumping characteristics, shear stress and streamline patterns using MATLAB code. The results highlight that velocity reduces with increasing the Forchheimer number and Hartmann number due to enhanced inertial and Lorentz forces. In the microchannel, the maximum pressure difference is observed at the region where the membrane is located, highlighting the effectiveness of the pumping mechanism. The significance of this study lies in its contribution to the advancement of MHD-based biomedical micropumps, providing valuable insights into controlled fluid transport within microfluidic systems. These findings are especially important for enhancing the controlled and smooth process of biofluid dynamics at microscale without any contamination, and addressing critical challenges in biomedical engineering.