Electromagnetohydrodynamic Flow in Porous Media: Multiscale Modeling, Experiments, and Macroscale Simulations

Electromagnetohydrodynamic (EMHD) flow in porous media presents a powerful mechanism for enhancing transport in microfluidic systems, filtration, enhanced oil recovery, CO₂ storage and electrochemical devices. This study investigates the coupled effect of externally applied electric and magnetic fields on single-phase fluid flow through saturated porous structures using a multiscale modeling framework. Starting from the pore scale, we solve the coupled Poisson Boltzmann, Stokes, and Lorentz force equations within a periodic representative elementary volume. An asymptotic homogenization technique is used to derive the effective macroscopic equations, incorporating electroosmotic and magnetohydrodynamic contributions to the momentum balance. The derived mobility and permeability tensors are validated through controlled experiments using Whatman filter paper with applied electric fields and transverse magnetic fields. The flow velocity and permeability measured experimentally are found to match the predicted macroscale trends. Finally, the upscaled EMHD model is used to simulate practical flow scenarios in lab-scale porous domains, showing improved control of wetting front dynamics and mixing. This work bridges micro- and macro-scale physics of field-driven flow, providing critical insights for the design of advanced porous media systems under multi-field actuation.