External inhomogeneous magnetic fields exert a body force (magnetization force) on electrically nonconducting and magnetically permeable fluids. The force acts on both paramagnetic and diamagnetic fluids and can be used to compensate for or to amplify the gravitational body force, unlike the Lorentz braking force that manifests only for electrically conducting liquids, such as liquid metals. The ability to influence two-phase flows through porous media by the application of external inhomogeneous magnetic fields is of interest in the operation of trickle-bed reactors for catalytic process intensification, particularly in oxidation catalysis, where the O2 paramagnetic properties may be propitious to macrogravity operation for enhancing liquid holdup and wetting efficiency. An isothermal 1-D two-fluid magnetohydrodynamics model based on volume-average mass and momentum balance equations to describe the gas-liquid downflow under a spatially uniform magnetic-field gradient. The slit model approximation was used for the derivation of drag force closures intervening in the momentum equations. The evolution of the trickle-bed magnetohydrodynamics was theoretically investigated in terms of liquid holdup and pressure drop under four gas-liquid combinations. Advantages of this novel approach of process intensification were rationalized in terms of catalytic reactions.
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