Modeling and simulation of trickle-bed magnetohydrodynamics in inhomogeneous magnetic fields

External inhomogeneous magnetic fields exert a magnetization body force. This force may prove practical in the case of electrically non-conducting and magnetically permeable fluids and may find positive echo in hydrodynamic intensification of chemical processes. Hence, in acting on paramagnetic or diamagnetic gases and liquids, this force can modify the direction as well as the magnitude of the gravitational force. As an intellectual illustration of the potential of this novel route, the ability to influence two-phase flows through packed bed reactors by application of external inhomogeneous magnetic fields was investigated theoretically. The analysis was carried out using an isothermal unidirectional two-fluid magneto-hydrodynamic model based on the volume–average mass and momentum balance equations for the description of two-phase down-flow throughout a vertically oriented and spatially uniform magnetic-field gradient. The magneto-hydrodynamics effects on trickle flow were displayed in terms of liquid hold-up and pressure drop under paramagnetic gas–diamagnetic liquid, paramagnetic gas and liquid, diamagnetic gas and liquid, diamagnetic gas–paramagnetic liquid combinations.