Capillary Rise of Magnetohydrodynamics Liquid into Deformable Porous Material

We have developed a mathematical model for capillary rise of magnetohydrodynamic fluids. The liquid starts to imbibe because of capillary suction in an undeformed and initially dry spongelike porous material. The driving force in our model is a pressure gradient across the evolving porous material that induces a stress gradient which in turn causes deformation that is characterized by a variable solid fraction. The problem is formulated as a non–linear moving boundary problem which we solve using the method of lines approach after transforming to a fixed computational domain. The summary of our finding includes a notable reduction in capillary rise and a decrease in solid deformation due to magnetic effects.