Capillary Rise of Magnetohydrodynamics Liquid into Deformable Porous Material


1 Department of Mathematics, Pennsylvania State University, York Campus, PA 17403 USA

2 Systems Engineering Department, King Fahd University of Petroleum and Minerals, PO Box 5067, Dhahran, 31261, Saudi Arabia.


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 sponge-like 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.