Capillary rise of a non-Newtonian liquid intoa deformable porous material

In this study we explore the one-dimensional capillary rise of a non-Newtonian, power-law fluid into rigid and deformable porous materials with and without gravity effects. For non-Newtonian flow in rigid porous materials with gravity, an equilibrium height equivalent to that for the classical Newtonian case is reached. However, the evolution toward the equilibrium solution differs between Newtonian and non-Newtonian cases. In the case of deformable porous material where both fluid and solid phases move, we use mixture theory to formulate the problem. Again equilibrium solutions exist and are the same for both Newtonian and non-Newtonian cases. In contrast to capillary rise in rigid porous material there are now two moving boundaries-the fluid height and the solid displacement at the bottom of the deforming porous material. In the absence of gravity effects, the model admits a similarity solution, which we compute numerically. With gravity present, the free boundary problem is solved numerically. In this case, the liquid rises to a finite height and the porous material deforms to a finite depth, following dynamics that depends on power-law index n and power-law consistency index μ ^*.