Javed Siddique, George Mason University


Capillary rise of Newtonian and non--Newtonian liquids into deformable porous materials


Abstract: We examine a mathematical model for capillary rise of a fluid into an initially dry and deformable porous material. We use mixture theory to formulate the model. We obtain analytic results for steady state positions of the wet porous material--dry porous material interface as well as liquid--wet material interface. The time-dependent free-boundary problem is solved numerically and the results compared to the steady state predictions. In the absence of gravity, the liquid rises to an infinite height and the porous material deforms to an infinite depth, following square-root in time scaling. In contrast, in the presence of gravity, the liquid rises to a finite height and porous material deforms to a finite depth. We also show results of basic experiments on capillary rise of water into a deformable sponge. Here we measured the capillary rise height and sponge deformation and compared with our theoretical predictions. For early times, the experimental data and theoretical predictions for these interface dynamics are in general agreement but for long time, the long time equilibrium predicted theoretical is not observed in our experimental data. Finally, we also examine the capillary rise of non--Newtonian liquid into deformable porous material. The results are then compared with Newtonian case.

Advisor: Daniel Anderson (George Mason University