We examine the effects of capillarity and gravity in a model of one-dimensional imbibition of
an incompressible liquid into a deformable porous material. We focus primarily on a
capillary rise problem but also discuss a capillary/gravitational drainage configuration in
which capillary and gravity forces act in the same direction. Models in both cases can be
formulated as nonlinear free-boundary problems. In the capillary rise problem, we identify
time-dependent solutions numerically and compare them in the long time limit to analytically …