 
Summary: Capillary rise of a liquid into a deformable porous material
J. I. Siddique,a
D. M. Anderson,b
and Andrei Bondarevc
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA
Received 25 September 2008; accepted 12 December 2008; published online 27 January 2009
We examine the effects of capillarity and gravity in a model of onedimensional 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
freeboundary problems. In the capillary rise problem, we identify timedependent solutions
numerically and compare them in the long time limit to analytically obtain equilibrium or steady
state solutions. A basic feature of the capillary rise model is that, after an early time regime governed
by zero gravity dynamics, the liquid rises to a finite, equilibrium height and the porous material
deforms into an equilibrium configuration. We explore the details of these solutions and their
dependence on system parameters such as the capillary pressure and the solid to liquid density ratio.
We quantify both net, or global, deformation of the material and local deformation that may occur
even in the case of zero net deformation. In the model for the draining problem, we identify
numerical solutions that quantify the effects of gravity, capillarity, and solid to liquid density ratio
on the time required for a finite volume of fluid to drain into the deformable porous material. In the
