 
Summary: Imbibition of a liquid droplet on a deformable porous substrate
Daniel M. Andersona
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030
Received 20 December 2004; accepted 14 June 2005; published online 2 August 2005
We consider the imbibition of a liquid droplet into a deformable porous substrate. The liquid in the
droplet is imbibed due to capillary suction in an initially dry and undeformed substrate. Deformation
of the substrate occurs as the liquid fills the pore space. In our model, a pressure gradient in the
liquid across the developing wet substrate region induces a stress gradient in the solid matrix which
in turn leads to an evolving solid fraction and hence deformation. For axisymmetric droplets, we
assume that the imbibition and substrate deformation at a given radial position are onedimensional
in the vertical direction . The coupling to the droplet geometry leads to axisymmetric
configurations for the deformed wet substrate. We show that the model chosen to describe the
dynamics of the liquid droplet, based in this case on existing models developed for droplet spreading
on rigid porous substrates, has little influence on the resultant swelling or shrinking of the
substratethese general trends can be effectively predicted by a onedimensional imbibition and
deformation modelbut does strongly influence the details of the wet substrate shape. We
characterize these predictions and in some cases can obtain analytical solutions for the evolution.
© 2005 American Institute of Physics. DOI: 10.1063/1.2000247
I. INTRODUCTION
In this paper we develop a model for the imbibition of a
