UNSTEADY-FLOW INDUCED DEFORMATION OF POROUS MATERIALS

The deformation of a porous material by an unsteady fluid flow within its pores is modeled by a non-linear diffusion equation. Mixture theory is used to derive the equation and to identify the range of frequencies for which inertia can be ignored. The unidirectional case in which a porous sponge is deformed by an applied fluid pressure gradient is solved analytically when the deformation is assumed infinitesimal. Perturbation techniques are then used to obtain approximate solutions for slow and fast compression rates when the constitutive equation and permeability function are non-linear. The finite deformation compression case is then solved numerically. It is shown that the mean permeability of a sponge experiencing an unsteady applied pressure can be greater than the permeability in the case of a steady mean pressure.