Diffusion through time-dependent media

In this theoretical paper we show how to solve a time-dependent diffusion e quation by means of a perturbation series. This technique is applied to the case of diffusion of a liquid through a time-dependent porous matrix. We c ompute to first order the phase and amplitude relations between the small d eformation of the transporting matrix and the corresponding variation of th e saturation at the surface. In particular we show that, for a large freque ncy range, there is a constant phase shift of pi/2 between the matrix and t he surface saturation variations. Since the conductivity is to first approx imation proportional to the saturation at the surface, this might explain t he observed phase relations observed in an experiment in a cave near Abarat subo (Japan).