Unidirectional infiltration in deformable porous media: Mathematical modeling and self-similar solution

This study is motivated by the necessity to develop models and to obtain mathematical results which can help in improving certain industrial processes used for manufacturing composite materials. We focus on unidirectional infiltration processes in deformable porous material and on the analytical study of the related mathematical problem. A key point in developing the model is the use of a set of Lagrangian coordinates fixed on the solid. This technique allows us to simplify the mathematical problem. In the Eulerian formalism, in fact, such a problem is a free boundary problem characterized by the presence of two time-dependent interfaces. The use of material coordinates fixed on the solid allows, vice-versa, to fix one boundary and so to obtain a nonlinear one-phase Stefan problem. The latter, then, has been studied from the analytical viewpoint. In particular, we have proved the existence of a solution exhibiting a serf-similar form.