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ZAMM Z. Angew. Math. Mech. 82 (2002) 2, 115124 Ambrosi, D.

Summary: ZAMM Z. Angew. Math. Mech. 82 (2002) 2, 115124
Ambrosi, D.
Infiltration through Deformable Porous Media
The equations driving the flow of an incompressible fluid through a porous deformable medium are derived in the frame-
work of the mixture theory. This mechanical system is described as a binary saturated mixture of incompressible compo-
nents. The mathematical problem is characterized by the presence of two moving boundaries, the material boundaries of
the solid and the fluid, respectively. The boundary and interface conditions to be supplied to ensure the well-posedness of
the initial boundary value problem are inspired by typical processes in the manufacturing of composite materials. They
are discussed in their connections with the nature of the partial stress tensors. Then the equations are conveniently
recast in a material frame of reference fixed on the solid skeleton. By a proper choice of the characteristic magnitudes of
the problem at hand, the equations are rewritten in non-dimensional form and the conditions which enable neglecting the
inertial terms are discussed. The second part of the paper is devoted to the study of one-dimensional infiltration by the
inertia-neglected model. It is shown that when the flow is driven through an elastic matrix by a constant rate liquid inflow
at the border some exact results can be obtained.
Key words: infiltration, mixture theory, inertia, Darcy's law, porous deformable media, moving boundaries
MSC (2000): 76S05
0. Introduction
The mathematical modelling of the infiltration of an incompressible fluid through a porous deformable solid is of inter-
est in a number of industrial and environmental applications. Notable examples are the manufacturing of composite
materials by injection molding and soil consolidation problems.


Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino


Collections: Mathematics