On Arbitrary Quantities in a Porous Medium with Incompressibility Constraint

Abstract

In this work, we consider the motion of a saturated porous medium with fluid, in which the densities of the pure solid and fluid are constants, whose equations of balance are established by the solid-fluid mixtures continuous theory without chemical reactions. Because of the constant densities that characterize the incompressibility constraint, each strain tensor is given by one arbitrary part over another constitutive, as well as the interaction force, interaction energy and the Helmholtz free energy. The arbitrary parts were determined based on entropic inequality, under the principle that the sum of the entropic outputs is zero for all motion compatible with the incompressibility constraint. As a result, it was shown that this principle produces different arbitrary pressures for solid and fluid phases and, moreover, it causes a great influence on the balance equations of linear momentum, since there are new interaction terms. Accordingly, the set of equations obtained generates systems with different ways for the motion of a porous medium, each system established on how the terms of arbitrary pressures and arbitrary interactions are grouped and interpreted
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