Mixture Theory-Based Poroelasticity and the Second Law of Thermodynamics - Continuum Mechanics of Anisotropic Materials - page 259

Chapter 10
Mixture Theory-Based Poroelasticity
and the Second Law of Thermodynamics

Here is an appropriate interpretation of the second law of thermodynamics:
Dissipation principle: For all thermodynamic processes that are admissible for a
given constitutive assumption, the entropy production must be positive or zero . The
decisive word in this postulate is the quantifier all it makes the postulate a restrictive
condition on the internal constitutive assumptions that can be imposed on systems
of the type under consideration. Indeed, if internal constitutive assumptions are laid
down at will and without restriction, the entropy production can be expected to be
positive or zero only for some but not for all admissible processes. Thus, the second
law is not a restriction on the kind of processes that can occur in nature, but a
restriction on the kind of material properties that physical systems occurring in
nature can have. Walter Noll, 8th International Congress on Thermal Stresses, 2009

10.1 Introduction

The title of this chapter makes reference to three topics; mixture theory,
poroelasticity, and the second law of thermodynamics. In Sect. 8.11 it was noted
that there are different major approaches to the development of the same
basic equations for the theory of poroelasticity. The first approach, the effective
medium approach, was the subject of Chap. 8 . The second approach, the mixture
theory approach, is one of the subjects of this chapter. It would be helpful to read or
reread the paragraphs in Sect. 8.11 that deal with this second approach as much of
the development of the subject described there will be detained in this Chapter.
A mixture is a material with two or more ingredients, the particles of which are
separable, independent, and uncompounded with each other. If the distinct phases
of a mixture retain their identity, the mixture is said to be immiscible; if they lose
their identity, the mixture is said to be miscible. Mixture theory provides a basis
upon which the poroelasticity model of Chaps. 8 and 9 may be extended to
multicomponent mixtures. The possible constituents of a mixture include a porous
solid, solvents and solutes and possibly other constituents. The theory of mixtures is