Theory of Porous Media

In general, many solids show an internal structure. On the one hand, this is due to the fact that several solids consist of different solid components, such as dense concrete without pores. On the other hand, solids can contain closed and open pores, such as ceramics and soils, as well as concrete. In the past, these materials were, in general, treated as one-component materials lacking an internal structure. Using such a model — one which consists of an ideal material classical continuum mechanics has been very successful. All defined mechanical terms (for example, stress) are thereby understood as average quantities. Classical continuum mechanics can therefore not answer questions concerning the change of pores and the different motions belonging to the phases of liquid-saturated porous solids.

Porous media theory is based on the fundamental axioms and principles of mechanics and thermodynamics. The development of the scientific treatment of mechanical problems started around 1600. It was Galileo Galilei who founded mechanics as a branch of science. He laid the corner stone for a scientific approach to the natural world — namely to gather experience of certain mechanical problems, to order them, to create a theory, and to prove this through selected experiments as he had done in the treatments of streangth of material and projectile motion.

The development of basic relations in the classical era: the stress concept, the elasticity law, the fundamental laws of Delesse, Fick, and Darcy, the foundation of the mixture theory by Maxwell and Stefan, as well as the foundation of thermodynamics, all these had provided enough background material in order to treat empty or fluid-saturated porous solids. Indeed, in this century, the theory of porous media has been at last firmly established based on the achievements of the nineteenth century.

In many branches of engineering, for example, in chemical engineering, material science, and soil mechanics, as well as in biomechanics, the different reactions of material systems undergoing external and/or internal loadings must be studied and described precisely in order to be able to predict the responses of these systems. Subsequently, the most important point of the investigation is to determine first the composition of the body, because one must know the physically and chemically differing materials that constitute the system under consideration. The material systems (or bodies) in these fields of engineering can be composed in various ways. On the one hand, solids can consist of different solid components, such as dense concrete, without considerable pores. On the other hand, solids can contain closed and open pores, such as ceramics and soils, as well as concrete. The pores can be filled with fluids and, due to the different material properties and the different motions, there may be interaction between the constituents. As was mentioned in Section 1, this fact makes the description of the mechanical (or the thermodynamic) behavior difficult.

In the historical part (Chapter 2 through 4) some highlights of the development of porous media theory have been traced from infancy to their current state. Among the highlights, the bitter dispute between the professors Fillunger and von Terzaghi at the Technische Hochschule in Vienna in the 1930s, with its tragic results, has a particular place. The affair is representative of the unrest and upheaval in middle Europe during this period. For porous media theory, the year 1936 is a landmark, because it is in this year that the precise and general formulation of the one-dimensional mechanical porous media theory by Fillunger came to light. It is clear with hindsight that Fillunger’s approach was about 35 years ahead of its time.