Theory of Porous Media — Past and Present

Porous solids filled with liquid or gas play an important role in engineering, e.g., in material science, petroleum industry, chemical engineering, and soil mechanics as well as in biomechanics. Although porous media are of considerable practical significance the description of their mechanical and thermodynamical behavior has been unsatisfactory for a long time. The theory to describe the complex thermodynamical behavior of such saturated porous solids has come to certain well-founded conclusions only recently. It is the goal of this paper to show the historical development of the porous media theory, which already started in the eighteenth century, formed in some areas by polemic disputes and tragic events in the lifes of the scientists involved. Furthermore, the current state of the research into this subject is discussed, whereby the state of the development of the material independent basic equations and the constitutive theory is illustrated. For a certain class of models general theorems, such as minimum and maximum problems, are derived and the uniqueness of solutions of boundary value problems is proved.