Highlights in the Historical Development of the Porous Media Theory: Toward a Consistent Macroscopic Theory

Abstract

First contributions to the theory of porous media were made by R Woltman in 1794 when he independently developed a more sophisticated earth pressure theory than C Coulomb, and surprisingly in another context introduced the concept of volume fractions. In the last century, further important contributions were published by A Delesse, A Fick, H Darcy, and J Stefan on the concept of surface fractions, the diffusion problem, ground-water flow, and the mixture theory, which are essential parts of the theory of porous media. In the twentieth century, the scientific discussion on porous media theories was opened by P Fillunger in 1913 in a paper about the uplift problem in saturated rigid porous solids. In subsequent articles, he investigated the phenomena of friction and capillarity and discovered the effect of effective stresses. In 1923, K von Terzaghi, founder of modern soil mechanics, started his investigations on saturated deformable porous solids within the framework of the calculation of the permeability coefficient of clay. In 1936, Fillunger founded the concept of the mechancial theory of liquid-saturated deformable porous solids. However, his substantial masterpiece was completely forgotten and ignored. The reason for this may lie in the fact that in the 1930’s deep hostility arose between Fillunger and von Terzaghi due to different scientific views on the porous media theory and soil mechanics, leading to a large controversy which ended very tragically. The works of von Terzaghi and Fillunger were continued by M Biot, G Heinrich, and I Frenkel in the next decades. Today, two important directions of the macroscopic porous media theory are commonly acknowledged. The first one is based on investigations by M Biot, and the second one proceeds from the mixture theory, restricted by the concept of volume fractions (porous media theory). In particular, the porous media theory has turned out to be an efficient tool to treat saturated and empty porous solids.