On the origin of Darcy’s law1

When one thinks about porous media, the immediate concepts that come to mind are porosity, permeability and Darcy’s law. The latter is probably one of the most important tools in hydrodynamics and engineering presenting numerous applications in oil recovery, chemical engineering, nuclear safety and many other engineering field. It has been first formulated by the French engineer Henri Darcy in 1856 in Appendix D of his famous book Fontaines publiques de la ville de Dijon [2] to describe flow through beds of sand. His column experiments (see Figure 1.1) showed that the total discharge is proportional to the total pressure drop divided by the fluid viscosity and that the linear coefficient, called permeability, is intrinsic to the investigated porous medium. Darcy’s law is the equation that governs the flow of fluid in porous media. If one opens any fluid dynamics textbook, however, one learns that fluid motion is described by the Navier-Stokes equations. So, what is this law? Are there any links between Darcy’s law and fluid mechanics theory? This Chapter introduces two different representations of the physics of fluid flow in porous media and their interrelation. These different approaches will lead us to the very definition of a porous medium.