Statistical Hydrodynamics in Porous Media

The statistics of disordered phenomena as exemplified by Einstein's theory of the Brownian motion is applied to the flow of fluids through porous media. It is shown that such a statistical treatment of the hydrodynamics in porous media automatically explains some well-known phenomena in a more satisfactory manner than do capillaric models. The statistical theory leads to a differential equation of motion of the fluid which is a modification of that of Darcy; notably a new macroscopic quantity is introduced which is termed ``dispersivity.'' This quantity is indicative of the sideways dispersion which a stream of fluid undergoes when it is passing through the porous medium. Under certain statistical assumptions outlined in the paper, the dispersivity becomes a constant of the porous medium. The new differential equation of motion of the fluid is discussed in detail and some indications about applications are given.