General statistical hydrodynamics in porous media

Summary

The study of fluid flow in the ground is based upon the physics of flow through porous media. The author has recently proposed a theory (2) of such flow based upon the statistics of disordered phenomena which, however, was applicable to a special type of flow only. In the present paper, the earlier theory is developed into a general theory applicable to any type of microscopic flow equation. It is shown that the qualitative analogy which is observed between the equations of flow through porous media and the equations of flow through capillaries can be logically explained without the assumption of capillaric models. Thus, a theorem is proven stating that the flow through porous media is described by the superposition of two effects: firstly, one corresponding to the average flow through a set of small channels, and secondly, a dispersivity effect. Finally, the results are applied to a variety of flow equations such as laminar flow, turbulent flow, and molecular streaming, all of which may occur in groundwater flow.