Abstract
From the second law of motion, the author has derived equations of the viscous flow of incompressible fluids through porous media from macroscopic point of view, under the assumption that the fundamental hydrodynamic relations between stress and rate-of-strain for viscous incompressible fluids are also satisfied by the fluids in pores and that the porous media are saturated, isotropic, and geometrically stable at a constant temperature.
An important point for consideration of macroscopic motion is its relationship tomicroscopic one. Such macroscopic quantities as velocity, pressure, etc. are, therefore, directly defined from the' corresponding microscopic ones from the standpoint that such physical quantities should be invariant in transformation; and the quantities thus defined are supposed to be analytical throughout the space through proper conception in order to render the subject amenable to exact mathematical treatment, though the microscopic ones defined only within the effective pores but not within the solid particles.
The equations of macroscopic motion derived on the basis of the above considerations involve inertia terms which have never been derived from the Navier-Stokes equation, and drag force terms by which the concept of drag in percolation flow is to be physically clarified ; but, on the other hand, they do not contain the so-called macroscopic viscous term, which cannot exist essentially, as shown in this paper. Moreover, it should be noted that the quite natural con equence that the drag force consists of viscous drag and pressure drag as shown here has never been verified theoretically and has been recognized even incorrectly, and a deeper exploration will result in more theoretical derivations of Darcy's or Forchheimer's law and, necessarily, also of “permeability”, clearing up the role of these in the fundamental equations.
