The Boundary Conditions Governing Fluid Motions in Porous Media

Abstract

Further work has shown that the second of conditions (2.4) of a recent paper (Philip 1957?), supposed to govern the potential distribution during fluid motion in a porous medium, holds only for the case of linear axial flow in tubes of general cross section. The stated condition implied that the equipotential surfaces intersected the fluid-solid interface (a stream surface) normally. This may be approximately true for all media, but it can be shown by reference to the "complete" Stokes-Navier equation ((1.9) of Philip 1957) to be not exact in general. It follows that equation (2.8) and the thermal analogy (Section III) presented in that paper hold exactly for axial flow in tubes of general cross section, but are merely approximations when applied to more general media. Exact analysis for the general medium promises to be complicated and will not be pursued here.