Toward an analytical theory of water flow through inhomogeneous porous media

Some rigorous mathematical results for the Buckingham‐Darcy flux law for water flow through an isotropic, nondeformable, inhomogeneous porous medium are presented. It is shown that the volumetric flux density vector, aside from the component due to gravity, may always be expressed in terms of a scalar and a vector matric flux potential. The vector matric flux potential will vanish for a homogeneous porous medium and for a one‐dimensional inhomogeneous porous medium. It follows from this result that the hydraulic conductivity will be a function only of the water potential in any one‐dimensional porous medium if its space derivative at constant water potential vanishes identically. In addition, it is shown that the vector matric flux potential is of no physical consequence insofar as the flow equation is concerned, regardless of the number of dimensions of space. The specification of that part of the flux density vector contributed by the vector potential appears in the law of momentum balance instead of in the law of mass balance.