TY - JOUR

T1 - Toward an analytical theory of water flow through inhomogeneous porous media

AU - Gupta, Vijay K.

AU - Sposito, Garrison

AU - Bhattacharya, R. N.

PY - 1977/2

Y1 - 1977/2

N2 - 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.

AB - 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.

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U2 - 10.1029/WR013i001p00208

DO - 10.1029/WR013i001p00208

M3 - Article

AN - SCOPUS:0017457021

VL - 13

SP - 208

EP - 210

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 1

ER -