Open AccessNonmonotone Saturation Profiles for Hydrostatic Equilibrium in Homogeneous Porous Media
Author(s) -
Hilfer R.,
Doster F.,
Zegeling P.A.
Publication year - 2012
Publication title -
vadose zone journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.036
H-Index - 81
ISSN - 1539-1663
DOI - 10.2136/vzj2012.0021
Subject(s) - hydrostatic equilibrium , saturation (graph theory) , observable , porous medium , mechanics , monotone polygon , homogeneous , statistical physics , thermodynamics , physics , porosity , mathematics , geology , geotechnical engineering , geometry , combinatorics , quantum mechanics
Recently, the observation of nonmonotonicity of traveling wave solutions for saturation profiles during constant‐flux infiltration experiments has highlighted the shortcomings of the traditional, seventy year old mathematical model for immiscible displacement in porous media. Several recent modifications have been proposed to explain these observations. The present paper suggests that nonmonotone saturation profiles might occur even at zero flux. Specifically, nonmonotonicity of saturation profiles is predicted for hydrostatic equilibrium, when both fluids are at rest. It is argued that in traditional theories with the widely used single‐valued monotone constitutive functions, nonmonotone profiles should not exist in hydrostatic equilibrium. The same applies to some modifications of the traditional theory. Nonmonotone saturation profiles in hydrostatic equilibrium arise within a generalized theory that contains the traditional theory as a special case. The physical origin of the phenomenon is simultaneous occurrence of imbibition and drainage. It is argued that indications for nonmonotone saturation profiles in hydrostatic equilibrium might have been observed in past experiments and could become clearly observable in a closed column experiment.