R. Hilfer, F. Doster, P. Zegeling
Vadose Zone Journal 11, vzj2012.0021 (2012)
doi:10.2136/vzj2012.0021
submitted on
Friday, September 30, 2011
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 saturations 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 singlevalued 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.
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