On the incompatibility of Richards' equation and finger‐like infiltration in unsaturated homogeneous porous media

Abstract

It is demonstrated by means of a mathematical proof that Richards' equation, in principle, cannot admit finger‐like solutions for three‐dimensional homogeneous unsaturated porous media flow, subject to monotone boundary conditions. This is demonstrated for any reasonable type of homogeneous porous material; the result is not dependent on any particular form of the hydraulic conductivity or the retention curve. Moreover, it is explained why hysteresis of the retention curve does not play any role in the proof. Consequently, the proof is true for any type of hysteretic behavior of the retention curve. An alternative approach to finger flow modeling is discussed which uses the ideas of cellular automata.