Modelling preferential flow through unsaturated porous media with the Preisach model and an extended Richards Equation to capture hysteresis and relaxation behaviour

The unsaturated flow of water in soil through unstable wetting fronts has been documented in literature. These instabilities can lead to the development of finger-flow profiles, whose paths can be "remembered"by a solid matrix of soil during future infiltration even after periods of desaturation. This process has been modelled for a 1D column of soil by the Richards equation, a non-equilibrium relaxation ODE, and Preisach hysteresis, all of which are required for finger flow. In this paper a comparison is made to similar work that use Parlange's model of hysteresis and show that similar results are achieved by instead including the Preisach model. In addition, the model allows for the strength of hysteresis to be changed by a single parameter thus allowing the potential of parameter fitting of data in the future.