Dynamic Non-Equilibrium Water Flow Under Various Boundary Conditions: A Modelling Approach

Abstract:

Soil water flow in laboratory experiments often presents complexities which include a dynamic behavior indicated by non-equilibrium between water content θ and water potential h which are known as “dynamic effects”. During the last six decades dynamic effects have been observed directly or indirectly as (1) non-uniqueness of the diffusivity vs water content function, (2) the flow rate dependence of the water retention curve, (3) a relaxation in the system-averaged water content in experiments with controlled pressure head boundary conditions and (4) as a relaxation of the pressure head while the flux density and macroscopic water content distribution appear to be constant. Macroscopically, all the observations mentioned above can be described by the following mechanism: Even in well sorted materials there are always some highly conducting pore paths in which the flow is initiated when the boundary condition is changed. This is followed by an equilibration phase during which a relatively small amount of water initially behind the wetting or drying front moves in the major flow direction. This second phase of equilibration is not instantaneous and is responsible for the observed drift in the θ vs h relationship at the REV scale.

Diamantopoulos et al. (2012) presented a model which describes dynamic effects in the case of Multistep Outflow experiments. They assumed that the water content is macroscopically portioned into two fractions: Water content in one fraction is in equilibrium with the pressure head whereas the equilibration of the water content in the second fraction lags behind. In this work we applied the non-equilibrium model of Diamantopoulos et al. (2012) to the four different observations of dynamic effects in laboratory experiments presented in the literature. Results show that the model predicted nonequilibrium effects very well in all four types of flow experiments.