Physically-based model of soil hydraulic properties accounting for variable contact angle and its effect on hysteresis

The description of soil water movement in the unsaturated zone requires the knowledge of the soil hydraulic properties, i.e. the water retention and the hydraulic conductivity function. A great amount of parameterizations for this can be found in the literature, the majority of which represent the complex pore space of soils as a bundle of cylindrical capillary tubes of various sizes. The assumption of zero contact angles between water and surface of the grains is also made. However, these assumptions limit the predictive capabilities of these models, leading often to errors in the prediction of water dynamics in soils. We present a pore-scale analysis for equilibrium liquid configuration in angular pores taking pore-scale hysteresis and the effect of contact angle into account. Furthermore, we propose a derivation of the hydraulic conductivity function, again as a function of the contact angle. An additional parameter was added to the conductivity function in order take into account effects which are not included in the analysis. Finally, we upscale our model from the pore to the sample scale by assuming a gamma statistical distribution of the pore sizes. Closed-form expressions are derived for both water retention and conductivity functions. The new model was tested against experimental data from multistep inflow/outflow (MSI/MSO) experiments for a sandy material. They were conducted using ethanol and water as the wetting liquid. Ethanol was assumed to form a zero contact angle with the soil grains. By keeping constant the parameters fitted from the ethanol MSO experiment we could predict the ethanol MSI dynamics based on our theory. Furthermore, by keeping constant the pore size distribution parameters from the ethanol experiments we could also predict very well the water dynamics for the MSO experiment. Lastly, we could predict the imbibition dynamics for the water MSI experiment by introducing a finite value of the contact angle. Most importantly, the predictions for both ethanol and water MSI/MSO dynamics were made by assuming a unique pore-size distribution.