Closed-Form Model for Hysteretic Hydraulic Properties Based on Angular Pores with Variable Contact Angles.

The accurate knowledge of the soil water retention and unsaturated hydraulic conductivity curves is crucial for modeling water flow in soil. It is common practice to fit an empirical model to experimental data of soil water retention and then calculate the unsaturated hydraulic conductivity curve by assuming that the soil can be represented as a bundle of capillary tubes. The resulting soil hydraulic functions are then used to predict water dynamics at larger spatial scales. It is well known that the nature of the SHPs is hysteretic, i.e. that the SHPs estimated from a drainage experiment do not coincide with those determined from an imbibition experiment conducted on the same sample. Further complications arise from the incomplete wetting of water at the solid matrix which results in finite value of the contact angle between the solid-water-air interface. We present a new mathematical model which describes the water retention and hydraulic conductivity curve taking into account hysteresis at the pore scale. It conceptualizes the pore space as a set of angular pores with a varying contact angle between solid and liquid. We derive a model of hydraulic conductivity, again as a function of contact angle, by assuming flow perpendicular to pore cross sections, upscale the model by assuming a log-normal statistical distribution of pore size, and derive closed-form expressions for both the water retention and hydraulic conductivity function. The new model was tested against experimental data from multistep inflow/outflow (MSI/MSO) experiments for a sandy material which were conducted using ethanol and water as wetting liquids. The proposed model described both imbibition and drainage of water and ethanol very well by assuming a unique pore size distribution of the sample and a contact angle of zero for ethanol.