A pore-scale model for simulating water flow in unsaturated soil

Pore-scale simulation and tomography have been used in a combination over the past decade to study some fundamental physical and biogeochemical processes in soil that are difficult or impossible to measure, one of which is water flow in unsaturated soil. Considering that an important application of pore-scale simulation in soil is to elucidate how convective water flow distributes soluble nutrients through the heterogeneous pore space when water flow is in steady state, we propose an alternative model in this paper to simulate unsaturated water flow at pore scale. The model is quasi-static, consisting of two steps. The first one is to determine water distribution in the pore geometry using a morphological model; once the water distribution is known under a pressure, the water–air interface is fixed in space. The second step is to simulate water flow numerically by solving the Stokes equations in which the water–air interface is treated as a boundary. We test the water flow model against analytical solution of thin water film flow over a non-slip solid wall, and then combine it with the morphological model to simulate water flow in 3D soil structures acquired using X-ray tomography at resolution of 10 µm. As a validation, we compare the permeability calculated by the model under different saturations with those estimated by the van Genuchten formula using the saturated permeability and water retention parameters obtained from the morphological model. We also discuss the pros and cons of the model and its implications in unsaturated soil modelling.