Evaluating the Impact of the Covariance of the Friction and Potential Gradient on Describing the Infiltration Process

During infiltration of water in soil, menisci form at the interface of water, grains, and air in the pores, inducing suction due to surface tension. Due to the random distribution of interconnected pores of different sizes, characteristic of porous media, differences in suction and friction inside pores give a diffusing infiltration front. The process of infiltration is often simulated by solving Richards' equation in which the water flux is calculated with Darcy's law. Underlying Darcy's law is the assumption that the gradients in flow potential and the flow resistance due to viscous forces are independent from each other. This paper shows that these parameters are dependent and negatively correlated. A new method for calculating flows in unsaturated porous media has been developed to evaluate the impact of the covariance on infiltration predictions. The results show that the impact is significant and leads to a reduction in infiltration rate and mean friction experienced during infiltration. The method thereby provides a physical explanation for the subdiffusion observed during water infiltration in soil and is consequently expected to provide more insights into the processes of infiltration.