Soil is not a solid sponge but a labyrinth of pores of various sizes. After rain, water does not fill them all at once: first the narrowest ones, then the wider ones. Physicists built a theory of this process based on a simple image — a set of communicating vessels. The flows between pores obey the laws of viscous fluid flow, and the driving force is the difference in chemical potentials. Roughly speaking, it is water's "desire" to occupy a particular pore, taking into account capillary forces and gravity.
The key turned out to be the dimensionless Damköhler number for each pore. When it is small, water manages to distribute evenly: this is the classic slow absorption described by the Richards equation. When the number is large, water darts through selected paths without having time to "look around." This gives rise to fast preferential flows, familiar to anyone who has seen a puddle disappear in minutes rather than hours after a downpour. The theory shows that these are not two different phenomena but a smooth transition governed by a single parameter.
This view makes dozens of ad hoc models unnecessary. All the necessary information about the soil is the geometry of the pore network, which can be measured with a microtomograph. There is no need to fit parameters to field data. The equation itself decides where water should flow slowly and where quickly.
The Damköhler number, which governs water behavior in soil, originally came from chemical engineering and described how fast a chemical reaction proceeds relative to the flow of matter. Now it also "works" right under our feet.