Governing equations for modeling preferential flow in unsaturated soil based on fractal theory

To characterize the quick and non-equilibrium movement of preferential flow, and to represent the flow and transport in the unsaturated soil-water system more accurately, fractal theory was incorporated into the continuum approach based on the fundamental theories of active region model (ARM) and the fractal properties of the preferential flow patterns which were observed widely in lab and field studies. The governing equations for controlling preferential soil water flow and solute transport were derived from the mass conservation principle in this research. Furthermore, the ARM was compared with the mobile-immobile region model (MIM) and the active fracture model (AFM) to show the differences and relationship between these approaches. This research provided theoretical directions and effective approaches for using ARM to solve the related flow and transport processes resulted from preferential flow in the unsaturated soil-water system.