Limits of applicability of the Richards equation from scaling capillary, gravity and viscous forces in unsaturated porous media

Interplay between capillary, gravity and viscous forces in unsaturated porous media gives rise to a range of complex flow phenomena that affect wetting front morphology, stability and dynamics (intermittency) of drainage. Different fluid distributions for similar average phase content may affect macroscopic transport properties of the unsaturated medium. Several unifying concepts emerge from scaling behavior in which gravitational force in excess of capillary pinning force scales linearly with the viscous force. The result is recast as a dimensionless generalized Bond number (difference between capillary and Bond number) that provides excellent predictive capabilities of wetting and drying front morphology. Evidence supports the generality of such scaling relationships for a wide range of flow regimes and drainage front morphologies. Based on limited experimental observations, the scaling relationships may define conditions for onset of unstable flows leading to enhanced liquid and gas entrapment, and provide a basis for delineation of the limits of applicability of the Richards equation for a certain range of generalized Bond number where capillary, gravity and viscous forces exert similar influences.