Capillary pressure overshoot for unstable wetting fronts is explained by Hoffman's velocity-dependent contact-angle relationship

Pore velocity-dependent dynamic contact angles provide a mechanism for explaining the formation of fingers/columns in porous media. To study those dynamic contact angles when gravity is present, rectangular capillary tubes were used to facilitate observation of the complete interface without geometric distortion. Results show that the Hoffman (1975) relationship between dynamic contact angle and water velocity applies to gravity-affected flow fields, and that it (when adjusted for nonzero static contact angles) can be used to model dynamic capillary pressures for unstable wettings fronts in porous media by assuming that (1) pressure at the wetting front is discontinuous, (2) the flow field behind the fingertip is highly heterogeneous, and (3) the front line advances one or a few pores at the time. We demonstrate the utility of the Hoffman relationship for porous media with a published infiltration experiment by calculating the capillary pressure successfully at the unstable wetting front as a function of the flux of water in the finger and the grain size diameter.