A phase field model of unsaturated flow

Citation Cueto-Felgueroso, L., and R. Juanes. " A phase field model of unsaturated flow. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. [1] We present a phase field model of infiltration that explains the formation of gravity fingers during water infiltration in soil. The model is an extension of the traditional Richards equation, and it introduces a new term, a fourth-order derivative in space, but not a new parameter. We propose a scaling that links the magnitude of the new term to the relative strength of gravity-to-capillary forces already present in Richards' equation. We exploit the thermodynamic framework to design a flow potential that constrains the water saturation to be between 0 and 1, its physically admissible values. The model predicts a saturation overshoot at the wetting front, which is in good agreement with experimental measurements. Two-dimensional numerical simulations predict gravity fingers with the appearance and characteristics observed in visual laboratory experiments. A linear stability analysis of the model shows that there is a direct relation between saturation overshoot and the strength of the front instability. Therefore our theory supports the conjecture that saturation overshoot, a pileup of water at the wetting front, is a prerequisite for gravity fingering.