Stability of a moving interface between two immiscible fluids of contrasting viscosities and densities is a classical problem in fluid mechanics. Further when a solid substrate is involved the problem becomes more complex with the addition of wettability of the solid surface with respect to the fluid combination. This is almost always the case when two fluids are involved such as in multi-phase flow in porous media such as soils. Being able to model the displacement of such interfaces has its uses in a myriad of applications ranging from hydrology to Carbon dioxide (CO2) sequestration, underground energy storage and nuclear waste disposal.
Numerical modeling of fingering type hydraulic instabilities during the imbibition process of a Fontainebleau sand sample (ref: SH Ommi, G Sciarra, P Kotronis A phase field model for partially saturated geomaterials describing fluid-fluid displacements. Part II : Stability analysis and two-dimensional simulations, Advances in Water Resources 164 (2022) 104201)
Contour plots of the saturation degree, the volumetric plastic strain and the deviatoric plastic strain of a heavily overconsolidated loamy soil under imbibition.