Parametric study of the interface behavior between two immiscible liquids flowing through a porous medium

When two immiscible liquids that coexist inside a porous medium are drained through an opening, a complex flow takes place in which the interface between the liquids moves, tilts and bends. The interface profiles depend on the physical properties of the liquids and on the velocity at which they are extracted. If the drainage flow rate, the liquids volume fraction in the drainage flow and the physical properties of the liquids are known, the interface angle in the immediate vicinity of the outlet ($heta$) can be determined. In this work, we define four nondimensional parameters that rule the fluid dynamical problem and, by means of a numerical parametric analysis, an equation to predict $heta$ is developed. The equation is verified through several numerical assessments in which the parameters are modified simultaneously and arbitrarily. In addition, the qualitative influence of each nondimensional parameter on the interface shape is reported.