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A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method. (English) Zbl 1381.76351

Summary: This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular, we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

MSC:

76S05 Flows in porous media; filtration; seepage
76T10 Liquid-gas two-phase flows, bubbly flows
76M12 Finite volume methods applied to problems in fluid mechanics
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