Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression

A numerical framework for modelling micro-scale multiphase flows with sharp interfaces has been developed. The suggested methodology is targeting the efficient and yet rigorous simulation of complex interface motion at capillary dominated flows (low capillary number). Such flows are encountered in various configurations ranging from micro-devices to naturally occurring porous media. The methodology uses as a basis the Volume-of-Fluid (VoF) method combined with additional sharpening smoothing and filtering algorithms for the interface capturing. These algorithms help the minimisation of the parasitic currents present in flow simulations, when viscous forces and surface tension dominate inertial forces, like in porous media. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation, which allows larger time steps at low capillary numbers to be utilised. In addition, an adaptive interface compression scheme is introduced for the first time in order to allow for a dynamic estimation of the compressive velocity only at the areas of interest and thus has the advantage of avoiding the use of a-priori defined parameters. The adaptive method is found to increase the numerical accuracy and to reduce the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model is verified against five different benchmark test cases. Moreover, numerical results are compared against analytical solutions as well as available experimental data, which reveal improved solutions relative to the standard VoF solver.