Diffuse interface model for incompressible two-phase flows with large density ratios

Abstract

We investigate the applicability of an incompressible diffuse interface model for two-phase incompressible fluid flows with large viscosity and density contrasts. Diffuse-interface models have been used previously primarily for density-matched fluids, and it remains unclear to what extent such models can be used for fluids of different density, thereby potentially limiting the application of these models. In this paper, the convective Cahn–Hilliard equation and the condition that the velocity field is divergence-free are derived from the conservation law of mass of binary mixtures in a straightforward way, for fluids with large density and viscosity ratios. Differences in the equations of motion with a previously derived quasi-incompressible model are shown to result from the respective assumptions made regarding the relationship between the diffuse fluxes of two species. The convergence properties of the model are investigated for cases with large density ratio. Quantitative comparisons are made with results from previous studies to validate the model and its numerical implementation. Tests show that the variation in volume during the computation is of the order of machine accuracy, which is consistent with our use of a conservative discretization scheme (finite volume methods) for the Cahn–Hilliard equation. Results of the method are compared with previous work for the change in topology of rising bubbles and Rayleigh–Taylor instability. Additional results are presented for head-on droplet collision and the onset of droplet entrainment in stratified flows.