A two-phase diffuse-interface model for Hele–Shaw flows with large property contrasts

A novel two-phase diffuse-interface model is used to simulate flows inside a Hele–Shaw cell. The model assumes that the two phases coexist inside the diffuse interface, with different velocities and properties. A separate equation is used to calculate the slip velocity between the two phases inside the diffuse interface. It is shown that for one-dimensional flows parallel to the diffuse interface, the results are independent of the diffuse-interface width, regardless of the magnitude of the density and viscosity contrasts between the phases. This two-phase approach is coupled with a phase-field equation for calculating the interface motion. The model is applied to a buoyancy-driven two-phase flow involving a Rayleigh–Taylor instability and validated through a comparison with available sharp-interface results. The flows and interface topology changes are investigated for large density and viscosity contrasts between the phases. The convergence of the results with respect to the interface width is examined in detail. It is shown that the two-phase model converges better than a standard diffuse-interface model that assumes the presence of a single velocity inside the diffuse interface. Remaining interface width dependencies can be attributed to the capillary stress term in the momentum equation.