Phase-field simulation of two-phase micro-flows in a Hele-Shaw cell

A two-phase diffuse interface model previously developed by the authors is used to simulate the buoyancy-driven flow and Rayleigh-Taylor instability of fluid layers inside a Hele-Shaw cell. The model assumes that the two phases coexist inside the diffuse interface with different properties and velocities. A separate momentum equation is used to calculate the slip velocity between the two phases within the diffuse interface. This two-phase approach is coupled with a phase-field equation for calculating the interface motion. The model is validated by comparing the calculated interface evolution, before any topology changes occur, to available results from a sharp interface model. Then, the flows and interface topology changes are investigated for fluid layers with a large density and viscosity contrasts. 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 standard diffuse interface models that assume a single velocity inside the diffuse interface.