Conservative Allen–Cahn–Navier–Stokes system for incompressible two-phase fluid flows

A new phase-field model for immiscible incompressible two-phase liquid flows has been developed. The model consists of a conservative Allen–Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier–Stokes equation. Even though most phase-field methods for the multiphase flows preserve total mass, the bulk phase concentrations tend to shift from equilibrium concentration values of a double-well potential. The proposed model has a good feature which avoids mass spreading to the bulk phases. To validate the new system, the deformation of a drop from the initial circular shape in shear flow is presented and compared with other numerical results.