“…In the latter approach, on the other hand, the mass averaged velocity is assumed to satisfy the mass conservation instead of incompressibility, leading to a slightly compressible mixture inside the interfacial region. In [21], the authors derived a quasi-incompressible phase model which allows the mixture to be slightly compressible inside the interface, see also [1]; a similar quasi-incompressible model, which admits an energy law, was proposed recently in [26]. On the other hand, incompressible phase-field models were derived in [5,10,27,2].…”