Abstract
Based on the conservative phase field model of Lowengrub and Truskinovsky for almost incompressible liquid binary mixtures, we propose an extended scheme for studying immiscible/miscible liquids. Below a critical temperature ${T}_{c}$, the liquids are immiscible with separating interfaces. Above ${T}_{c}$ interfacial effects vanish and the liquids become perfectly miscible. The free energy density of the system depends not only on the system composition through the phase field $\ensuremath{\phi}$ but also on the reduced temperature $r=({T}_{c}\ensuremath{-}T)/{T}_{c}$. The free energy transforms through ${T}_{c}$ to permit a two-phase system in the subcritical (immiscible) regime and a mono phase in the supercritical (miscible) regime.
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