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In this paper we propose a mathematical model of phase separation for aquasi-incompressible binary mixture where the spinodal decomposition is inducedby an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phaseseparation is considered in the framework of phase field modeling so that thetransition is described by an additional field, the concentration c. Theevolution of concentration is described by the Cahn-Hilliard equation and inour model is coupled with the Navier-Stokes equation. Since thermal effect areincluded, the whole set of evolution equations is set up for the velocity, theconcentration, the temperature and the heat flux. The model is compatible withthermodynamics and a maximum theorem holds.

Phase separation in quasi incompressible fluids: Cahn-Hilliard model in the Cattaneo-Maxwell framework