Dynamics of phase separation of sheared binary mixtures after a nonisothermal quenching

When a symmetric regular binary mixture, subjected to a constant shear, is quenched into the unsteady region of its phase diagram under a temperature gradient, it phase separates following very complicated patterns. The phase separation process is simulated using a thermodynamics-based phase-field model where the fundamental balance equations are coupled with the constitutive equations for the diffusive fluxes of chemical species, momentum, and energy by applying the rules of nonequilibrium thermodynamics. The evolution of phase separation shows distinct features, being more complex than a simple superposition of patterns emerging in a shear flow and under a thermal gradient when taken individually. The imposed temperature gradient causes a preferential nucleation at the cooler wall, so that the emerging droplets drift towards the center of the domain while following the imposed flow field, causing a change in droplet movement as they cross the domain centerline and enhancing coalescence. The imposed temperature gradient breaks the symmetry compared to instantaneous quenching, with stable droplets which remain attached to the cooler wall and move coherently with it. The capillary number (NCa) determines breakup and phase separation evolving as stripes for NCa≫1, while droplets nucleate and grow for NCa1. The Lewis number (NLe) affects the pace and propagation of phase separation: for NLe>10 phase separation takes place rather uniformly, being similar to instantaneous quenching, while for NLe<0.1 the mixture cools slowly and a phase separation front proceeds from the cooler wall. A similar behavior is induced by a composition-dependent thermal conductivity. The mixture dimensionless heat capacity (Nc) has a significant effect on phase separation because, for Nc1, heat dissipation counterbalances the effect of the applied temperature quench, thus retarding or even reversing the process of phase separation. These results and the variety of patterns reproduced by the model highlight the necessity of integrating a consistent thermodynamic description to the hydrodynamics and heat transport in phase-field modeling.