Liquid Mixture Convection during Phase Separation in a Temperature Gradient

We simulate the phase separation of a low-viscosity binary mixture, assuming that the fluid system is confined between two walls that are cooled down to different temperatures below the critical point of the mixture, corresponding to quenches within the unstable range of its phase diagram. Spinodal decomposition patterns for critical and off-critical mixtures are studied numerically in 2D in the creeping flow limit and for large Lewis number, together with their dependence on the fluidity coefficient. For off-critical mixtures, our numerical results reproduce the large-scale unidirectional migration of phase separating droplets that was observed experimentally by Califano et al. (Phys.of Fluids 17, 094109 (2005)), who measured typical speeds that are quite larger than the Marangoni velocity. To understand this finding, we then studied the temperature-gradient-induced motion of an isolated droplet of the minority phase embedded in a continuous phase, showing that when the drop is near local equilibrium, its speed is of the same order as the Marangoni velocity, i.e.~it is proportional to the unperturbed temperature gradient and the fluidity coefficient. However, far from local equilibrium, i.e.~for very large unperturbed temperature gradients, the drop first accelerates to a speed that is larger than the Marangoni velocity, then, later, it decelerates, exhibiting an increase-decrease behavior, as described by Yin et al. (Phys.of Fluids 20, 082101 (2008)). Such behavior is due to the large non-equilibrium, Korteweg-driven convection, which at first accelerates the droplets to relatively large velocities, and then tends to induce an approximately uniform inside temperature distribution, so that the drop experiences an effective temperature gradient that is much smaller than the unperturbed one, and consequently decelerates.