Moving Cooling Source Induced Phase Separation in Binary Liquids: an interplay of competing velocities

We investigate phase separation dynamics in a binary mixture subjected to a moving cooling source from which cold temperature fronts propagate radially outward into the mixture. The motion of the source introduces two distinct velocity scales: $v_s$ associated with the translation of the source, and $v$ related to the propagation of the cooling thermal fronts. Competition between the two velocities determines how long a region of the fluid experiences a temperature change, which directly controls phase separation. A modified Cahn Hilliard Cook framework is employed, incorporating explicit coupling between the time-dependent temperature and concentration fields. Our numerical simulation results reveal that the evolving patterns and kinetics strongly depend on both the ratio and absolute magnitudes of these two competing velocities. Same value of $v_s/v$ yields distinctly different patterns for different $v$. The temperature profile delineating spatial regions with local temperatures above and below the demixing temperature controls the shape of the patterns formed. The rich parameter space enables one to engineer desired pattern structures by tuning the two velocities.