Phase field modeling in liquid binary mixtures: Isothermal and nonisothermal problems

Based on the conservative phase field model developed by Lowengrub and Truskinovsky [Proc. R. Soc. London A 454, 2617 (1998)] 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, the interfacial effects vanish, and the liquids become perfectly miscible. The free-energy density of the system depends not only on the phase field variable phi (which describes the system composition), but also on the reduced temperature r = (T-c - T )/T-c which measures the distance to the critical point described by T. The free energy suffers transformations through T-c in a way to permit a two-phase system in the subcritical (immiscible) regime and a monophase in the supercritical (miscible) regime. Numerical simulations in two spatial dimensions have been performed for isothermal problems (with r as control parameter) as well as for nonisothermal problems with the energy equation describing the temperature distribution. These simulations reveal the behavior of liquid mixtures and droplet coalescence placed in temperature gradients with temperatures continuously varying from T < T-c to T > T-c, problems that could be of large interest in phase transitions in micro- and nanofluidics.

Automated summary

This study proposes an extended scheme based on the phase field model to investigate immiscible/miscible liquids. The research finds that the liquids are immiscible below the critical temperature and perfectly miscible above it. Numerical simulations reveal the behavior of liquid mixtures and droplets in temperature gradients.