Lattice Boltzmann study of thermal phase separation: Effects of heat conduction, viscosity and Prandtl number

We investigate the effects of heat conduction, viscosity, and Prandtl number on thermal liquid-vapor separation via a lattice Boltzmann model for van der Waals fluids. The set of Minkowski measures on the density field enables to divide exactly the stages of the spinodal decomposition (SD) and domain growth. The duration t(SD) of the SD stage decreases with increasing the heat conductivity kappa(T) but increases with increasing the viscosity eta. The two relations can be fitted by t(SD) = a+ b/kappa(T) and t(SD) = c+ d eta +(e eta)(3), respectively, where a, b, c, d and e are fitting parameters. For fixed Prandtl number Pr, when eta is less than a critical value eta(c), t(SD) shows an inverse power-law relationship with eta. However, when eta > eta(c), t(SD) for Pr > 1 shows qualitatively different behavior. From the evolution of the Peclet number Pe, the separation procedure can also be divided into two stages. During the first stage, the convection effects become more dominant with time over those of the diffusivity, while they are reverse in the second stage. Copyright (C) EPLA, 2012