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

¹ North China Institute of Aerospace Engineering - Langfang 065000, PRC
² National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26, Beijing 100088, PRC
³ State Key Laboratory for GeoMechanics and Deep Underground Engineering, SMCE, China University of Mining and Technology (Beijing) - Beijing 100083, PRC

^a Xu_Aiguo@iapcm.ac.cn
^b lyj@aphy.iphy.ac.cn

Received: 17 November 2011
Accepted: 5 January 2012

Abstract

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 κ_T but increases with increasing the viscosity η. The two relations can be fitted by t_SD=a+b/κ_T and t_SD=c+dη+(eη)³, respectively, where a, b, c, d and e are fitting parameters. For fixed Prandtl number Pr, when η is less than a critical value η_c, t_SD shows an inverse power-law relationship with η. However, when η>η_c, t_SD for Pr>1 shows qualitatively different behavior. From the evolution of the Péclet 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.