Lattice Boltzmann study of thermal phase separation: Effects of heat conduction, viscosity and Prandtl number
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
Accepted: 5 January 2012
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 tSD of the SD stage decreases with increasing the heat conductivity κT but increases with increasing the viscosity η. The two relations can be fitted by tSD=a+b/κT and tSD=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 ηc, tSD shows an inverse power-law relationship with η. However, when η>ηc, tSD 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.
PACS: 47.11.-j – Computational methods in fluid dynamics / 47.20.Hw – Morphological instability; phase changes / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2012