Mass and Volume Conservation in Phase Field Models for Binary Fluids

作     者：Jie Shen Xiaofeng Yang Qi Wang 

作者机构：Department of MathematicsPurdue UniversityWest LafayetteIN 46907USA Department of Mathematics and NanoCenter at USCUniversity of South CarolinaColumbiaSC 29028USA School of MathematicsNankai UniversityTianjin 300071P.R.China Beijing Computational Science Research CenterBeijing 100084P.R.China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2013年第13卷第4期

页      面：1045-1065页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：partially supported by NSF grants DMS-0915066 and AFOSR FA9550-11-1-0328 partially supported by NSF grants DMS-0819051,DMS-0908330,SC EPSCOR award the USC startup fund partially supported by the ARO grant W911NF-09-1-0389 and the USC startup fund 

主　　题：Phase field model compressibility multiphase fluid flows spectral methods 

摘      要：The commonly used incompressible phase field models for non-reactive,binary fluids,in which the Cahn-Hilliard equation is used for the transport of phase variables(volume fractions),conserve the total volume of each phase as well as the material volume,but do not conserve the mass of the fluid mixture when densities of two components are *** this paper,we formulate the phase field theory for mixtures of two incompressible fluids,consistent with the quasi-compressible theory[28],to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid *** this formulation,the mass-average velocity is no longer divergence-free(solenoidal)when densities of two components in the mixture are not equal,making it a compressible model subject to an internal *** one formulation of the compressible models with internal constraints(model 2),energy dissipation can be clearly *** efficient numerical method is then devised to enforce this compressible internal *** simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model *** comparisons show that(a)predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin;and(b)predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing *** numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.