Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Method

作     者：Pengtao Sun Chun Liu Jinchao Xu 

作者机构：Department of Mathematical SciencesUniversity of NevadaLas Vegas4505 Maryland ParkwayLas VegasNV 89154USA Department of MathematicsThe Pennsylvania State UniversityUniversity ParkPA 16802USA 

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

年 卷 期：2009年第6卷第10期

页      面：1095-1117页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Pengtao Sun was supported in part by Research Development Award of University of Nevada Las Vegas 2220-320-980C Chun Liu was supported in part by National Science Foundation Grant DMS-0707594 Jinchao Xu was supported in part by National Science Foundation Grant DMS-0609727 and Alexander H.Humboldt Foundation This work was also supported by the Center for Computational Mathematics and Applications of Penn State 

主　　题：Phase field Navier-Stokes equations Marangoni effects temperature dependent surface tension mixed Taylor-Hood finite element Newton’s method 

摘      要：In this paper,we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the *** employ an energetic variational phase field model to describe its physical phenomena,and obtain the corresponding governing equations defined by a modi-fied Navier-Stokes equations coupled with phase field and energy transport.A mixed Taylor-Hood finite element discretization together with full Newton’s method are applied to this strongly nonlinear phase field model on a specific *** different boundary conditions of temperature,the resulting numerical solutions illustrate that the thermal energy plays a fundamental role in the interfacial dynamics of two-phase *** particular,it gives rise to a dynamic interfacial tension that depends on the direction of temperature gradient,determining the movement of the interface along a sine/cosine-like curve.