Volume 6, Issue 5
Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method

Pengtao Sun, Chun Liu & Jinchao Xu

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Commun. Comput. Phys., 6 (2009), pp. 1095-1117.

Published online: 2009-06

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  • Abstract

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 interface. We employ an energetic variational phase field model to describe its physical phenomena, and obtain the corresponding governing equations defined by a modified 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 domain. Under 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 flows. In 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.

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@Article{CiCP-6-1095, author = {}, title = {Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {5}, pages = {1095--1117}, abstract = {

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 interface. We employ an energetic variational phase field model to describe its physical phenomena, and obtain the corresponding governing equations defined by a modified 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 domain. Under 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 flows. In 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7718.html} }
TY - JOUR T1 - Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method JO - Communications in Computational Physics VL - 5 SP - 1095 EP - 1117 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7718.html KW - AB -

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 interface. We employ an energetic variational phase field model to describe its physical phenomena, and obtain the corresponding governing equations defined by a modified 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 domain. Under 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 flows. In 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.

Pengtao Sun, Chun Liu & Jinchao Xu. (2020). Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method. Communications in Computational Physics. 6 (5). 1095-1117. doi:
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