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A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

Published online by Cambridge University Press:  04 February 2015

Z. Guo  and
P. Lin
Z. Guo
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
P. Lin*
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK
*
†Email address for correspondence: plin@maths.dundee.ac.uk
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Abstract

In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier–Stokes equations with additional stress term, Cahn–Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary convections in a two-layer fluid system and thermocapillary migration of a drop are computed using a continuous finite element method. The results are compared with the corresponding analytical solutions and the existing numerical results as validations for our model.

JFM classification

Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Thermocapillarity

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Papers
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Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 226 - 271
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© 2015 Cambridge University Press 

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