@Article{CiCP-6-1095,
author = {Pengtao Sun, Chun Liu and Jinchao Xu},
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 = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7718.html}
}