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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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.

Original languageEnglish (US)
Pages (from-to)1095-1117
Number of pages23
JournalCommunications in Computational Physics
Volume6
Issue number5
DOIs
Publication statusPublished - Nov 1 2009

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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