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

DOI:

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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