TY - JOUR
T1 - Phase field model of thermo-induced marangoni effects in the mixtures and its numerical simulations with mixed finite element method
AU - Sun, Pengtao
AU - Liu, Chun
AU - Xu, Jinchao
PY - 2009/11
Y1 - 2009/11
N2 - 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.
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.
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U2 - 10.4208/cicp.2009.v6.p1095
DO - 10.4208/cicp.2009.v6.p1095
M3 - Article
AN - SCOPUS:74349125040
SN - 1815-2406
VL - 6
SP - 1095
EP - 1117
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 5
ER -