A phase field model for liquid-vapour  phase transitions

Valeria Berti; Mauro Fabrizio; Diego Grandi

doi:10.3934/dcdss.2013.6.317

Article Contents

2013, Volume 6, Issue 2: 317-330. Doi: 10.3934/dcdss.2013.6.317

This issue Previous Article Free energies and pseudo-elastic transitions for shape memory alloys Next Article A well-posedness result for irreversible phase transitions with a nonlinear heat flux law

A phase field model for liquid-vapour phase transitions

1.
University of Bologna, Department of Mathemathics, I-40126, Bologna

Received: July 2011

Revised: November 2011

Published online: November 2012

Abstract / Introduction Related Papers Cited by

Abstract

We propose a model describing the liquid-vapour phase transition according to a phase-field method. A phase variable $φ$ is introduced whose equilibrium values $φ=0$ and $φ=1$ are associated with the liquid and vapour phases. The phase field obeys Ginzburg-Landau equation and enters the constitutive relation of the density, accounting for the sudden density jump occurring at the phase transition. In this paper we concern ourselves especially with the problems arising in the phase field approach due to the existence of the critical point in the coexistence line, which entails the merging of the phases described by $φ$.

Keywords:

Mathematics Subject Classification: 35Q56, 76T10, 82B27.

Citation:

Related Papers

Cited by

References

[1]	M. Fabrizio, Ice-water and liquid-vapour phase transitions by a Ginzburg-Landau model, Journal of Mathematical Physics, 49 (2008), 102902.doi: 10.1515/bfup.2008.027.
[2]	L. P. Kadanoff, et al., Static phenomena near critical points: Theory and experiment, Reviews of Modern Physics, 39 (1967), 395-431.
[3]	P. M. Chaikin and T. C. Lubensky, "Principles of Condensed Matter Physics," Cambridge University Press, 1995.doi: 10.1016/1053-8127(95)00142-B.
[4]	A. Berti and C. Giorgi, A phase-field model for liquid-vapor transitions, J. Non-Equilib. Thermodyn, 34 (2009), 219-247.
[5]	M. Fabrizio, Ginzburg-Landau equations and first and second order phase transitions, Int. J. Eng. Sci., 44 (2006), 529-539.
[6]	F. Fried and M. E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Physica D, 68 (1993), 326-343.
[7]	M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions," Springer, Berlin, 1996, chapter 4.
[8]	M. Fremond, "Non-smooth Thermomechanics," Springer, Berlin, 2001.
[9]	M. Fabrizio, C. Giorgi and A. Morro, A thermodynamic approach to ferromagnetism and phase transitions, Int J. Eng Sci., 47 (2009), 821-839.doi: 10.1080/14735780802696351.