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Non-isothermal phase-field models and evolution equation

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Języki publikacji
EN
Abstrakty
EN
Phase transitions between two phases are modelled as space regions where a phase field, or order parameter, changes smoothly. The literature shows a seeming contradiction in that some papers lead to the use of the reduced chemical potential through the temperature, others do not. The paper has a threefold purpose. First, to revise the arguments of known approaches and possibly generalize the associated schemes. Secondly, to show that a further approach is possible which involves the phase field as an internal variable. Thirdly, to contrast the various schemes and the corresponding results. It follows that differences arise because different fields enter the models and different forms are considered for the balance of energy and the second law of thermodynamics.
Rocznik
Strony
257--271
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • University of Genova, DIBE, VIA Opera Pia 11 a, 16145 Genova, Italy
Bibliografia
  • 1. L.D. LANDAU and V.L. GINZBURG, On the theory of superconductivity, [in:] Collected papers of L.D. Landau, D. ter HAAR [Ed.], 546-568, Pergamon, Oxford 1965.
  • 2. I. MULLER, Thermodynamics of mixtures and phase field theory, Int. J. Solids Structures, 38, 1105-1113, 2001.
  • 3. H.W. ALT and I. PAWLOW, A mathematical model of dynamics of non-isothermal phase separation, Physica D 59, 389-416, 1992.
  • 4. M. BROKATE and J. SPREKELS, Hysteresis and phase transitions, Springer, New York 1996.
  • 5. C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, [in:] Handbuch der Physik, S. FLOGGE, [Ed.], p. 513, Springer Berlin 1965.
  • 6. M.E. GURTIN, D. POLIGNONE and J. VINALS, Two-phase binary fluids and immiscible fluids described by an order parameter, Math, Models Methods Appl. Sci., 6, 815-831, 1996.
  • 7. W. KOSINSKI, Hyperbolic framework for thermoelastic materials, Arch. Mech., 50, 423-450,1998.
  • 8. K. SAXTON and R. SAXTON, Some effects of phase transition on heat propagation, Arch. Mech., 54, 635-646, 2002.
  • 9. G.A. RUDERMAN, D.S. STEWART and J.J.-I. YOH, A thermomechanical model for en-' ergetic materials with phase transformations, SIAM J. Appl. Math., 63, 510-537, 2002.
  • 10. S.R. DE GROOT and P. MAZUR, Non-equilibrium thermodynamics, Dover, New York 1984.
  • 11. D. JOU, J. CASAS-VAZQUEZ and G. LEBON, Extended irreversible thermodynamics, Springer, Berlin 2001.
  • 12. I. Muller, Thermodynamics, Pitman, London 1985.
  • 13. M. FABRIZIO, C. GIORGI and A. MORRO, A thermodynamic approach to non-isothermal » phase-field evolution in continuum physics, Physica D, 214, 144-156, 2006.
  • 14. M.E. GURTIN, Configurational forces as basic concepts of continuum physics, Springer, New York 2000.
  • 15. E. FRIED and M.E. GURTIN, Continuum theory of thermally induced phase transitions based on an order parameter, Physica D, 68, 326-343, 1993.
  • 16. E, BONETTI, P. COLLI and M. FREMOND, A phase field model with thermal memory governed by the entropy balance, Math. Mod. Meth, Appl. Sci., 13, 1565-1588, 2003.
  • 17. 0. PENROSE and P. FIFE, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D, 43, 44-62, 1990.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0004-0012
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