Skip to main content
Erschienen in: Meccanica 9/2014

01.09.2014 | New Trends in Fluid and Solid Mechanical Models

A phase-field model for quasi-incompressible solid–liquid transitions

verfasst von: Alessia Berti, Claudio Giorgi

Erschienen in: Meccanica | Ausgabe 9/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

According to a unified thermodynamic scheme, we derive the general kinetic equation ruling the phase-field evolution in a binary quasi-incompressible mixture for both transition and separation phenomena. When diffusion effects are negligible in comparison with source and production terms, a solid–liquid phase transition induced by temperature and pressure variations is obtained. In particular, we recover the explicit expression of the liquid–pressure curve separating the solid from the liquid stability regions in the pressure–temperature plane. Consistently with physical evidence, its slope is positive (negative) for substances which compress (expand) during the freezing process.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Berti A, Giorgi C (2009) A phase-field model for liquid–vapor transitions. J Non Equilib Thermodyn 34:219–247CrossRefMATHADS Berti A, Giorgi C (2009) A phase-field model for liquid–vapor transitions. J Non Equilib Thermodyn 34:219–247CrossRefMATHADS
2.
Zurück zum Zitat Berti A, Giorgi C (2013) Phase-field modeling of transition and separation phenomena in continuum thermodynamics. AAPP Phys Math Nat Sci 91(S1) Berti A, Giorgi C (2013) Phase-field modeling of transition and separation phenomena in continuum thermodynamics. AAPP Phys Math Nat Sci 91(S1)
3.
Zurück zum Zitat Berti A, Giorgi C, Morro A (2014) Mathematical modeling of phase transition and separation in fluids: a unified approach. Discrete Continuous Dyn Syst Ser B Berti A, Giorgi C, Morro A (2014) Mathematical modeling of phase transition and separation in fluids: a unified approach. Discrete Continuous Dyn Syst Ser B
4.
Zurück zum Zitat Berti A, Berti V, Grandi D (2011) Well-posedness of an isothermal diffusive model for binary mixtures of incompressible fluids. Nonlinearity 24:3143-3164CrossRefMATHMathSciNetADS Berti A, Berti V, Grandi D (2011) Well-posedness of an isothermal diffusive model for binary mixtures of incompressible fluids. Nonlinearity 24:3143-3164CrossRefMATHMathSciNetADS
5.
Zurück zum Zitat Berti V, Fabrizio M, Giorgi C (2007) Well-posedness for solid–liquid phase transitions with a fourth-order nonlinearity. Phys D 236:13–21CrossRefMATHMathSciNet Berti V, Fabrizio M, Giorgi C (2007) Well-posedness for solid–liquid phase transitions with a fourth-order nonlinearity. Phys D 236:13–21CrossRefMATHMathSciNet
6.
Zurück zum Zitat Brokate M, Sprekels J (1996) Hysteresis and phase transitions. Springer, New York Brokate M, Sprekels J (1996) Hysteresis and phase transitions. Springer, New York
7.
Zurück zum Zitat Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system I. Interfacial energy. J Chem Phys 28:258–267CrossRefADS Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system I. Interfacial energy. J Chem Phys 28:258–267CrossRefADS
8.
Zurück zum Zitat Fabrizio M, Giorgi C, Morro A (2006) A thermodynamic approach to non-isotermal phase-field evolution in continuum physics. Phys D 214:144–156CrossRefMATHMathSciNet Fabrizio M, Giorgi C, Morro A (2006) A thermodynamic approach to non-isotermal phase-field evolution in continuum physics. Phys D 214:144–156CrossRefMATHMathSciNet
9.
Zurück zum Zitat Fabrizio M, Giorgi C, Morro A (2011) Phase separation in quasi-incompressible Cahn–Hilliard fluids. Eur J Mech B Fluids 50:281–287CrossRefMathSciNet Fabrizio M, Giorgi C, Morro A (2011) Phase separation in quasi-incompressible Cahn–Hilliard fluids. Eur J Mech B Fluids 50:281–287CrossRefMathSciNet
10.
Zurück zum Zitat Fabrizio M (2008) Ice–water and liquid–vapor phase transitions by a Ginzburg–Landau model. J Math Phys 49:102902 Fabrizio M (2008) Ice–water and liquid–vapor phase transitions by a Ginzburg–Landau model. J Math Phys 49:102902
11.
Zurück zum Zitat Frémond M (2001) Non-smooth thermomechanics. Springer, New york Frémond M (2001) Non-smooth thermomechanics. Springer, New york
12.
Zurück zum Zitat Fried E, Gurtin ME (1993) Continuum theory of thermally induced phase transitions based on an order parameter. Phys D 68:326–343CrossRefMATHMathSciNet Fried E, Gurtin ME (1993) Continuum theory of thermally induced phase transitions based on an order parameter. Phys D 68:326–343CrossRefMATHMathSciNet
15.
Zurück zum Zitat Gurtin ME, Polignone D, Viñals J (1996) Two-phase binary fluids and immiscible fluids described by an order parameter. Math Model Methods Appl Sci 6:815–831CrossRefMATH Gurtin ME, Polignone D, Viñals J (1996) Two-phase binary fluids and immiscible fluids described by an order parameter. Math Model Methods Appl Sci 6:815–831CrossRefMATH
16.
Zurück zum Zitat Jones RAL (2002) Soft condensed matter. Oxford University Press, New York Jones RAL (2002) Soft condensed matter. Oxford University Press, New York
17.
Zurück zum Zitat Landau LD, Ginzburg VL (1965) On the theory of superconductivity. In: Collected papers of L.D. Landau. D. ter Haar (ed). Pergamon,Oxford Landau LD, Ginzburg VL (1965) On the theory of superconductivity. In: Collected papers of L.D. Landau. D. ter Haar (ed). Pergamon,Oxford
18.
Zurück zum Zitat Lowengrub J, Truskinovsky L (1998) Quasi-incompressible Cahn–Hilliard fluids and topological transitions. Proc R Soc Lond A 454:2617–2654CrossRefMATHMathSciNet Lowengrub J, Truskinovsky L (1998) Quasi-incompressible Cahn–Hilliard fluids and topological transitions. Proc R Soc Lond A 454:2617–2654CrossRefMATHMathSciNet
20.
Zurück zum Zitat Müller I (1985) Thermodynamics. Pitman, Boston Müller I (1985) Thermodynamics. Pitman, Boston
21.
Zurück zum Zitat Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Phys D 43:44–62CrossRefMATHMathSciNet Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Phys D 43:44–62CrossRefMATHMathSciNet
22.
Zurück zum Zitat Singer-Loginova I, Singer HM (2008) The phase-field technique for modeling multiphase materials. Rep Prog Phys 71:106501–106533CrossRefADS Singer-Loginova I, Singer HM (2008) The phase-field technique for modeling multiphase materials. Rep Prog Phys 71:106501–106533CrossRefADS
23.
Zurück zum Zitat Wang S-L, Sekerka RF, Wheeler AA, Murray BT, Coriell SR, Braun RJ, McFadden GB (1993) Thermodynamically-consistent phase-field models for solidification. Phys D 69:189–200CrossRefMATHMathSciNet Wang S-L, Sekerka RF, Wheeler AA, Murray BT, Coriell SR, Braun RJ, McFadden GB (1993) Thermodynamically-consistent phase-field models for solidification. Phys D 69:189–200CrossRefMATHMathSciNet
Metadaten
Titel
A phase-field model for quasi-incompressible solid–liquid transitions
verfasst von
Alessia Berti
Claudio Giorgi
Publikationsdatum
01.09.2014
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 9/2014
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-014-9909-x

Weitere Artikel der Ausgabe 9/2014

Meccanica 9/2014 Zur Ausgabe

New Trends in Fluid and Solid Mechanical Models

A unified approach to invariants of plane elasticity tensors

New Trends in Fluid and Solid Mechanical Models

“Cold convection” in porous layers salted from above

New Trends in Fluid and Solid Mechanical Models

Hele-Shaw flow with a small obstacle

New Trends in Fluid and Solid Mechanical Models

Kirchhoff plates with viscous boundary dissipation

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.