Phase-field modeling of transition and separation phenomena in continuum thermodynamics

In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type....
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Claudio Giorgi [verfasserIn] Alessia Berti [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch ; Italienisch

Erschienen:	2013

Übergeordnetes Werk:	In: Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali - Accademia Peloritana dei Pericolanti, 2005, 91(2013), S1, p A3
Übergeordnetes Werk:	volume:91 ; year:2013 ; number:S1, p A3

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.1478/AAPP.91S1A3

Katalog-ID:	DOAJ015789659

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520			\|a In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model.
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spelling	10.1478/AAPP.91S1A3 doi (DE-627)DOAJ015789659 (DE-599)DOAJe37750751da6445aa2662b07678ae267 DE-627 ger DE-627 rakwb eng ita Q1-390 Claudio Giorgi verfasserin aut Phase-field modeling of transition and separation phenomena in continuum thermodynamics 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model. Science (General) Alessia Berti verfasserin aut In Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali Accademia Peloritana dei Pericolanti, 2005 91(2013), S1, p A3 (DE-627)626608163 (DE-600)2555347-1 18251242 nnns volume:91 year:2013 number:S1, p A3 https://doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/article/e37750751da6445aa2662b07678ae267 kostenfrei http://dx.doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/toc/0365-0359 Journal toc kostenfrei https://doaj.org/toc/1825-1242 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 91 2013 S1, p A3
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allfieldsGer	10.1478/AAPP.91S1A3 doi (DE-627)DOAJ015789659 (DE-599)DOAJe37750751da6445aa2662b07678ae267 DE-627 ger DE-627 rakwb eng ita Q1-390 Claudio Giorgi verfasserin aut Phase-field modeling of transition and separation phenomena in continuum thermodynamics 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model. Science (General) Alessia Berti verfasserin aut In Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali Accademia Peloritana dei Pericolanti, 2005 91(2013), S1, p A3 (DE-627)626608163 (DE-600)2555347-1 18251242 nnns volume:91 year:2013 number:S1, p A3 https://doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/article/e37750751da6445aa2662b07678ae267 kostenfrei http://dx.doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/toc/0365-0359 Journal toc kostenfrei https://doaj.org/toc/1825-1242 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 91 2013 S1, p A3
allfieldsSound	10.1478/AAPP.91S1A3 doi (DE-627)DOAJ015789659 (DE-599)DOAJe37750751da6445aa2662b07678ae267 DE-627 ger DE-627 rakwb eng ita Q1-390 Claudio Giorgi verfasserin aut Phase-field modeling of transition and separation phenomena in continuum thermodynamics 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model. Science (General) Alessia Berti verfasserin aut In Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali Accademia Peloritana dei Pericolanti, 2005 91(2013), S1, p A3 (DE-627)626608163 (DE-600)2555347-1 18251242 nnns volume:91 year:2013 number:S1, p A3 https://doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/article/e37750751da6445aa2662b07678ae267 kostenfrei http://dx.doi.org/10.1478/AAPP.91S1A3 kostenfrei https://doaj.org/toc/0365-0359 Journal toc kostenfrei https://doaj.org/toc/1825-1242 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 91 2013 S1, p A3
language	English Italian
source	In Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali 91(2013), S1, p A3 volume:91 year:2013 number:S1, p A3
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title	Phase-field modeling of transition and separation phenomena in continuum thermodynamics
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title_auth	Phase-field modeling of transition and separation phenomena in continuum thermodynamics
abstract	In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model.
abstractGer	In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model.
abstract_unstemmed	In the framework of continuum thermodynamics a new approach to phase transition and separation phenomena is developed by emphasizing their nonlocal character. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. The second law of thermodynamics is satisfied by virtue of an extra entropy flux which arises from its nonlocal formulation. Such an extra flux is proved to be nonvanishing inside the transition layer, only. Different choices of the state variables distinguish transition form separation models. The former case involves the gradients of the main fields up to the second order, whereas in the latter all gradients up to the fourth order are needed and the total mass of the phase-field is conserved. In both cases, necessary and sufficient restrictions on the constitutive equations are derived from thermodynamics. On this background, some applications to scalar-valued models are developed. A simple model of the temperature-induced first-order transition is derived in connection with a state space involving second-order gradients. Dynamical models of phase separation in a binary fluid mixture are discussed and the classical nonisothermal Cahn-Hilliard system is obtained as a special case of a fourth-gradient model.
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title_short	Phase-field modeling of transition and separation phenomena in continuum thermodynamics
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Phase-field modeling of transition and separation phenomena in continuum thermodynamics

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