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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10126187%21RIV13-GA0-11320___
rdf:type
n18:Vysledek skos:Concept
dcterms:description
We provide a thermodynamic basis for the development of models that are usually referred to as %22phase-field models%22 for compressible, incompressible, and quasi-incompressible fluids. Using the theory of mixtures as a starting point, we develop a framework within which we can derive %22phase-field models%22 both for mixtures of two constituents and for mixtures of arbitrarily many fluids. In order to obtain the constitutive equations, we appeal to the requirement that among all admissible constitutive relations that which is appropriate maximizes the rate of entropy production (see Rajagopal and Srinivasa in Proc R Soc Lond A 460:631-651, 2004). The procedure has the advantage that the theory is based on prescribing the constitutive equations for only two scalars: the entropy and the entropy production. Unlike the assumption made in the case of the Navier-Stokes-Fourier fluids, we suppose that the entropy is not only a function of the internal energy and the density but also of gradients of the partial densities or the concentration gradients. The form for the rate of entropy production is the same as that for the Navier-Stokes-Fourier fluid. As observed earlier in Heida and Malek (Int J Eng Sci 48(11):1313-1324, 2010), it turns out that the dependence of the rate of entropy production on the thermodynamical fluxes is crucial. The resulting equations are of the Cahn-Hilliard-Navier-Stokes type and can be expressed both in terms of density gradients or concentration gradients. As particular cases, we will obtain the Cahn-Hilliard-Navier-Stokes system as well as the Korteweg equation. Compared to earlier approaches, our methodology has the advantage that it directly takes into account the rate of entropy production and can take into consideration any constitutive assumption for the internal energy (or entropy). We provide a thermodynamic basis for the development of models that are usually referred to as %22phase-field models%22 for compressible, incompressible, and quasi-incompressible fluids. Using the theory of mixtures as a starting point, we develop a framework within which we can derive %22phase-field models%22 both for mixtures of two constituents and for mixtures of arbitrarily many fluids. In order to obtain the constitutive equations, we appeal to the requirement that among all admissible constitutive relations that which is appropriate maximizes the rate of entropy production (see Rajagopal and Srinivasa in Proc R Soc Lond A 460:631-651, 2004). The procedure has the advantage that the theory is based on prescribing the constitutive equations for only two scalars: the entropy and the entropy production. Unlike the assumption made in the case of the Navier-Stokes-Fourier fluids, we suppose that the entropy is not only a function of the internal energy and the density but also of gradients of the partial densities or the concentration gradients. The form for the rate of entropy production is the same as that for the Navier-Stokes-Fourier fluid. As observed earlier in Heida and Malek (Int J Eng Sci 48(11):1313-1324, 2010), it turns out that the dependence of the rate of entropy production on the thermodynamical fluxes is crucial. The resulting equations are of the Cahn-Hilliard-Navier-Stokes type and can be expressed both in terms of density gradients or concentration gradients. As particular cases, we will obtain the Cahn-Hilliard-Navier-Stokes system as well as the Korteweg equation. Compared to earlier approaches, our methodology has the advantage that it directly takes into account the rate of entropy production and can take into consideration any constitutive assumption for the internal energy (or entropy).
dcterms:title
On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework
skos:prefLabel
On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework
skos:notation
RIV/00216208:11320/12:10126187!RIV13-GA0-11320___
n18:predkladatel
n19:orjk%3A11320
n3:aktivita
n14:P
n3:aktivity
P(GA201/09/0917), P(LC06052)
n3:cisloPeriodika
63
n3:dodaniDat
n5:2013
n3:domaciTvurceVysledku
n20:1315595
n3:druhVysledku
n16:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n15:predkladatel
n3:idSjednocenehoVysledku
156379
n3:idVysledku
RIV/00216208:11320/12:10126187
n3:jazykVysledku
n12:eng
n3:klicovaSlova
Navier-Stokes-Fourier fluid, rate of entropy production; Cahn-Hilliard equations
n3:klicoveSlovo
n6:Cahn-Hilliard%20equations n6:Navier-Stokes-Fourier%20fluid n6:rate%20of%20entropy%20production
n3:kodStatuVydavatele
CH - Švýcarská konfederace
n3:kontrolniKodProRIV
[37345A9D34A5]
n3:nazevZdroje
Zeitschrift für Angewandte Mathematik und Physik
n3:obor
n7:BK
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n4:LC06052 n4:GA201%2F09%2F0917
n3:rokUplatneniVysledku
n5:2012
n3:svazekPeriodika
2012
n3:tvurceVysledku
Málek, Josef Heida, Martin Rajagopal, K. R.
n3:wos
000299505900007
s:issn
0044-2275
s:numberOfPages
24
n9:doi
10.1007/s00033-011-0139-y
n13:organizacniJednotka
11320