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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F14%3A10284148%21RIV15-MSM-11320___
rdf:type
skos:Concept n19:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1007/s00707-013-1038-4
dcterms:description
A theory describing the behavior of chemically non-reacting binary mixtures can be based on a detailed formulation of the governing equations for the individual components of the mixture or on treating the mixture as a single homogenized continuous medium. We argue that if we accept that both approaches can be used to describe the behavior of the given mixture, then the requirement on the equivalence of these approaches places restrictions on the possible structure of the internal energy, entropy, Helmholtz potential, and also of the diffusive, energy, and entropy fluxes. (The equivalence of the approaches is understood in the sense that the quantities used in one approach can be interpreted in terms of the quantities used in the other approach and vice versa. Further, both approaches must lead to the same predictions concerning the evolution of the physical system under consideration). In the case of a general chemically non-reacting binary mixture of components at the same temperature, we show that these restrictions can indeed be obtained by purely algebraic manipulations. An important outcome of this analysis is, for example, a general form of the evolution equation for the diffusive flux. The restrictions can be further exploited in the specification of thermodynamically consistent constitutive relations for quantities such as the interaction (drag) force or the Cauchy stress tensor. As an example of the application of the current framework, we derive, among others, a generalization of Fick's law and we recover several non-trivial results obtained by other techniques. The qualitative features of the derived generalization of Fick's law are demonstrated by a numerical experiment. A theory describing the behavior of chemically non-reacting binary mixtures can be based on a detailed formulation of the governing equations for the individual components of the mixture or on treating the mixture as a single homogenized continuous medium. We argue that if we accept that both approaches can be used to describe the behavior of the given mixture, then the requirement on the equivalence of these approaches places restrictions on the possible structure of the internal energy, entropy, Helmholtz potential, and also of the diffusive, energy, and entropy fluxes. (The equivalence of the approaches is understood in the sense that the quantities used in one approach can be interpreted in terms of the quantities used in the other approach and vice versa. Further, both approaches must lead to the same predictions concerning the evolution of the physical system under consideration). In the case of a general chemically non-reacting binary mixture of components at the same temperature, we show that these restrictions can indeed be obtained by purely algebraic manipulations. An important outcome of this analysis is, for example, a general form of the evolution equation for the diffusive flux. The restrictions can be further exploited in the specification of thermodynamically consistent constitutive relations for quantities such as the interaction (drag) force or the Cauchy stress tensor. As an example of the application of the current framework, we derive, among others, a generalization of Fick's law and we recover several non-trivial results obtained by other techniques. The qualitative features of the derived generalization of Fick's law are demonstrated by a numerical experiment.
dcterms:title
On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures
skos:prefLabel
On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures
skos:notation
RIV/00216208:11320/14:10284148!RIV15-MSM-11320___
n3:aktivita
n5:I n5:P
n3:aktivity
I, P(LL1202)
n3:cisloPeriodika
11
n3:dodaniDat
n16:2015
n3:domaciTvurceVysledku
n14:1315595 n14:2071681 n14:6433448
n3:druhVysledku
n9:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n4:predkladatel
n3:idSjednocenehoVysledku
34469
n3:idVysledku
RIV/00216208:11320/14:10284148
n3:jazykVysledku
n13:eng
n3:klicovaSlova
continua; diffusion; complex fluids; boundary-conditions
n3:klicoveSlovo
n11:diffusion n11:boundary-conditions n11:complex%20fluids n11:continua
n3:kodStatuVydavatele
AT - Rakouská republika
n3:kontrolniKodProRIV
[2915309A06CF]
n3:nazevZdroje
Acta Mechanica
n3:obor
n7:BJ
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
4
n3:projekt
n15:LL1202
n3:rokUplatneniVysledku
n16:2014
n3:svazekPeriodika
225
n3:tvurceVysledku
Průša, Vít Málek, Josef Rajagopal, K. R. Souček, Ondřej
n3:wos
000343904300011
s:issn
0001-5970
s:numberOfPages
30
n10:doi
10.1007/s00707-013-1038-4
n18:organizacniJednotka
11320