On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126186" target="_blank" >RIV/00216208:11320/12:10126186 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00033-011-0189-1" target="_blank" >http://dx.doi.org/10.1007/s00033-011-0189-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00033-011-0189-1" target="_blank" >10.1007/s00033-011-0189-1</a>

Result language
angličtina
Original language name
On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework
Original language description
Starting from a simplified framework of the theory of interacting continua in which the mass balance equations are considered for each constituent but the balance of linear momentum and the balance of energy are considered for the mixture as a whole, weprovide a thermodynamic basis for models that include the Allen-Cahn and Stefan equations as particular cases. We neglect the mass flux due to diffusion associated with the components of the mixture but permit the possibility of mass conversion of the phases. As a consequence of the analysis, we are able to show that the reaction (source) term in the mass balance equation leads to the Laplace operator that appears in the Allen-Cahn model and that this term is not related to a diffusive process. This study is complementary to that by Heida et al. (Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) 63, 145-169, 2012), where we neglected mass conversion of the species but considered mass diffusion effects and derived the constitutive
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BK - Liquid mechanics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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