On the pitfalls of diffuse interface methods in problems involving non-material interfaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10494326" target="_blank" >RIV/00216208:11320/24:10494326 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Pa3.GNuS30" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Pa3.GNuS30</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2024.104725" target="_blank" >10.1016/j.ijnonlinmec.2024.104725</a>
Alternative languages
Result language
angličtina
Original language name
On the pitfalls of diffuse interface methods in problems involving non-material interfaces
Original language description
In this paper, we discuss the implications of applying traditional diffuse-interface techniques to problems involving mass flux across the interface such as the phase change front. In a simplified setting of stationary radial flow and linear viscous fluid, we confirm by analytical tools in the framework of Colombeau algebra that the numerical solutions to such problems approximate in fact modified physical problems that involve additional surface tension-like stress localized in the interfacial zone. The arising dynamical surface tension depends on the viscosity and density profiles within the interface. Expanding the setting to models of power-law fluids, we show that the dynamic surface tension vanishes in the limit of interfacial width going to zero for shear-thinning fluids. In contrast, for the shear-thickening case, the diffuse interface numerical solutions to the considered class of problems cannot be assigned any straightforward physical meaning, as the dynamic surface tension becomes unbounded with decreasing interfacial width and the traction jump in the limiting case cannot be even represented by any classical distribution. Consequently, our findings raise questions regarding the broad applicability of diffuse interface techniques in scenarios involving non-material interfaces, underscoring the necessity for further investigation.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA22-20388S" target="_blank" >GA22-20388S: Evolving Ice Shells - processes shaping planetary ice shells inferred from numerical modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Non-Linear Mechanics
ISSN
0020-7462
e-ISSN
1878-5638
Volume of the periodical
162
Issue of the periodical within the volume
June
Country of publishing house
GB - UNITED KINGDOM
Number of pages
15
Pages from-to
104725
UT code for WoS article
001298141100001
EID of the result in the Scopus database
2-s2.0-85190497365