On the pitfalls of diffuse interface methods in problems involving non-material interfaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the pitfalls of diffuse interface methods in problems involving non-material interfaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the pitfalls of diffuse interface methods in problems involving non-material interfaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-20388S" target="_blank" >GA22-20388S: Vývoj vnějších slupek ledových měsíců z pohledu numerického modelování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Non-Linear Mechanics

ISSN

0020-7462

e-ISSN

1878-5638

Svazek periodika

162

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

104725

Kód UT WoS článku

001298141100001

EID výsledku v databázi Scopus

2-s2.0-85190497365