Towards systematic approach to boundary conditions in mixture and multiphasic incompressible models: Maximum Entropy principle estimate

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00367597" target="_blank" >RIV/68407700:21340/23:00367597 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ijengsci.2023.103902" target="_blank" >https://doi.org/10.1016/j.ijengsci.2023.103902</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijengsci.2023.103902" target="_blank" >10.1016/j.ijengsci.2023.103902</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Towards systematic approach to boundary conditions in mixture and multiphasic incompressible models: Maximum Entropy principle estimate

Popis výsledku v původním jazyce

The single continuum model formulation, no matter how complex the considered constitutive relations are, cannot describe important phenomena stemming from constituents' interactions. In contrast, mixture theory is a successful framework for providing thermodynamically con-sistent governing equations in the bulk allowing for the inclusion of details in the material structure and interactions. Despite its ubiquitous applications, a fundamental open problem, a framework for the assessment of boundary conditions, persisted.Our objective is to relate these boundary conditions of mixtures to those of a single continuum and, hence, derive their possible form. To obtain such an estimation, we suggest using the Maximum Entropy (MaxEnt) principle yielding the least biased estimate (when measured by the entropy) of the values of the state variables on the more detailed level based on the knowledge of the state on the less detailed level. In the case of mixtures, the total mixture quantities represent the less detailed description, whereas the quantities related to each phase of the mixture represent the more detailed level, and the mapping (projection) connecting the two levels usually follows from the conservation of total mixture quantities. Therefore, once we have entropy on the detailed level and the aforementioned projection, from the MaxEnt principle, we get the least biased estimate of the decomposition of the total mixture state variables into variables corresponding to each constituent.These estimates can be used to obtain the interfacial conditions between two mixtures: we consider the decomposition of the total mixture quantities to partial quantities on both sides of the interface independently and match the mixture quantities at the interface using classical boundary conditions for a single phase. In this way, we may connect the well-developed theory for single continuum boundary conditions to the boundary conditions in mixtures. The generality of such an approach

Název v anglickém jazyce

Towards systematic approach to boundary conditions in mixture and multiphasic incompressible models: Maximum Entropy principle estimate

Popis výsledku anglicky

The single continuum model formulation, no matter how complex the considered constitutive relations are, cannot describe important phenomena stemming from constituents' interactions. In contrast, mixture theory is a successful framework for providing thermodynamically con-sistent governing equations in the bulk allowing for the inclusion of details in the material structure and interactions. Despite its ubiquitous applications, a fundamental open problem, a framework for the assessment of boundary conditions, persisted.Our objective is to relate these boundary conditions of mixtures to those of a single continuum and, hence, derive their possible form. To obtain such an estimation, we suggest using the Maximum Entropy (MaxEnt) principle yielding the least biased estimate (when measured by the entropy) of the values of the state variables on the more detailed level based on the knowledge of the state on the less detailed level. In the case of mixtures, the total mixture quantities represent the less detailed description, whereas the quantities related to each phase of the mixture represent the more detailed level, and the mapping (projection) connecting the two levels usually follows from the conservation of total mixture quantities. Therefore, once we have entropy on the detailed level and the aforementioned projection, from the MaxEnt principle, we get the least biased estimate of the decomposition of the total mixture state variables into variables corresponding to each constituent.These estimates can be used to obtain the interfacial conditions between two mixtures: we consider the decomposition of the total mixture quantities to partial quantities on both sides of the interface independently and match the mixture quantities at the interface using classical boundary conditions for a single phase. In this way, we may connect the well-developed theory for single continuum boundary conditions to the boundary conditions in mixtures. The generality of such an approach

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-22092S" target="_blank" >GA20-22092S: Víceškálová termodynamika: okrajové podmínky, integrace a aplikace</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

International Journal of Engineering Science

ISSN

0020-7225

e-ISSN

1879-2197

Svazek periodika

191

Číslo periodika v rámci svazku

103902

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

—

Kód UT WoS článku

001024479100001

EID výsledku v databázi Scopus

2-s2.0-85163441657