Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
---|---|---|
Article Number | 32 | |
Number of page(s) | 20 | |
Section | Mathematical methods | |
DOI | https://doi.org/10.1051/mmnp/2023036 | |
Published online | 30 November 2023 |
Thermodynamical Modeling of Multiphase Flow System with Surface Tension and Flow
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho, Toyonaka, Osaka, 560-8531, Japan
* Corresponding author: iti@sigmath.es.osaka-u.ac.jp
Received:
14
February
2023
Accepted:
20
October
2023
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow by our energetic variational and thermodynamic approaches. More precisely, we apply our energy densities, the first law of thermodynamics, and the law of conservation of total energy to derive our multiphase flow system with surface tension and flow. We study the conservative forms and conservation laws of our system by using the surface transport theorem and integration by parts. Moreover, we investigate the enthalpy, the entropy, the Helmholtz free energy, and the Gibbs free energy of our model by applying the thermodynamic identity. The key idea of deriving surface tension and viscosities is to make use of both the first law of thermodynamics and our energy densities.
Mathematics Subject Classification: 80M30 / 35Q79 / 76-10 / 80-10 / 35A15
Key words: Multiphase flow / surface flow / mathematical modeling / first law of thermodynamics / energetic variational approach
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.