Next Article in Journal
Quantum Dynamics in a Fluctuating Environment
Previous Article in Journal
A Pseudo-Random Beamforming Technique for Improving Physical-Layer Security of MIMO Cellular Networks
Previous Article in Special Issue
Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems
Open AccessArticle

On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

1
Institute for Mathematics, Martin-Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germany
2
Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, PSF 4120, D-39016 Magdeburg, Germany
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1039; https://doi.org/10.3390/e21111039
Received: 24 September 2019 / Revised: 15 October 2019 / Accepted: 19 October 2019 / Published: 25 October 2019
(This article belongs to the Special Issue Second Law: Survey and Application)
Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point. View Full-Text
Keywords: Euler equations; phase transition; entropy principle; sharp interface; non-classical shock Euler equations; phase transition; entropy principle; sharp interface; non-classical shock
Show Figures

Figure 1

MDPI and ACS Style

Hantke, M.; Thein, F. On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations. Entropy 2019, 21, 1039.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop