Multicomponent thermodynamics with instabilities and diffuse interfaces fluids

Vincent Giovangigli; Yoann Le Calvez; Guillaume Ribert; Vincent Giovangigli; Yoann Le Calvez; Guillaume Ribert

doi:10.3934/math.20241270

AIMS Mathematics

2024, Volume 9, Issue 9: 25979-26034. doi: 10.3934/math.20241270

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Multicomponent thermodynamics with instabilities and diffuse interfaces fluids

1.
CMAP, CNRS, École Polytechnique, 91128 Palaiseau, France
2.
CORIA, CNRS, Av. de l'Université, 76801 Saint-Etienne-du-Rouvray, France

Received: 30 March 2024 Revised: 05 June 2024 Accepted: 13 June 2024 Published: 06 September 2024
MSC : 80A17, 76B45, 35Q35

We investigated the mathematical structure of Gibbsian multicomponent thermodynamics with instabilities. We analyzed the construction of such thermodynamics from a pressure law using ideal gases as the low density limit. The fluid mixtures were allowed to have mechanically and chemically unstable states that were excluded in previous work on supercritical fluids, and the Soave-Redlich-Kwong cubic equation of state was specifically considered. We also investigated the mathematical structure of extended thermodynamics in the presence of cohesive forces—capillary effects—for a simplified diffuse interface fluid model. The thermodynamic formalism was validated by comparison with experimental data for mixtures of ethane and nitrogen. Very good agreement with experimental data was obtained for specific heats, multiphase equilibrium, and critical points, and we also analyzed the structure of strained jets of ethane.
- multicomponent thermodynamics,
- mathematical structure,
- extended thermodynamics,
- diffuse interface,
- strained flows
Citation: Vincent Giovangigli, Yoann Le Calvez, Guillaume Ribert. Multicomponent thermodynamics with instabilities and diffuse interfaces fluids[J]. AIMS Mathematics, 2024, 9(9): 25979-26034. doi: 10.3934/math.20241270

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Abstract

We investigated the mathematical structure of Gibbsian multicomponent thermodynamics with instabilities. We analyzed the construction of such thermodynamics from a pressure law using ideal gases as the low density limit. The fluid mixtures were allowed to have mechanically and chemically unstable states that were excluded in previous work on supercritical fluids, and the Soave-Redlich-Kwong cubic equation of state was specifically considered. We also investigated the mathematical structure of extended thermodynamics in the presence of cohesive forces—capillary effects—for a simplified diffuse interface fluid model. The thermodynamic formalism was validated by comparison with experimental data for mixtures of ethane and nitrogen. Very good agreement with experimental data was obtained for specific heats, multiphase equilibrium, and critical points, and we also analyzed the structure of strained jets of ethane.

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