Integrable extended van der Waals model

Giglio, Francesco, Landolfi, Giulio and Moro, Antonio (2016) Integrable extended van der Waals model. Physica D: Nonlinear Phenomena, 333. pp. 293-300. ISSN 0167-2789

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Inspired by the recent developments in the study of the thermodynamics of van der Waals fluids via the theory of nonlinear conservation laws and the description of phase transitions in terms of classical (dissipative) shock waves, we propose a novel approach to the construction of multi-parameter generalisations of the van der Waals model. The theory of integrable nonlinear conservation laws still represents the inspiring framework. Starting from a macroscopic approach, a four parameter family of integrable extended van der Waals models is indeed constructed in such a way that the equation of state is a solution to an integrable nonlinear conservation law linearisable by a Cole–Hopf transformation. This family is further specified by the request that, in regime of high temperature, far from the critical region, the extended model reproduces asymptotically the standard van der Waals equation of state. We provide a detailed comparison of our extended model with two notable empirical models such as Peng–Robinson and Soave’s modification of the Redlich–Kwong equations of state. We show that our extended van der Waals equation of state is compatible with both empirical models for a suitable choice of the free parameters and can be viewed as a master interpolating equation. The present approach also suggests that further generalisations can be obtained by including the class of dispersive and viscous-dispersive nonlinear conservation laws and could lead to a new type of thermodynamic phase transitions associated to nonclassical and dispersive shock waves.

Item Type: Article
Additional Information: Funding information: F.G. has been partially supported by the Department of Mathematics and Physics Ennio de Giorgi of the University of Salento through a special young student training program. G.L has been partially supported by PRIN 2010 — MIURTeorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite (Grant number 2010JJ4KPA_003). A.M. has been partially supported by Progetto giovani GNFM-INdAM 2014 “Aspetti geometrici e analitici dei sistemi integrabili”.
Uncontrolled Keywords: van der Waals model, nonlinear conservation laws, integrability
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Dr Antonio Moro
Date Deposited: 06 Jun 2016 08:48
Last Modified: 04 Oct 2021 10:45

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