Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional
Date
2024-01-04
Authors
Journal Title
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Publisher
Physics of Fluids
Abstract
We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.
Description
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Antony N. Beris, Brian J. Edwards; Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional. Physics of Fluids 1 January 2024; 36 (1): 013102. https://doi.org/10.1063/5.0180407 and may be found at https://doi.org/10.1063/5.0180407. © 2024 Author(s). Published under an exclusive license by AIP Publishing.
Keywords
soft matter, hamiltonian mechanics, nonequilibrium thermodynamics, thermodynamic properties, calculus of variations, Navier Stokes equations
Citation
Antony N. Beris, Brian J. Edwards; Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional. Physics of Fluids 1 January 2024; 36 (1): 013102. https://doi.org/10.1063/5.0180407