| Several seemingly distinct formalisms have been developed recently as an alternative to the modern conventional approach for describing the mechanics and thermodynamics of complex fluids under dynamical conditions. Two of these approaches for isolated thermodynamic systems are the single generator Bracket Formalism and the more recent GENERIC Formalism incorporating a second generating functional. The interrelationships between these two alternate approaches are examined on an abstract level and direct connections are determined for some specific examples of fluid systems: a compressible, nonisothermal, isotropic fluid, an arbitrary fluid with an unspecified internal variable, and a chemically reactive fluid system. In so doing, new physical insight is obtained regarding the thermodynamic origins of key elements of each formalism. For purely macroscopic systems, it is shown that the GENERIC degeneracy condition on the dissipative metric matrix ensures global energy conservation, produces a symmetric metric matrix, and allows this matrix to be split into purely thermodynamic and kinematical components for systems with linear dissipation. The last realization leads to the natural driving forces expressed in bracket form being constrained Volterra derivatives of the entropy functional with respect to the system variables. The use of this concept in the Bracket Formalism provides a symmetric, bilinear dissipation bracket without the need for an explicit energy correction term.
for LaTeX users @article{BJEdwards1998-23,
author = {B. J. Edwards},
title = {An Analysis of Single and Double Generator Thermodynamic Formalisms for the Macroscopic Description of Complex Fluids},
journal = {J. Non-Equilib. Thermodyn.},
volume = {23},
pages = {301-333},
year = {1998}
}
\bibitem{BJEdwards1998-23} B.J. Edwards,
An Analysis of Single and Double Generator Thermodynamic Formalisms for the Macroscopic Description of Complex Fluids,
J. Non-Equilib. Thermodyn. {\bf 23} (1998) 301-333.BJEdwards1998-23
B.J. Edwards
An Analysis of Single and Double Generator Thermodynamic Formalisms for the Macroscopic Description of Complex Fluids
J. Non-Equilib. Thermodyn.,23,1998,301-333 |
mk@mat.ethz.ch
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