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Report on the workshop on rheology and thermodynamics École Polytechnique of Montreal August 14–16, 1996
Journalof l~on~Ncwtonian Fluid Mechanics ELSEVIER
J. Non-Newtonian Fluid Mech., 69 (1997) 105-107
Workshop Report
Report on the workshop on rheology and thermodynamics Ecole Polytechnique of Montreal August 14-16, 1996
1. Introduction
Substantial interest has been developed over the past few years on the influence of thermodynamics on rheology as documented by several articles (e.g.A.I. Leonov, Rheol. Acta 15, 85 (1976), 21, 683 (1982); M. Grmela, Physica D, 21, 179 (1986), Phys. Letters A, 130, 81 (1988) Phys. Rev. E, 47, 351 (1993); G.A. Maugin and R. Drouot, Int. J. Eng. Sci. 21, 705 (1983)), review articles (e.g.M. Grmela in 'Rheological Modelling: Thermodynamical and Statistical Approaches', Lecture Notes in Physics edited by J. Casas-Vazquez and D. Jou, Vol. 381, 99 (1991); R.J.J. Jongschaap, Rep. Progr. Phys. 53, 1 (1990)) and books (e.g.A.N. Beris and B.J. Edwards, 'Thermodynamics of Flowing Systems', Oxford (1994); D. Jou, J. Casas-Vazquez and G. Lebon, 'Extended Irreversible Thermodynamics', Springer (1993), I. Miiller and T. Ruggeri, 'Extended Thermodynamics', Springer (1993); B.C. Eu, Kinetic Theory and Irreversible Thermodynamics', Wiley (1992); S. Sieniutycz, 'Conservation Laws in Variational Thermodynamics', Kluwer (1994)) that have appeared on this and closely related subjects. This influence becomes more important when multiple transport phenomena need to be considered together, especially in the presence of temperature variations. However, so far, no significant effort has been developed to reconcile the various approaches that have, more or less independently, been developed to obtain the governing equations. With the opportunity of the recent international congress of rheology which attracted several of the key investigators into the Quebec region, I undertook the initiative and organized an informal workshop on Rheology and Thermodynamics in the l~cole Polytechnique of Montreal which took place between August 14 and 16, 1996. Scope of the workshop has been to address the interrelationship of the various approaches, to identify recent successes in applications and outline the challenges and opportunities of the future. About 20 scientists together with graduate students from the l~cole Polytechnique and McGill University participated (see the list of participants below).
037%0257/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 7 - 0 2 5 7 ( 9 6 ) 0 1 530-3
106
Workshop Report
2. Topics of discussion
A rheological model is said to be compatible with thermodynamics if predictions based on the model agree with results of the observations constituting the basis of equilibrium thermodynamics. The question arises as to what are the features of the governing equations of the rheological models that guarantee their compatibility with thermodynamics. This question, often in a somewhat different context, has been studied, amongst others, by Clausius (Clausius inequality), Boltzmann (Boltzmann's H-theorem), Onsager and Casimir (Onsager-Casimir reciprocity relations), in linear irreversible thermodynamics, rational thermodynamics and extended irreversible thermodynamics. Recently, it has been argued that an analysis of the compatibility of rheological models with thermodynamics (in the form of the so called Poisson bracket formulations or the Matrix Model) provide a general structure that can serve as a pivotal point, about which the translation of a physical insight into the governing equations is organized. The first day of the workshop was devoted to discussing recent advances in nonequilibrium thermodynamics (in particular, recent formulations of the Clausius inequality, extended irreversible thermodynamics, internal-state-variable thermodynamics, Lagrangian formulations). The role of the compatibility with thermodynamics in rheological modeling was the subject of discussions in the second day (in particular, the Hamiltonian--Poisson Bracket--dissipation bracket formulations and the Matrix Model). Connections with molecular simulations and numerical rheology were explored in the third day.
3. Conclusions from discussions
The compatibility of dynamics with thermodynamics is one of the fundamental problems of nonequilibrium statistical mechanics. Closely related to this problem are the problems of the emergence of irreversibility, pattern formation, and of other new features in macroscopic dynamics. At present, there still exists a wide range of views and approaches to these problems. Relations among some of them are known; in the most part, however, their relation remain unclear. The diversity of views was reflected in discussions at the Workshop. All participants agreed however that discussions at the Workshop and, in particular, discussions of the fundamental problems of nonequilibrium statistical mechanics in the context of more specific problems arising in rheology are very useful for both fundamental understanding and rheology. In particular, thermodynamic considerations become essential when non-isothermal effects are taken into account. It has to emphasized that in rheology, a new rheological model arises as a result of expressing a new physical insight into macromolecular dynamics in mathematical form. The objective of the compatibility-with-thermodynamics analysis is to provide a general setting for expressing a given physical insight in intrinsically consistent governing equations. The compatibility-withthermodynamics analysis does not replace the search for new physical insights but is complementary to it. It provides a guidance to the appropriate projections from microscopic to macroscopic levels of description as well as placing constraints on the type and form of dissipative processes, where most of the phenomenology is introduced. A similar situation arises in thermodynamics. In order to introduce a new thermodynamic equation of state, a physical
Workshop Report
107
insight into the specific nature of the system under consideration is needed. The insight has to be then expressed in an intrinsically consistent way. Here, general thermodynamics provides the setting. The compatibility-with-thermodynamics analysis plays thus the same role in dynamical theories as general thermodynamics plays in static (equilibrium) theories. After the Workshop, the majority of the participants continued to discuss rheology and thermodynamics in the context of the Symposium on Thermodynamic Approaches to Rheological Modeling and Simulation that took place as a part of the XIIth International Congress on Rheology (Quebec City, August 18-23). I would like to believe that the new contacts between researches in thermodynamics and rheology that were created on the Workshop and on the Symposium will lead to the advancement of our knowledge and will give rise to Workshops on the same subject in the future.
4. Acknowledgments I would like to express my gratitude to the Research Office, Department of Chemical Engineering and Polymer Institute (CRASP) of l~cole Polytechnique of Montreal for providing financial support for the workshop.
5. Participants A.N. Beris (Univ. of Delaware), P.J. Carreau (l~cole Polytechnique de Montr6al), J. CasasVazquez (Univ. Autonoma de Barcelona), C. Chan Man Fong (Univ. of Sherbrooke), B.Z. Dlugogorski (Univ. of Newcastle), R. Drouot (Univ. Pierre et Marie-Curie, Paris VI), B.J. Edwards (Univ. of Delaware), B.C. Eu (McGill Univ.), L.S. Garcia-Colin (Univ. Autonoma, Mexico), M. Grmela (l~cole Polytechnique de Montrdal), R.J.J. Jongschaap (Univ. of Twente, The Netherlands), D. Jou (Univ. Autonoma de Barcelona), H.C. Ottinger (ETH-Zfirich), N. Phan-Thien (Univ. of Sy.dney), A. Rey (McGill Univ.), S. Sieniutycz (Warsaw Tech. Univ.), graduate students from Ecole Polytechnique of Montreal and McGill Univ. Miroslav Grmela, l~cole Polytechnique of Montreal
J. Non-Newtonian Fluid Mech., 69 (1997) 105-107
Workshop Report
Report on the workshop on rheology and thermodynamics Ecole Polytechnique of Montreal August 14-16, 1996
1. Introduction
Substantial interest has been developed over the past few years on the influence of thermodynamics on rheology as documented by several articles (e.g.A.I. Leonov, Rheol. Acta 15, 85 (1976), 21, 683 (1982); M. Grmela, Physica D, 21, 179 (1986), Phys. Letters A, 130, 81 (1988) Phys. Rev. E, 47, 351 (1993); G.A. Maugin and R. Drouot, Int. J. Eng. Sci. 21, 705 (1983)), review articles (e.g.M. Grmela in 'Rheological Modelling: Thermodynamical and Statistical Approaches', Lecture Notes in Physics edited by J. Casas-Vazquez and D. Jou, Vol. 381, 99 (1991); R.J.J. Jongschaap, Rep. Progr. Phys. 53, 1 (1990)) and books (e.g.A.N. Beris and B.J. Edwards, 'Thermodynamics of Flowing Systems', Oxford (1994); D. Jou, J. Casas-Vazquez and G. Lebon, 'Extended Irreversible Thermodynamics', Springer (1993), I. Miiller and T. Ruggeri, 'Extended Thermodynamics', Springer (1993); B.C. Eu, Kinetic Theory and Irreversible Thermodynamics', Wiley (1992); S. Sieniutycz, 'Conservation Laws in Variational Thermodynamics', Kluwer (1994)) that have appeared on this and closely related subjects. This influence becomes more important when multiple transport phenomena need to be considered together, especially in the presence of temperature variations. However, so far, no significant effort has been developed to reconcile the various approaches that have, more or less independently, been developed to obtain the governing equations. With the opportunity of the recent international congress of rheology which attracted several of the key investigators into the Quebec region, I undertook the initiative and organized an informal workshop on Rheology and Thermodynamics in the l~cole Polytechnique of Montreal which took place between August 14 and 16, 1996. Scope of the workshop has been to address the interrelationship of the various approaches, to identify recent successes in applications and outline the challenges and opportunities of the future. About 20 scientists together with graduate students from the l~cole Polytechnique and McGill University participated (see the list of participants below).
037%0257/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 7 - 0 2 5 7 ( 9 6 ) 0 1 530-3
106
Workshop Report
2. Topics of discussion
A rheological model is said to be compatible with thermodynamics if predictions based on the model agree with results of the observations constituting the basis of equilibrium thermodynamics. The question arises as to what are the features of the governing equations of the rheological models that guarantee their compatibility with thermodynamics. This question, often in a somewhat different context, has been studied, amongst others, by Clausius (Clausius inequality), Boltzmann (Boltzmann's H-theorem), Onsager and Casimir (Onsager-Casimir reciprocity relations), in linear irreversible thermodynamics, rational thermodynamics and extended irreversible thermodynamics. Recently, it has been argued that an analysis of the compatibility of rheological models with thermodynamics (in the form of the so called Poisson bracket formulations or the Matrix Model) provide a general structure that can serve as a pivotal point, about which the translation of a physical insight into the governing equations is organized. The first day of the workshop was devoted to discussing recent advances in nonequilibrium thermodynamics (in particular, recent formulations of the Clausius inequality, extended irreversible thermodynamics, internal-state-variable thermodynamics, Lagrangian formulations). The role of the compatibility with thermodynamics in rheological modeling was the subject of discussions in the second day (in particular, the Hamiltonian--Poisson Bracket--dissipation bracket formulations and the Matrix Model). Connections with molecular simulations and numerical rheology were explored in the third day.
3. Conclusions from discussions
The compatibility of dynamics with thermodynamics is one of the fundamental problems of nonequilibrium statistical mechanics. Closely related to this problem are the problems of the emergence of irreversibility, pattern formation, and of other new features in macroscopic dynamics. At present, there still exists a wide range of views and approaches to these problems. Relations among some of them are known; in the most part, however, their relation remain unclear. The diversity of views was reflected in discussions at the Workshop. All participants agreed however that discussions at the Workshop and, in particular, discussions of the fundamental problems of nonequilibrium statistical mechanics in the context of more specific problems arising in rheology are very useful for both fundamental understanding and rheology. In particular, thermodynamic considerations become essential when non-isothermal effects are taken into account. It has to emphasized that in rheology, a new rheological model arises as a result of expressing a new physical insight into macromolecular dynamics in mathematical form. The objective of the compatibility-with-thermodynamics analysis is to provide a general setting for expressing a given physical insight in intrinsically consistent governing equations. The compatibility-withthermodynamics analysis does not replace the search for new physical insights but is complementary to it. It provides a guidance to the appropriate projections from microscopic to macroscopic levels of description as well as placing constraints on the type and form of dissipative processes, where most of the phenomenology is introduced. A similar situation arises in thermodynamics. In order to introduce a new thermodynamic equation of state, a physical
Workshop Report
107
insight into the specific nature of the system under consideration is needed. The insight has to be then expressed in an intrinsically consistent way. Here, general thermodynamics provides the setting. The compatibility-with-thermodynamics analysis plays thus the same role in dynamical theories as general thermodynamics plays in static (equilibrium) theories. After the Workshop, the majority of the participants continued to discuss rheology and thermodynamics in the context of the Symposium on Thermodynamic Approaches to Rheological Modeling and Simulation that took place as a part of the XIIth International Congress on Rheology (Quebec City, August 18-23). I would like to believe that the new contacts between researches in thermodynamics and rheology that were created on the Workshop and on the Symposium will lead to the advancement of our knowledge and will give rise to Workshops on the same subject in the future.
4. Acknowledgments I would like to express my gratitude to the Research Office, Department of Chemical Engineering and Polymer Institute (CRASP) of l~cole Polytechnique of Montreal for providing financial support for the workshop.
5. Participants A.N. Beris (Univ. of Delaware), P.J. Carreau (l~cole Polytechnique de Montr6al), J. CasasVazquez (Univ. Autonoma de Barcelona), C. Chan Man Fong (Univ. of Sherbrooke), B.Z. Dlugogorski (Univ. of Newcastle), R. Drouot (Univ. Pierre et Marie-Curie, Paris VI), B.J. Edwards (Univ. of Delaware), B.C. Eu (McGill Univ.), L.S. Garcia-Colin (Univ. Autonoma, Mexico), M. Grmela (l~cole Polytechnique de Montrdal), R.J.J. Jongschaap (Univ. of Twente, The Netherlands), D. Jou (Univ. Autonoma de Barcelona), H.C. Ottinger (ETH-Zfirich), N. Phan-Thien (Univ. of Sy.dney), A. Rey (McGill Univ.), S. Sieniutycz (Warsaw Tech. Univ.), graduate students from Ecole Polytechnique of Montreal and McGill Univ. Miroslav Grmela, l~cole Polytechnique of Montreal