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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i1.40
pages 35-51


F. Chinesta
EADS Corporate International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, 44321 Nantes Cedex 3, France
Miroslav Grmela
Ecole Polytechnique de Montreal, C.P. 6079 suc. Centre-ville, Montreal, H3C 3A7, Quebec, Canada


Separation of scales becomes problematic in complex fluids. Some sort of multiscale analysis is inevitable. We show that a sufficiently general formulation of thermodynamics provides a unified framework for such analysis. Among the illustrations of the framework, we develop a basis for (i) an extension of the Simha-Somcynski equilibrium theory of polymeric fluids to a rheological theory and (ii) a new approach to the formulation of governing equations of direct molecular simulations of fluids subjected to flow and temperature gradients.


  1. Arnold, V. I., Mathematical Methods of Classical Mechanics.

  2. Beris, A. N. and Edwards, B. J., Thermodynamics of Flowing Systems.

  3. Edwards, B. J., Dressler, M., Grmela, M., and Ait-Kadi, A., Rheological models with microstructural constraints. DOI: 10.1007/s00397-002-0256-9

  4. Grmela, M., Particle and bracket formulations of kinetic equations.

  5. Grmela, M., Nonequilibrium extension of the Simha-Somcynski equilibrium theory of polymeric fluids.

  6. Grmela, M., Thermodynamical lift of the nonlinear Onsager-Casimir vector field.

  7. Grmela, M., Mesoscopic dynamics and thermodynamics: Applications in polymeric fluids. DOI: 10.1007/3-540-53996-4_37

  8. Grmela, M., Coupling between microscopic and macroscopic dynamics in NEMD. DOI: 10.1016/0375-9601(93)90542-8

  9. Grmela, M. and Ottinger, H. C., Dynamics and thermodynamics of complex fluids: General formulation. DOI: 10.1103/PhysRevE.56.6620

  10. Grmela, M., Complex fluids subjected to external influences. DOI: 10.1016/S0377-0257(00)00186-5

  11. Grmela, M., Reciprocity relations in thermodynamics. DOI: 10.1016/S0378-4371(02)00564-2

  12. Grmela, M., Geometry of mesoscopic dynamics and thermodynamics. DOI: 10.1016/j.jnnfm.2003.11.009

  13. Grmela, M., Extensions of classical hydrodynamics. DOI: 10.1007/s10955-008-9558-3

  14. Grmela, M., Contact geometry of nonequilibrium thermodynamics.

  15. Grmela, M., Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering. DOI: 10.1016/S0065-2377(10)39002-8

  16. Henderson, D., Hole theory of liquids and dense gases. I equation of state. DOI: 10.1063/1.1701387

  17. Kaufman, A. N., Dissipative Hamiltonian systems: A unifying principle. DOI: 10.1016/0375-9601(84)90634-0

  18. Marsden, J. E. and Weinstein, A., Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids. DOI: 10.1016/0167-2789(83)90134-3

  19. Morrison, P. J., Bracket formulation for irreversible classical fields. DOI: 10.1016/0375-9601(84)90635-2

  20. Ottinger, H. C. and Grmela, M., Dynamics and thermodynamics of complex fluids: Illustration of the general formalism. DOI: 10.1103/PhysRevE.56.6633

  21. Ottinger, H. C., Beyond Equilibrium Thermodynamics.

  22. Sarti, G. C. and Marrucci, G., Thermomechanics of dilute polymer solutions: Multiple bead-spring model. DOI: 10.1016/0009-2509(73)80008-9

  23. Simha, R. and Somcynski, T., On the statistical thermodynamics of spherical and chain molecule fluids. DOI: 10.1021/ma60010a005

  24. Utracki, L. A. and Simha, R., Free volume and viscosity of polymer-compressed gas mixtures during extrusion foaming. DOI: 10.1002/1099-0488(20010201)39:3<342::AID-POLB1007>3.0.CO;2-Y

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