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Mesoscopic continuum thermodynamics for mixtures of particles with orientation

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Abstract

The aim of the present paper is a continuum theoretical framework for mixtures of different chemical components, including the possibility of chemical reactions. The molecules are assumed to have an orientational degree of freedom, i.e. they are needle-shaped or planar. In the first case the microscopic director is the orientation of the particle long axis, in the second case it is the unit vector normal to the disc. This orientation is introduced as an additional variable in the domain of the field quantities. On this enlarged domain, the mesoscopic space, balance equations are derived. Compared to usual continuum theory, additional fluxes in orientation space occur. These are constitutive functions, like internal energy, heat flux and stress tensor. The restrictions on constitutive functions imposed by the second law of thermodynamics are derived by the method of Liu. Therefore, this new approach is very promising, since microscopic features of the particles, discarded in traditional continuous thermodynamics, become now an important part in the understanding of chemical systems. In addition, the results presented here can be extended to the study of other complex materials such as alloys, ferrofluids, carbon fibers, etc.

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Notes

  1. Materials consisting of spherical particles with interactions depending only on the inter-particle distances.

  2. In this category one includes the model presented in this text, polymers, alloys, nanoparticles, colloids, membranes, surfaces, and biological systems, among many others.

References

  1. C. Papenfuss, W. Muschik, in Applied Wave Mathematics, ed. by E. Quak, T. Soomere (Springer, Berlin, 2009), p. 85

    Google Scholar 

  2. W. Muschik, C. Papenfuss, H. Ehrentraut, Concepts of Continuum Thermodynamics (Kielce University of Technology, Kielce, 1996)

    Google Scholar 

  3. E. Cosserat, F. Cosserat, C. R. Acad. Sci. 145, 1139 (1907)

    Google Scholar 

  4. E. Cosserat, F. Cosserat, Théorie des Corps Déformable (Hermann, Paris, 1909)

    Google Scholar 

  5. A.C. Eringen, E.S. Suhubi, Int. J. Eng. Sci. 2, 189 (1964)

    Article  Google Scholar 

  6. A.C. Eringen, C.B. Kafadar, in Continuum Physics, ed. by A.C. Eringen (Academic Press, New York, 1976), p. 1

    Google Scholar 

  7. G. Capriz, Continua with Microstructure (Springer, Berlin, 1989)

    Book  Google Scholar 

  8. W. Muschik, H. Ehrentraut, C. Papenfuss, in Geometry, Continua, and Microstructure, ed. by G.A. Maugin (Hermann, Paris, 1999), p. 49

    Google Scholar 

  9. S. Blenk, H. Ehrentraut, W. Muschik, Phys. A 174, 119 (1991)

    Article  Google Scholar 

  10. S. Blenk, H. Ehrentraut, W. Muschik, Liq. Cryst. 14, 1221 (1993)

    Article  Google Scholar 

  11. W. Muschik, H. Ehrentraut, C. Papenfuss, J. Non-Equilib. Thermodyn. 25, 179 (2000)

    Article  CAS  Google Scholar 

  12. W. Muschik, C. Papenfuss, H. Ehrentraut, J. Non-Newton. Fluid Mech. 119, 91 (2004)

    Article  CAS  Google Scholar 

  13. W. Muschik, C. Papenfuss, Tech. Mech. 30, 252 (2010)

    Google Scholar 

  14. P. Ván, C. Papenfuss, W. Muschik, Phys. Rev. E 62, 6206 (2000)

    Article  Google Scholar 

  15. P. Ván, C. Papenfuss, W. Muschik, J. Phys. A Math. Gen. 37, 5315 (2004)

    Article  Google Scholar 

  16. C. Papenfuss, V. Ciancio, P. Rogolino, Tech. Mech. 22, 132 (2002)

    Google Scholar 

  17. K.-C. Chen, J. Non-Equilib. Thermodyn. 23, 255 (2008)

    Google Scholar 

  18. A. Palumbo, C. Papenfuss, P. Rogolino, J. Non-Equilib. Thermodyn. 30, 401 (2005)

    Article  CAS  Google Scholar 

  19. C. Papenfuss, Comput. Mater. Sci. 19, 45 (2000)

    Article  Google Scholar 

  20. C.A. Truesdell, Rational Thermodynamics, 2nd edn. (Springer, Berlin, 1984)

    Book  Google Scholar 

  21. S. Blenk, H. Ehrentraut, W. Muschik, J. Non-Equilib. Thermodyn. 16, 67 (1991)

    Article  CAS  Google Scholar 

  22. I. Müller, Arch. Ration. Mech. Anal. 26, 118 (1967)

    Article  Google Scholar 

  23. I. Müller, Arch. Ration. Mech. Anal. 28, 01 (1968)

    Article  Google Scholar 

  24. I. Müller, Thermodynamics (Pitman Publishing, Boston, 1985)

    Google Scholar 

  25. K. Hutter, K. Jöhnk, Continuum Methods of Physical Modeling (Springer, Berlin, 2010)

  26. M.C. Reis, Y. Wang, A.B.M.S. Bassi, Contin. Mech. Thermodyn. 26, 753 (2014)

    Article  CAS  Google Scholar 

  27. M.C. Reis, A.B.M.S. Bassi, J. Math. Chem. 52, 441 (2014)

    Article  CAS  Google Scholar 

  28. I.-S. Liu, Arch. Ration. Mech. Anal. 46, 131 (1972)

    Google Scholar 

  29. H. Eherntraut, W. Muschik, J. Non-Equilib. Thermodyn. 21, 175 (1996)

    Google Scholar 

  30. I.-S. Liu, Continuum Mechanics (Springer, Berlin, 2002)

    Book  Google Scholar 

  31. J.R. Carpenter, M.L. Timmermans, J. Phys. Oceanogr. 44, 289 (2014)

    Article  Google Scholar 

  32. D.E. O’Reilly, E.M. Peterson, J. Chem. Phys. 55, 2155 (1971)

    Article  Google Scholar 

  33. T.L. Hill, Proc. Nat. Acad. Sci. USA 72, 4918 (1975)

    Article  CAS  Google Scholar 

  34. W.B. Russel, Ann. Rev. Fluid Mech. 13, 425 (1981)

    Article  Google Scholar 

  35. J. Keizer, Chem. Rev. 87, 167 (1987)

    Article  CAS  Google Scholar 

  36. A. Von Jena, H.E. Lessing, Ber. Bunsenges. Phys. Chem. 83, 181 (1979)

    Article  Google Scholar 

  37. S. Weiss, Science 283, 1676 (1999)

    Article  CAS  Google Scholar 

  38. K.I. Morozov, J. Magn. Magn. Mater. 122, 98 (1993)

    Article  Google Scholar 

  39. D. Wang, U. Kreutzer, Y. Chung, T. Jue, Biophys. J. 73, 2764 (1997)

    Article  CAS  Google Scholar 

  40. Dor Ben-Amotz, J.M. Drake, J. Chem. Phys. 89, 1019 (1988)

    Article  CAS  Google Scholar 

  41. D. Shoup, G. Lipari, A. Szabo, Biophys. J. 36, 697 (1981)

    Article  CAS  Google Scholar 

  42. W. Muschik, C. Papenfuss, H. Ehrentraut, Proc. Estonian Acad. Sci. Phys. Math. 46, 94 (1997)

    CAS  Google Scholar 

  43. S. Blenk, W. Muschik, ZAMM 74, T331 (1994)

    Article  Google Scholar 

  44. P. Ván, Annalen der Physik 12, 142 (2003)

    Article  Google Scholar 

  45. V.A. Cimmelli, P. Ván, J. Math. Phys. 46, 112901 (2005)

    Article  Google Scholar 

  46. P. Ván, Contin. Mech. Thermodyn. 17, 165169 (2005)

    Article  Google Scholar 

Download references

Acknowledgements

The first author acknowledges financial support from the São Paulo Research Foundation, FAPESP (Grant 2016/08563-2).

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Authors and Affiliations

  1. Department of Physical Chemistry, Institute of Chemistry, University of Campinas, UNICAMP, Campinas, Brazil

    Caio César Ferreira Florindo & Adalberto Bono Maurizio Sacchi Bassi

  2. Department of Engineering 2, Hochschule für Technik und Wirtschaft Berlin (University of Applied Sciences), Berlin, Germany

    Christina Papenfuss

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  1. Caio César Ferreira Florindo
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  2. Christina Papenfuss
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  3. Adalberto Bono Maurizio Sacchi Bassi
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Correspondence to Caio César Ferreira Florindo.

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Florindo, C.C.F., Papenfuss, C. & Bassi, A.B.M.S. Mesoscopic continuum thermodynamics for mixtures of particles with orientation. J Math Chem 55, 1985–2003 (2017). https://doi.org/10.1007/s10910-017-0778-0

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