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Dissipative Fluids with Microstructure

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Rational Continua, Classical and New

Abstract

A variational principle is proposed which allows us to derive the equations of motion for a dissipative fluid with general microstructure. The only constitutive ingredients are the densities of the free energy and the dissipation, both subject to appropriate invariance requirements. The strict interplay between the microstructures considered here and those studied by Capriz is also examined in some detail.

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References

  1. Ericksen, J.L. (1961): Conservation laws for liquid crystals. Trans. Soc. Rheology 5, 23–34

    Article  MathSciNet  ADS  Google Scholar 

  2. Leslie, F.M. (1968): Some constitutive equations for liquid crystals. Arch. Rational Mech. Anal. 28, 265–283

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. de Gennes, P.G., Prost, J. (1993): The physics of liquid crystals. Second ed. Clarendon Press, Oxford

    Google Scholar 

  4. Hess, S. (1975): Irreversible thermodynamics of non-equilibrium alignment phenomena in molecular liquids and in liquid crystals. I; II. Z. Naturforsch. 30a, 728–738

    ADS  Google Scholar 

  5. Hess, S. (1975): Irreversible thermodynamics of non-equilibrium alignment phenomena in molecular liquids and in liquid crystals. I; II. Z. Naturforsch. 30a, 1224–1232

    ADS  Google Scholar 

  6. Sonnet, A.M., Maffettone, PL., Virga, E.G. (2002): Continuum theory for nematic liquid crystals with tensorial order. J. Non-Newton. Fluid Mech. To appear

    Google Scholar 

  7. Ericksen, J.L. (1990): Liquid crystals with variable degree of orientation. Arch. Rational Mech. Anal. 113, 97–120

    Article  MathSciNet  ADS  Google Scholar 

  8. Leslie, F.M. (1992): Continuum theory for nematic liquid crystals. Contin. Mech. Thermodyn. 4, 167–175

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Sonnet, A.M., Virga, E.G. (2001): Dynamics of dissipative ordered fluids. Phys. Rev. E 64, 031705

    Article  ADS  Google Scholar 

  10. Capriz, G. (1989): Continua with microstructure. Springer, New York

    Book  MATH  Google Scholar 

  11. Strutt, J.W.S. (Lord Rayleigh) (1873): Some general theorems relating to vibrations. Proc. London Math. Soc. 4, 357–368

    Article  MATH  Google Scholar 

  12. Whittaker, E.T. (1937): A treatise on the analytical dynamics of particles and rigid bodies. Fourth ed. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  13. Biot, M.A. (1955): Variational principles in irreversible thermodynamics with application to viscoelasticity. Phys. Rev. (2) 97, 1463–1469

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Lavenda, B.H. (1978): Thermodynamics of irreversible processes. Macmillan, London

    Google Scholar 

  15. Green, A.E., Rivlin, R.S. (1964): Multipolar continuum mechanics. Arch. Rational Mech. Anal. 17, 113–147

    Article  MathSciNet  ADS  MATH  Google Scholar 

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© 2003 Springer-Verlag Italia, Milano

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Sonnet, A.M., Virga, E.G. (2003). Dissipative Fluids with Microstructure. In: Podio-Guidugli, P., Brocato, M. (eds) Rational Continua, Classical and New. Springer, Milano. https://doi.org/10.1007/978-88-470-2231-7_13

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  • DOI: https://doi.org/10.1007/978-88-470-2231-7_13

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-2233-1

  • Online ISBN: 978-88-470-2231-7

  • eBook Packages: Springer Book Archive

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