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Canonical distribution functions in polymer dynamics. (I). Dilute solutions of flexible polymers

Author

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  • Ilg, Patrick
  • Karlin, Iliya V.
  • Öttinger, Hans Christian

Abstract

The quasi-equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how macroscopic and constitutive equations are derived therefrom and how these constitutive equations can be implemented numerically. In addition, a measure for the accuracy of the quasi-equilibrium approximation is proposed that can be evaluated while integrating the constitutive equations. In the example considered, it is confirmed that the accuracy of the approximation is increased by including more macroscopic variables. In steady elongational flow, it is found that more macroscopic variables need to be included above the coil-stretch transition to achieve the same accuracy as below.

Suggested Citation

  • Ilg, Patrick & Karlin, Iliya V. & Öttinger, Hans Christian, 2002. "Canonical distribution functions in polymer dynamics. (I). Dilute solutions of flexible polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 367-385.
    • Handle: RePEc:eee:phsmap:v:315:y:2002:i:3:p:367-385
    DOI: 10.1016/S0378-4371(02)01017-8
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    Citations

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    Cited by:

    1. Gorban, Alexander N. & Karlin, Iliya V., 2006. "Quasi-equilibrium closure hierarchies for the Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 325-364.
    2. Rienäcker, G. & Kröger, M. & Hess, S., 2002. "Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 537-568.
    3. Lelièvre, Tony & Samaey, Giovanni & Zieliński, Przemysław, 2020. "Analysis of a micro–macro acceleration method with minimum relative entropy moment matching," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3753-3801.
    4. Ilg, Patrick, 2008. "Macroscopic thermodynamics of flowing polymers derived from systematic coarse-graining procedure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6484-6496.

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