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New constitutive equations derived from a kinetic model for melts and concentrated solutions of linear polymers

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Abstract

In this paper, new constitutive equations for linear entangled polymer solutions and melts are derived from a recently proposed kinetic model (Fang et al. 2004) by using five closure approximations available in the literature. The simplest closure approximation considered is that due to Peterlin (1966). In this case, a mean-field-type Fokker-Planck equation underlying the evolution equation for an equilibrium averaged polymer segment orientation tensor is shown to be consistent with the fluctuation-dissipation theorem (Kubo et al. 1985). We compare the performance of the five new constitutive equations in their capacity to faithfully reproduce the predictions of the modified encapsulated FENE dumbbell model of Fang et al. (2004) for a number of shear and extensional flows. Comparisons are also made with the experimental data of Kahvand (1995) and Bhattacharjee et al. (2002, 2003). In the case of the Hinch-Leal and Bingham closures (Hinch and Leal 1976; Chaubal and Leal 1998) a combination with the quadratic closure of Doi (1981) is found to be necessary for stability in fast flows. The Hinch-Leal closure approximation, modified in this way, is found to outperform the other closures and its mathematical description is considerably simpler than that of the Bingham closure.

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Acknowledgements

The authors would like to thank Massimiliano Grosso for his help on the application of the Bingham closure and pointing out some typing errors in the paper by Grosso et al. (2000a). The authors would also like to thank Markus Hütter for useful discussions on the subject of the fluctuation-dissipation theorem. The insights provided by the referees are acknowledged with gratitude.

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Author notes

  1. Robert G. Owens

    Present address: Département de mathématiques et de statistique, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal, QC, H3C 3J7, Canada

Authors and Affiliations

  1. Engineering and Environmental Geology Laboratory, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Jiannong Fang

  2. Fluid Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Robert G. Owens

Authors
  1. Jiannong Fang
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Correspondence to Jiannong Fang.

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Fang, J., Owens, R.G. New constitutive equations derived from a kinetic model for melts and concentrated solutions of linear polymers. Rheol Acta 44, 577–590 (2005). https://doi.org/10.1007/s00397-005-0440-9

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  • DOI: https://doi.org/10.1007/s00397-005-0440-9

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