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Networks and Heterogeneous Media

2009, Volume 4, Issue 4: 625-647. doi: 10.3934/nhm.2009.4.625
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Kinetic models for polymers with inertial effects

  • 1.
    3-Université de Toulouse (UPS, INSA, UT1, UTM) & CNRS, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne, F-31062 Toulouse
  • 2.
    Department of Mathematics, Iowa State University, Ames, IA 50011
  • Received: 01 January 2009 Revised: 01 September 2009

  • Primary: 76A05, 82A51, 82D60; Secondary: 82A40.

  • Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function f(t,x,n,n˙) for a polymer molecule positioned at x to be oriented along direction n while embedded in a n˙ environment created by inertial effects. It is shown that the probability distribution function of the extended model, when converging, will lead to well accepted kinetic models when inertial effects are ignored such as the Doi models for rod like polymers, and the Finitely Extensible Non-linear Elastic (FENE) models for Dumbbell like polymers.

    Citation: Pierre Degond, Hailiang Liu. Kinetic models for polymers with inertial effects[J]. Networks and Heterogeneous Media, 2009, 4(4): 625-647. doi: 10.3934/nhm.2009.4.625

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  • Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function f(t,x,n,n˙) for a polymer molecule positioned at x to be oriented along direction n while embedded in a n˙ environment created by inertial effects. It is shown that the probability distribution function of the extended model, when converging, will lead to well accepted kinetic models when inertial effects are ignored such as the Doi models for rod like polymers, and the Finitely Extensible Non-linear Elastic (FENE) models for Dumbbell like polymers.


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