Kinetic models for polymers with inertial effects

Pierre Degond; Hailiang Liu; Pierre Degond; Hailiang Liu

doi:10.3934/nhm.2009.4.625

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

Pierre Degond ^{1
,},
Hailiang Liu ^{2
,}

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 $f(t, x, n, \dot n)$ for a polymer molecule positioned at $x$ to be oriented along direction $n$ while embedded in a $\dot n$ 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.
- Polymers,
- kinetic description,
- Brownian forces,
- Rod like models,
- Dumbbell model
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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Abstract

Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function $f(t, x, n, \dot n)$ for a polymer molecule positioned at $x$ to be oriented along direction $n$ while embedded in a $\dot n$ 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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