Kinetic models for polymers with inertial effects

TL;DR

This paper introduces novel kinetic models for polymers that incorporate inertial effects, bridging the gap between classical models and more physically comprehensive descriptions, with convergence to established models when inertial effects are neglected.

Contribution

The paper derives new kinetic models for Dumbbell-like and rigid-rod polymers that include inertial effects, extending existing models to more accurately describe polymer dynamics.

Findings

Models converge to Doi models for rod-like polymers

Models converge to FENE models for Dumbbell-like polymers

Inertial effects are incorporated into kinetic descriptions

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.