Canonical Distribution Functions in Polymer Dynamics: II. Liquid--Crystalline Polymers

TL;DR

This paper develops a systematic approach using the quasi--equilibrium approximation to derive constitutive equations for liquid--crystalline polymers from kinetic models, including numerical methods and accuracy measures.

Contribution

It introduces a systematic method to derive constitutive equations from kinetic models of liquid--crystalline polymers using the maximum entropy principle.

Findings

Derivation of constitutive equations from kinetic models.

Development of numerical implementation based on the quasi--equilibrium manifold.

Proposal of an accuracy measure for the approximation.

Abstract

The quasi--equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid--crystalline polymers. It is demonstrated how kinetic models of liquid--crystalline polymers can be approximated in a systematic way, how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom. The numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi--equilibrium manifold thus derived is developed and illustrated for particular examples. Finally, a measure of the accuracy of the quasi--equilibrium approximation is proposed that can be implemented into the numerical integration of the constitutive equation.