Derivation of a non-objective Oldroyd model from the Boltzmann equation

TL;DR

This paper derives a non-objective viscoelastic model from the Boltzmann equation, highlighting inertial effects in stress behavior, and provides exact solutions for specific flow types.

Contribution

It introduces a novel non-objective viscoelastic model derived from kinetic theory, accounting for inertial effects absent in standard models.

Findings

Stress obeys a viscoelastic constitutive equation with inertial effects

Exact solutions obtained for simple shear and elongational flows

Model differs from standard polymeric liquid models in objective properties

Abstract

I calculate the hydrodynamic limit of the BGK approximation of the Boltzmann equation for the case of a long stress relaxation time and find that the stress obeys a viscoelastic constitutive equation. The constitutive equation is different from standard constitutive equations used for polymeric liquids in that it is not ``objective'' because inertial effects are important. I calculate the exact solution for the stresses for simple shear flow and elongational flow.