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

Alexander J. Wagner
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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.

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Alexander J. Wagner. 2001-05-03. Derivation of a non-objective Oldroyd model from the Boltzmann equation. https://arxiv.org/abs/cond-mat/0105067

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