TITLE:
Stress Waves in Polymeric Fluids
AUTHORS:
Karan S. Surana, Michael D. Kitchen
KEYWORDS:
Classical Continuum Theory, Viscoelastic Fluids, Polymeric Liquids, Stress Waves, Memory, Rheology
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.12 No.1,
March
21,
2022
ABSTRACT: This paper demonstrates the existence, propagation, transmission,
reflection, and interaction of deviatoric stress waves in polymeric fluids for
which the mathematical models are derived using conservation and balance laws
(CBL) of Classical Continuum Mechanics (CCM) and the constitutive theories are
based on the entropy inequality and representation theorem. The physical
mechanisms of deformation in polymeric liquids that enable the stress wave physics are identified and
are demonstrated to be valid using Maxwell, Oldroyd-B, and Giesekus polymeric
fluids, and are illustrated using model problem studies. We assume polymeric
fluids to be isotropic and homogeneous at the macro scale so that the CBL of
the CCM can be used to derive their mathematical models. For simplicity, we
assume the polymeric fluids to be incompressible in the present work.