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Abstract Non-Newtonian fluid mechanics and computational rheology widely exploit elastic dumbbell models such as Oldroyd-B and FENE-P for a continuum description of viscoelastic fluid flows. However, these constitutive equations fail to accurately capture some characteristics of realistic polymers, such as the steady extension in simple shear and extensional flows, thus questioning the ability of continuum-level modeling to predict the hydrodynamic behavior of viscoelastic fluids in more complex flows. Here, we present seven elastic dumbbell models, which include different microstructurally inspired terms, i.e., (i) the finite polymer extensibility, (ii) the conformation-dependent friction coefficient, and (iii) the conformation-dependent non-affine deformation. We provide the expressions for the steady dumbbell extension in shear and extensional flows and the corresponding viscosities for various elastic dumbbell models incorporating different microscopic features. We show the necessity of including these microscopic features in a constitutive equation to reproduce the experimentally observed polymer extension in shear and extensional flows, highlighting their potential significance in accurately modeling viscoelastic channel flow with mixed kinematics.
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This content will become publicly available on September 26, 2026
Linearized Navier Stokes equations at high Reynolds numbers: A unified approach to inviscid damping, vorticity depletion and enhanced dissipation
In this article, we give an introduction to asymptotic stability in two dimensional incompressible flows, and a non-technical overview of the recent proof of uniform-in-viscosity inviscid damping and vorticity depletion near periodic shear flows on a non-square torus.
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- Award ID(s):
- 1945179
- PAR ID:
- 10644409
- Publisher / Repository:
- EMS Press
- Date Published:
- Journal Name:
- EMS Surveys in Mathematical Sciences
- ISSN:
- 2308-2151
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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