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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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Master curves for FENE-P fluids in steady shear flow
The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number (Wi), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter (L), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high Wi as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of Wi , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is Wi/L and it is only in strong shear flows exceeding Wi/L > 1 that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of Wi/L when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects.
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- Award ID(s):
- 2027870
- PAR ID:
- 10475776
- Editor(s):
- Poole, Robert J
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Non-Newtonian Fluid Mechanics
- Volume:
- 313
- Issue:
- C
- ISSN:
- 0377-0257
- Page Range / eLocation ID:
- 104944
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jnnfm.2022.104944
