Paper Number
PO97
Session
Poster Session
Title
Master curves for FENE-P fluids in steady shear flow
Presentation Date and Time
October 12, 2022 (Wednesday) 6:30
Track / Room
Poster Session / Riverwalk A
Authors
- Yamanidouzisorkhabi, Sami (MIT, Mechanical Engineering)
- Bischofberger, Irmgard (MIT)
- McKinley, Gareth H. (Massachusetts Institute of Technology, Mechanical Engineering)
Author and Affiliation Lines
Sami Yamanidouzisorkhabi, Irmgard Bischofberger and Gareth H. McKinley
Mechanical Engineering, MIT, Cambridge, MA 02139
Speaker / Presenter
Yamanidouzisorkhabi, Sami
Keywords
theoretical methods; polymer solutions
Text of Abstract
The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of viscoelastic flows due to its simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent parameters, which 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), i.e. the ratio of 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, commonly denoted β. 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 set of equations do not readily reveal the key shear-thinning physics that dominate at high Wi as a result of the finite extensibility of the polymer chain. In this poster we evaluate 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 construct universal master curves for these two material functions and 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.