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 wall-bounded viscoelastic shear flows due to its relative simplicity accuracy predicting macroscopic properties dilute polymer solutions. model contains three independent material parameters, which expressed dimensionless form correspond a Weissenberg number ( Wi ), i.e. , the ratio relaxation time scale characteristic flow scale, finite extensibility parameter L corresponding fully extended length root mean square end-to-end separation chain under equilibrium conditions, solvent viscosity ratio, commonly denoted ? . An exact solution for rheological predictions steady simple available (Sureshkumar et al., 1997), but resulting nonlinear nested set equations do not readily reveal key shear-thinning physics that dominates at high as result chain. In this note we review way evaluating functions characterizing evolution polymeric contributions stress first normal difference rate increases, provide asymptotic expansions function show it fact possible construct universal master curves these two well ratio. Steady experiments on highly elastic solutions different extensibilities also follow identified curves. governing / only strong exceeding ? 1 effects chains dominate stresses field. We suggest reporting magnitude when performing or simulating shear-dominated with will help clarify effects. • Asymptotic are calculated. Master exist fluids flow. Governing (Weissenberg number)/(finite extensibility). Reporting clarifies