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 nu...

Spring bead models are commonly used in the constitutive equations for polymer melts. One such model based on kinetic theory—the finitely extensible nonlinear elastic dumbbell incorporating a Peterlin closure approximation (FENE-P)—has previously been applied to study concentration-dependent anisotropy with inclusion of mean-field term account intermolecular forces dilute solutions background p...

We investigate finite amplitude stability of spatially inhomogeneous steady state an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at non-uniform temperature. For wide class models including the Oldroyd-B model, Giesekus FENE-P Johnson–Segalman and Phan–Thien–Tanner model we prove that is stable subject to any perturbation.

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in t...

In this paper we mainly investigate the inviscid limit for strong solutions of finite extensible nonlinear elastic (FENE) dumbbell model. By virtue Littlewood-Paley theory, first obtain a uniform estimate solution to FENE model with viscosity in Besov spaces. Moreover, show that data-to-solution map is continuous. Finally, prove converges Euler system couple Fokker-Planck equation. Furthermore,...

Reduction in surface shear stress in turbulent boundary layers implies suppression of turbulent momentum flux, a large-eddy phenomenon. The physics by which dilute concentrations of long-chain molecules alter large-eddy structure and momentum flux is not well understood. Experiment, however, indicates an essential mix of turbulent velocity fluctuations, polymer molecules, and mean shear. We stu...