We review recent analytical and computational results for macroscopic-microscopic beadspring models that arise from the kinetic theory of dilute solutions of incompressible polymeric fluids with noninteracting polymer chains, involving the coupling of the unsteady Navier– Stokes system in a bounded domain Ω ⊂ Rd, d = 2 or 3, with an elastic extra-stress tensor as right-hand side in the momentum...

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional viscosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Maxwell (UCM) models to represent the behavior of so-called Boger fluids in axisymme...

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 present a new closure for the mean rate of stretching of a dissolved polymer by homogeneous isotropic turbulence. The polymer is modeled by a bead-spring-type model (e.g., Oldroyd B, FENE-P, Giesekus) and the analytical closure is obtained assuming the Lagrangian velocity gradient can be modeled as a Gaussian, white-noise stochastic process. The resulting closure for the mean stretching depe...

In this talk, we present some joint work with current and former colleagues at Penn State (C. Liu, P. Yu and Y. Hyon) on moment closure approximations of multiscale complex fluid models. Moment closure not only provides a computationally feasible approach to simulate many multiscale phenomena but also offers insight to the understanding of the underlying physical processes. We will discuss some...

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...

A thin filament model is used to analyze the stability of a viscoelastic thread subject to uniaxial stretching. Linear stability analysis is carried out for a number of different constitutive models, namely the Johnson–Segalman, Giesekus, Phan–Thien Tanner, and FENE–CR. Our analysis shows that stability is controlled by the competing effects of surface tension which is destabilizing and axial n...