The FENE dumbbell model consists of the incompressible NavierStokes equation for the solvent and the Fokker-Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit √ b which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in terms of the elongation parameter b. Thro...

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...

In this paper we will discuss several issues related to the moment-closure approximation of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability density function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro-macro models which consists of the coupled incompressible Navier-Stokes equations an...

We present a brief survey of recent results concerning the existence of global-in-time weak solutions in a bounded Lipschitz domain in R, d ∈ {2, 3}, to a class of kinetic models for dilute polymeric liquids with noninteracting polymer chains. The mathematical model is a coupled Navier–Stokes–Fokker–Planck system. The velocity and the pressure of the fluid satisfy a Navier–Stokes-like system of...

We study the existence of global-in-time weak solutions to a coupled microscopicmacroscopic bead-spring model with microscopic cut-off, which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ Rd, d = 2 or 3, for the velocity and the pressure...

We consider the finite element approximation of the Oldroyd-B system of equations, which models a dilute polymeric fluid, in a bounded domain D ⊂ R, d = 2 or 3, subject to no flow boundary conditions. Our schemes are based on approximating the velocity field with continuous piecewise quadratics and either (a) piecewise constants or (b) continuous piecewise linears for the pressure and the symme...