We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: A. Name1, A. Name2, C. R. Acad. Sc...

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker–Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth conve...

A method will be given to determine lower bounds for the invariants of a configuration tensor in 3D flows. For some well-known differential models these lower bounds will be given. Except for the Giesekus and the FENE-P model the lower bounds are the values in equilibrium.

The finitely extensible nonlinear elastic (FENE) dumbbell model consists of the incompressible Navier–Stokes equation for the solvent and the Fokker–Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit m0 which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in t...

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...

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior of Oldroyd-B model. Here, we compare response simplified linear form Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] finitely extensible nonlinear elastic (“FENE”) dumbbell follows Peterlin ...

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...