Rheological models for polymer solutions and melts based on the finitely extensible non-linear elastic (FENE) dumbbell theory are reviewed in this study. The FENE-P model that is a well-known Peterlin approximation of the FENE model, indicates noticeable deviation from original FENE predictions and also experimental results, especially in the transient flow. In addition, both FENE and FENE-P mo...

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and the FENE model with the Peterlin approximation (FENE-P) are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous...

bstract We investigate four crucial properties for testing and evaluating a moment closure approximation of the FENE dumbbell model for dilute olymer solutions: non-negative configuration distribution function, energy dissipation, accuracy of approximation and computational expense. hrough mathematical analysis, numerical experiments and comparisons with closure model FENE-P and FENE-YDL, we pr...

One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global exist...

We present a study of the rheology and optical properties during the start-up of uniaxial extensional and shear flow for freely-draining, Kramers bead-rod chains using Brownian dynamics simulations. The viscous and elastic contributions to the polymer stress are unambiguously determined via methods developed in our previous publication [1]. The elastic contribution to the polymer stress is much...

We study the well-posedness of a multi-scale model of polymeric fluids. The microscopic model is the kinetic theory of the finitely extensible nonlinear elastic (FENE) dumbbell model. The macroscopic model is the incompressible non-Newton fluids with polymer stress computed via the Kramers expression. The boundary condition of the FENE-type Fokker-Planck equation is proved to be unnecessary by ...

We consider the finite extensible nonlinear elasticity (FENE) dumbbell model in viscoelastic polymeric fluids. We employ the maximum entropy principle for FENE model to obtain the solution which maximizes the entropy of FENE model in stationary situations. Then we approximate the maximum entropy solution using the second order terms in microscopic configuration field to get an probability densi...

We present some analytical and numerical studies on the finite extendible nonlinear elasticity (FENE) model of polymeric fluids and its several moment-closure approximations. The well-posedness of the FENE model is established under the influence of a steady flow field. We further infer existence of long-time and steady-state solutions for purely symmetric or antisymmetric velocity gradients. T...

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and F...

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of stationary states and the convergence towards t...