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...

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 present a mesoscopic numerical solver for the constitutive equation of dilute polymer solutions, as described by Fokker–Planck bead-spring dumbbell models with linear spring forces, such Oldroyd-B, FENE-P (finitely extensible nonlinear elastic Peterlin closure), and C-FENE-P (charged FENE-P). The configuration density function is expanded into series Hermite polynomials, we show that only se...

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...

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...

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...