The relaxation of dilute polymer solutions following stretch in uniaxial extensional flow is investigated via Brownian dynamic simulations of a flexible freely-draining bead-rod chain. The bead-rod chain simulations are compared to Brownian dynamic simulations of a FENE dumbbell and numerical calculations of a FENE-PM chain. A universal relaxation curve for the stress decay from steady-state is...

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 studied coupled systems of the Fokker–Planck equation and the Navier–Stokes equation modeling the Hookean and the finitely extensible nonlinear elastic (FENE)-type polymeric flows. We proved the continuous embedding and compact embedding theorems in weighted spaces that naturally arise from related entropy estimates. These embedding estimates are shown to be sharp. For the Hookean polymeric ...

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elon...

We prove global well-posedness for the microscopic FENE model under a sharp boundary requirement. The well-posedness of the FENE model that consists of the incompressible Navier-Stokes equation and the Fokker-Planck equation has been studied intensively, mostly with the natural flux boundary condition. Recently it was illustrated by C. Liu and H. Liu [2008, SIAM J. Appl. Math., 68(5):1304–1315]...

In this paper we mainly investigate the inviscid limit for strong solutions of finite extensible nonlinear elastic (FENE) dumbbell model. By virtue Littlewood-Paley theory, first obtain a uniform estimate solution to FENE model with viscosity in Besov spaces. Moreover, show that data-to-solution map is continuous. Finally, prove converges Euler system couple Fokker-Planck equation. Furthermore,...

Abstract Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious comp...

System parameters and steady-state convergence criteria For purposes of this work, a mesh size of was used. Steady state equilibrium was determined using the less stringent of the two error criteria as defined below: \* MERGEFORMAT (1) \* MERGEFORMAT (2) The time step used was determined using the maximum value of the FENE force relative to the spatial discretization and rounded for convenience...