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 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 have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a crossslot geometry for a FENE-CR fluid, and we describe the changes required for perform...

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...

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 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...

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 ...

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 ...

Spring bead models are commonly used in the constitutive equations for polymer melts. One such model based on kinetic theory—the finitely extensible nonlinear elastic dumbbell incorporating a Peterlin closure approximation (FENE-P)—has previously been applied to study concentration-dependent anisotropy with inclusion of mean-field term account intermolecular forces dilute solutions background p...