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 precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation...

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...

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 revisit the rapid stretching of a liquid filament under the action of a constant imposed tensile force, a problem which was first considered by Matta & Tytus [JNNFM vol. 35, pp 215-229, 1990]. A liquid bridge formed from a viscous Newtonian fluid or from a dilute polymer solution is first established between two cylindrical disks. The upper disk is held fixed and may be connected to a force ...

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...

Recently singular solutions have been discovered in purely elongational flows of visco-elastic fluids. We surmise that these solutions are the mathematical structures underlying the so-called birefringent strands seen experimentally. In order to facilitate future experimental studies of these we derive a number of asymptotic results for the scaling of the width and extension of the near-singula...

The Oldroyd-B fluid has become the starting point for almost all complex flow calculations and analysis involving behavior of dilute polymer solutions. reasons this are clear: based on kinetic theory high molecular weight “phantom” chains near equilibrium, resulting model, in its simplest form, produces a single mode description solution constitutive equation terms symmetric dyad order paramete...