We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov an...

One of the newest of viscoelastic RANS turbulence models for drag reducing channel flow with polymer additives is studied in different flow and rheological properties. In this model, finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of polymer solution and turbulence model is developed in the k-ϵ-(ν^2 ) ̅-f framework. The geome...

Reduction in surface shear stress in turbulent boundary layers implies suppression of turbulent momentum flux, a large-eddy phenomenon. The physics by which dilute concentrations of long-chain molecules alter large-eddy structure and momentum flux is not well understood. Experiment, however, indicates an essential mix of turbulent velocity fluctuations, polymer molecules, and mean shear. We stu...

Observations are presented of several novel phenomena involved in the dynamics of a pendant drop of viscoelastic micellar fluid falling through air. Generally, when a drop falls a filament forms connecting it to the orifice; the filament eventually breaks due to an instability. The filament dynamics and instabilities reported here are very different from the standard Newtonian and non-Newtonian...

Filament stretching experiments are used to follow the evolution in the flow-induced birefringence (FIB) and the tensile force in polymeric fluid threads undergoing uniaxial elongation. The tests are performed with several monodisperse polystyrene solutions spanning concentrations from 0.025 to 12 wt.%, and the measurements are used to investigate the extent of hysteresis in the polymeric stres...

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely join...

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker–Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth conve...

We consider the microscopic equation of FENE (finite extensible nonlinear elasticity) models for polymeric fluids under a steady flow field. This paper will show for the underlying Fokker-Planck type of equations, any pre-assigned distribution on boundary will become redundant once the non-dimensional number Li := Hb kBT ≥ 2, where H is the elasticity constant, √ b is the maximum dumbbell exten...