We review recent analytical and computational results for macroscopic-microscopic beadspring models that arise from the kinetic theory of dilute solutions of incompressible polymeric fluids with noninteracting polymer chains, involving the coupling of the unsteady Navier– Stokes system in a bounded domain Ω ⊂ Rd, d = 2 or 3, with an elastic extra-stress tensor as right-hand side in the momentum...

To explore the kinetics and morphology of flow induced crystallization of polymers, a nucleation-growth evolution model for spherulites and shish-kebabs is built based on Schneider rate model and Eder model. The model considers that the spherulites are thermally induced, growing like spheres, while the shish-kebabs are flow induced, growing like cylinders, with the first normal stress differenc...

Viscoelastic flow in a square cavity is studied in detail for the FENE-CR model with a given value of extensibility. A finite volume method was employed to predict both the steady flows resulting from movement of the top cavity wall and also the recoil flows that follow the cessation of that lid-wall motion, when the fluid possesses viscoelastic properties. It is shown that this recoil flow can...

Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function f(t, x, n, ṅ) for a polymer molecule positioned at x to be oriented along direction n while embedded in a ṅ environment created by inertial effects. It is shown that the probability distribution function of the extended model, when converging, will lead to well acc...

The FENE-P model of a fluid is particularly suitable for describing the rheology of dilute polymer solutions (Newtonian solvents containing small amounts of dissolved polymer) as a result of its ability to capture nonlinear effects arising from the finite extensibility of the polymer chains. In extensional flows, these polymer solutions exhibit dramatically different behavior from the correspon...

A high molecular polymer solution with viscoelasticity has the effect of reducing frictional drag, which is quite practical for energy saving. Effective simulations viscoelastic flows in a pipeline Reynolds number realized by incorporating constitutive equation into k−ε−v′2¯−f turbulence model. The Finitely Extensive Nonlinear Elastic Peterlin (FENE-P) model employed characterizing viscoelastic...

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...