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...

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...

A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical postprocessing, and thermodynamic projector. Thermodynamic projector is the tool to transform almost arbitrary anzatz to a thermodynamically consistent model, the postprocessing is the cheapest way to improve the sol...

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...

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...

A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical post-processing, and the thermodynamic projector. The thermodynamic projector is the tool to transform almost any anzatz to a thermodynamically consistent model. The post-processing is the cheapest way to improve the...

This survey paper reviews recent developments concerning the existence of global weak solutions to Fokker–Planck equations with unbounded drift terms, and coupled Navier–Stokes–Fokker–Planck systems of partial differential equations, that arise in finitely extensible nonlinear elastic (FENE) type kinetic models of incompressible dilute polymeric fluids in the case of general noncorotational flow.

Abstract The multiscale modeling of complex fluids under small and large amplitude oscillatory shear flow using non-linear kinetic transient network models is presented. kinetics microstates analogous to chemical kinetics, which defines the physical macromolecule interaction in a Newtonian fluid, concentration variable maximum length extension for each microstate. effect important parameters li...

The theory for the non-isothermal rheology of polymer fluids proposed in Curtiss and Bird (Adv Polym Sci 125:1–101, 1996) used several approximations including so-called linear gradient temperature field Brownian forces. While it had significant advantage dealing with equations, involved may have led to non-physical predictions. This work is a continuation (1996) that obtains corresponding non-...