We construct a general family of Galerkin methods for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier– Stokes equations in a bounded domain Ω ⊂ Rd, d = 2 or 3, for the veloci...

Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation ...

A thin filament model is used to analyze the stability of a viscoelastic thread subject to uniaxial stretching. Linear stability analysis is carried out for a number of different constitutive models, namely the Johnson–Segalman, Giesekus, Phan–Thien Tanner, and FENE–CR. Our analysis shows that stability is controlled by the competing effects of surface tension which is destabilizing and axial n...

In this paper, we propose a new entropy satisfying finite volume method to solve the FokkerPlanck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. Both semi-discrete and fully discrete schemes satisfy all three desired properties: i) mass conservation, ii) positivity preserving, and iii) entropy satisfying. These ensure that the computed solution is a probability den...

In the String & Binders Switch (SBS) model 1,2 a chromatin filament is represented as a self-avoiding (SAW) polymer chain, composed by N beads. Each bead of the chain interacts with diffusing Brownian particles (binders) having a molar concentration c. The scale of their binding energy to a cognate polymer bead is named í µí°¸!"#. The beads of the chain and the binders are subject to Brownian m...

We study the flow around a periodic array of cylinders using mesoscopic viscoelastic fluid that mimics polymeric solutions. model our employing novel method based on Smoothed Dissipative Particle Dynamics and FENE springs. characterize static dynamic properties solutions compare results with theoretical predictions Zimm model. After rheological characterization modeled solutions, we simulate co...

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...