We study the existence of global-in-time weak solutions to a coupled microscopic-macroscopic bead-spring model which 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 ⊂ R, d = 2 or 3, for the velocity and the pressure of the fluid, with an ela...

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a general class of coupled FENE-type finitely extensible nonlinear elastic dumbbell models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded d...

Abstract We investigate the linear and nonlinear shear rheology of a marginally entangled H-polymer melt two solutions made by diluting high molecular weight H-polymers in oligomer. In order to approach nearly unentangled state, dilution is conducted at volume fractions such that attain similar number entanglements melt. Start-up experiments demonstrate behavior analogous with comparable span c...

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker-Planck-Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from [1], where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurat...

We present an enhanced moment-closure approximation to the finiteextensiblenonlinear-elastic (FENE) models of polymeric fluids. This new moment-closure method involves the perturbation of the equilibrium probability distribution function (PDF), which takes into account of the drastic split into two spikes and centralized behavior under the large macroscopic flow effects. The resulting macroscop...

In this paper, we propose an entropy satisfying conservative method to solve the Fokker-Planck 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 in the sense that these schemes satisfy discrete entropy inequal...

Background: Animal and in vitro studies have shown that 25-OH vitamin D plays a significant role in different parts of body. Few data exist about the role of 25- OH vitamin D in reproduction. Insufficient levels during pregnancy are potentially associated with increased risk of preeclampsia, insulin resistance and gestational diabetes mellitus. Recently, few studies have assessed the prognostic...