Polymers

Keywords: existence results, weak solutions, strong solutions, micro-macro models.

Abstract: Systems coupling fluids and polymers
are of great interest in many branches of applied physics, chemistry
and biology. There are many models to describe them.
We will present here several existence results of weak or strong solutions. In particular we will consider the FENE, the Doi
and FENE-P models.

Keywords: Microfluidics, polymer solutions, Brownian dynamics, blood flow

We report on recent experimental and theoretical work on
the
pinch-off of dilute solutions of flexible polymers. Owing to
the
strong extensional hardening of such solutions, pinch-off of a
liquid drop is delayed. Instead, long threads of uniform
thickness
form, whose radius decreases exponentially in time. We derive a
relationship between the thread radius and the extensional
viscosity.
When the thread radius has decreased to about 10 microns, the
thread

In this talk, the effects of fluid elasticity on the dynamics
of filament thinning and drop breakup processes are
investigated in a cross-slot microchannel. Elasticity effects
are examined using dilute aqueous polymeric solutions of
molecular weight (MW) ranging from 1.5 x 10(^3) to 1.8 ×
10(^7). Results for polymeric fluids are compared to those for
a viscous Newtonian fluid. The shearing or continuous phase
that induces breakup is mineral oil. All fluids possess similar

In 1975 Doi and Edwards predicted that entangled polymer melts and
solutions can have a constitutive instability, signified by a
decreasing stress for shear rates greater than the inverse of the
reptation time. Early experiments did not support this, and more
sophisticated theories were developed that incorporated Marrucci's idea (1996) of
removing constraints by advection; this produced a monotonically
increasing stress and thus stable constitutive behavior. Recent
experiments have suggested that entangled polymer solutions may

Using concepts developed over the years by de Gennes, Doi, Edwards, Marrucci, Rubinstein, McLeish, Milner, and others, a kind of standard model for entangled polymer relaxation and rheology has been developed, which, like the standard model of high-energy physics, has a number of ad hoc assumptions and fitting parameters. The “standard model” of polymer relaxation is based on a phenomenological tube surrounding each polymer chain that represents the effect on that chain of non-crossability constraints imposed by surrounding chains.

I will briefly review multiscale approach to modelling of entangled polymers, which includes molecular dynamics (MD), single chain stochastic models (slip-springs) and the tube model. After that I will concentrate on the link between many chain (MD) and single chain models. I will report results from molecular dynamics simulations on stress relaxation and show the detailed comparison with slip-spring model. In the second part of the talk I will turn to the issue of microscopic definition of entanglement in molecular dynamics.

Recent developments in dilute polymer solution rheology are reviewed, and placed
within the context of the general goals of predicting the complex flow of complex
fluids. In particular, the interplay between the use of polymer kinetic theory and
continuum mechanics to advance the microscopic and the macroscopic description,
respectively, of dilute polymer solution rheology is delineated. The insight that
can be gained into the origins of the high Weissenberg number problem through an

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