Modeling Strong Extensional Flows of Polymer
Solutions and Melts

Professor
Antony Beris

University of Delaware

Abstract: Constitutive
models for polymeric flows have been traditionally
based on the Gaussian approximation assumption about
the form of the distribution function dictating the
conformation of polymer chains. However, although
this is a fairly good approximation near
equilibrium, it becomes consistently worst at high
levels of extension when the chain distribution is
fairly degenerate. The use of a maximum
extensibility (in the form used in a traditional
FENE-P like model) does not improve this
situation---it actually makes it worst! Thus, as an
artifact of this approximation, we have the paradox
of an estimated extended free energy that becomes
infinite in the limit of perfect chain extension.
These observations are not limited to dilute polymer
solutions but also hold for polymer melts where the
role of individual chains is replaced by that of
chain segments between entanglements. In fact, a new
NonEquilibrium Microscopic Lattice-based Monte Carlo
technique that we have recently developed within our
research group has been used in a nonequilibrium
multiscale simulation to develop a new,
thermodynamically consistent, constitutive model
correcting the FENE-P expression for free energy (so
called FENE-PB --- B standing for Bounded Free
Energy) at high levels of extension. The model
restores the consistency between the microscopic
simulations and the macroscopic estimates for a
dense amorphous phase (modeled by a Phan Thien and
Tanner equation using the FENE-PB model to account
for finite extensibility and a bounded free energy)
quite a lot---up to the point where excluded volume
effects are important. This new approximation can
therefore be used under a variety of situations and
it is expected to produce significant differences
when there is a significant chain extension. [slides]