  Although the non-equilibrium behaviour of polymer solutions is generally well
understood, particularly in extensional flow, there remain several unanswered
questions for dilute solutions in simple shear flow, and full quantitative
agreement with experiments has not been achieved. For example, experimental
viscosity data exhibit qualitative differences in shear-thinning exponents,
shear rate for onset of shear-thinning and high-shear Newtonian plateaus
depending on polymer semiflexibility, contour length and solvent quality. While
polymer models are able to incorporate all of these effects through various
spring force laws, bending potentials, excluded volume (EV) potentials, and
hydrodynamic interaction (HI), the inclusion of each piece of physics has not
been systematically matched to experimentally observed behaviour. Furthermore,
attempts to develop multiscale models (in the sense of representing an
arbitrarily small or large polymer chain) which can make quantitative
predictions are hindered by the lack of ability to fully match the results of
bead-rod models, often used to represent a polymer chain at the Kuhn step
level, with bead-spring models, which take into account the entropic
elasticity.In light of these difficulties, this work aims to develop a general
model based on the so-called FENE-Fraenkel spring, originally formulated by
Larson and coworkers [J. Chem. Phys. 124 (2006), 10.1063/1.2161210], which can
span the range from rigid rod to traditional entropic spring, as well as
include a bending potential, EV and HI. As we show, this model can reproduce,
and smoothly move between, a wide range of previously observed polymer solution
rheology in shear flow.
