Dilute polymer solutions under shear flow: comprehensive qualitative analysis using a bead-spring chain model with a FENE-Fraenkel spring

TL;DR

This paper develops a comprehensive bead-spring chain model with a FENE-Fraenkel spring to better understand dilute polymer solutions under shear flow, capturing various rheological behaviors and bridging different polymer models.

Contribution

The work introduces a versatile FENE-Fraenkel spring-based model that unifies multiple physical effects and can replicate a wide range of experimental shear flow behaviors of dilute polymers.

Findings

Model reproduces shear-thinning and Newtonian plateaus.

Smoothly transitions between rigid rod and entropic spring behaviors.

Matches experimental rheological data across different polymer conditions.

Abstract

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.