Dynamics of weakly strain-hardening fluids in filament stretching devices

Abstract

We investigate the transient viscoelastic response of weakly strain-hardening fluids to imposed elongational deformation in filament-stretching devices. We combine time-dependent finite-element simulations with quantitative experimental measurements on a rheologically well-characterized test fluid to investigate how well the device reproduces the ideal transient uniaxial extensional viscosity that is predicted theoretically. A concentrated polymer solution containing 5.0 wt% monodisperse polystyrene is used as the test fluid and the experiments are conducted using the filament-stretching rheometer, developed by Spiegelberg et al. The axisymmetric numerical simulations incorporate the effects of viscoelasticity, surface tension, fluid inertia and a deformable free surface. Single and multi-mode versions of the Giesekus constitutive equation are used to model the rheology of the shear-thinning test fluid. Excellent agreement between the measured transient Trouton ratio and the numerical predictions over a range of deformation rates is reported. The numerical simulations also reveal some important aspects of the fluid kinematics exhibited by weakly strain-hardening fluids during stretching—including a rapid necking of the filament diameter near the axial mid-plane of the fluid column, and an associated elastic recoil phenomenon near the rigid end-plates. This necking instability of a viscoelastic filament can be understood through a generalized Considère criterion, as recently documented by Hassager et al. As a consequence of this necking, spatial and temporal homogeneity in the extensional deformation of the filament is never achieved, even at large Hencky strains. This is in sharp contrast to the numerical and experimental studies for strongly strain-hardening dilute polymer solutions that have been reported to-date. Nonetheless, the present computational rheology study shows that filament stretching devices can still be used to accurately extract the transient extensional viscosity function for weakly strain-hardening fluids, provided that the evolution history of the tensile force at the end-plate and the filament radius at the mid-plane are carefully measured and that the experimental data are correctly processed.