The stability of viscoelastic fluids in complex flows : the role of shear and extensional rheology

Abstract

Understanding the flow of polymeric fluids is important for optimizing commercial processes such as injection molding and fiber spinning. The combination of streamwise curvature and elastic normal stresses can lead to the onset of elastic flow instabilities, severely rate-limiting such processes. This thesis focuses on the stability of two complex non-Newtonian flows of dilute polystyrene solutions: the viscometric flow between a rotating cone-and-plate and the flow through an axisymmetric contraction-expansion. Torsional shear flows of elastic fluids with closed streamlines can accumulate heat from viscous dissipation resulting in spatial nonuniformities in the temperature profile and viscometric properties. In this thesis, a detailed study of the effect of viscous heating on the steady shearing of elastic fluids between a rotating cone-and-plate is performed. The relative importance of viscous heating and elasticity can be quantified by a new dimensionless thermoelastic number. This parameter is a fluid material property which is a function of polymer molecular weight, geometry and temperature. As the thermoelastic number is increased, strong temperature gradients reduce the elasticity of the test fluid and delay the onset of the instability, eventually stabilizing the flow completely. The flow of elastic fluids into an axisymmetric abrupt contraction-expansion is a complex flow containing regions of both shear and extension that tests the limits of current viscoelastic constitutive models.

(cont.) A large extra pressure drop above that measured for a similar Newtonian fluid is documented and found to correlate to the stress-conformation hysteresis observed in transient uniaxial extension measurements. Laser Doppler velocimetry, particle image velocimetry and flow induced birefringence are used to investigate the global kinematics upstream of contraction-expansions of various contraction ratios and degrees of re-entrant corner curvature. For a contraction ratio of beta=2 a steady elastic lip vortex is observed whereas for 4<beta<8, no lip vortex is observed and instead a corner vortex is seen. At large Deborah numbers a time-dependent elastic flow instability is observed. Measurements of the transient extensional rheology show that the differing vortex growth pathways in viscoelastic fluids can be systematically understood in terms of a dimensionless ratio of the normal stress differences in shear and in extension.