The procedures currently in use for measurement of normal stresses at high shear rates utilize the flow at the exit of a capillary or slit. These methods, which follow from a common analytical framework, require the measurement of the excess exit pressure, in the case of a polymer melt or concentrated solution, and the jet swell or reactive thrust, in the case of a dilute solution. In both cases, the normal stresses calculated from experimental data are excessively high, and the methods provide only a weak upper bound to the actual viscometric functions. We present here an analysis and critical appraisal of capillary and slit methods of normal stress measurement. The source of error is shown to be associated with the velocity profile rearrangement at the exit. Available data for both solutions and melts show that velocity rearrangement calculations for inelastic and second-order fluids are inadequate for real viscoelastic liquids, and that available experimental results for velocity rearrangement in viscoelastic liquids are not sufficiently precise for the calculations required. We conclude that a detailed understanding of velocity profile rearrangement of viscoelastic liquids is essential before exit flow measurements can be used for normal stress measurements.

Capillary and slit methods of normal stress measurements

The state of the problem of elastic turbulence is critically discussed. It is shown that the development of elastic turbulence is associated with the transition of polymer systems to the high elastic state.



Model experiments with a narrow-MWD polybutadiene have been carried out. The method of vizualization of the flow in a flat slit with the aid of circular-polarized light has been used. The results of polarization-optical investigation are compared with the results of capillary viscometry and dynamic measurements at small amplitudes. It is shown, in accordance with theoretical predictions, that when a polymer passes from the fluid to the high elastic state with an increase in the shear rate, it ceases to behave as a fluid under shear. This is accompanied by various forms of flow perturbation at the duct exit and entrance and inside the duct. Perturbations at the duct entrance and exit are due to stress concentration in these zones. The transition of a polymer to the high elastic state near the walls inside the duct gives rise to the “stick-slip” process or to continuous slippage along the duct walls, depending on the velocity of polymer movement. This can be clearly traced by the changes in the interference band pattern. Still higher velocities result in an intensive process of continuity break (rupture) in the polymer and in its chaotic movement in the duct as an aggregate of irregularly shaped lumps, which, relaxing, may form a continuous body again. Attention is drawn to the significance of these observations for a quantitative description of the viscosity anomaly of polymer systems and of the relationship between the viscosity anomaly with various flow irregularities and perturbations in such systems.

Critical regimes of shear in linear polymers

The rheological properties of a series of sixteen polyethylene melts with different molecular weights, molecular weight distributions and types of long chain branching have been investigated. Measurement of shear viscosity, principal normal stress difference and elongational flow response are included. The behavior of high density polyethylenes and linear low density polyethylenes are described in an equivalent way in terms of their molecular weights and molecular weight distribution. The LDPE response is different, being strongly influenced by the extent of long chain branching. This appears to elevate normal stresses, and introduce substantial “strain rate hardening” in uniaxial extension. The experimental data are interpreted in terms of the theory of second-order fluids and the convected Maxwell model. The influence of long chain branching as well as molecular weight distribution on constitutive equation parameters is discussed.

A comparative experimental study of the isothermal shear and uniaxial elongational rheological properties of low density, high density and linear low density polyethylenes

The resistance to flow of molten polymers (exhibiting memory effects) through granular beds was investigated. The data were correlated using simple methods of rheological characteristics of polymer melts.

Resistance to flow of molten polymers through granular beds

New slit die rheometer: some results with a butadiene-styrene block copolymer

Measurements were taken of both viscous and elastic properties of polystyrene melts, using a capillary rheometer recently constructed byHan. The viscous property is determined from the slope of the axial pressure distribution, and the elastic property is determined from the exit pressure, which is obtained at the tube exit when the straight line portion of the axial pressure profile is extrapolated to the exit of the tube. Previous studies ofHan demonstrated that the exit pressure thus obtained can be correlated with die swell ratios, and that the exit pressure is equal to the normal stress difference for polymer melts in fully developed viscometric flow. The present study of polystyrene melts corroborates all previous correlations obtained with high density polyethylene and polypropylene melts as regard the exit pressure measurements. A salient feature of the method employed here is that it requires only a single capillary, long enough to assure that flow is fully developed.

T. C. Yu

Papers

Rheological properties of polystyrene melts