Index of content:
Volume 18, Issue 3, September 1974

Radial Flow of Non‐Newtonian Fluids Between Parallel Plates
View Description Hide DescriptionDiverging radial flow between parallel plates was studied under isothermal steady‐state conditions. Flow rates Q and radial pressure distributions were measured for one Newtonian liquid and three non‐Newtonian polymer solutions. The powerlaw viscosity model, with parameters evaluated from cone‐and‐plate viscometry, was remarkably good in fitting data and, in most cases, also for describing Thus, for these polymer fluids with only moderate viscoelasticity (Weissenberg number <1), more sophisticated rheological modeling is not needed for predicting flow rate and pressure distributions. However, tracer experiments hinted at the presence of instabilities and/or secondary flows.

Transient and Steady Shear Behavior of SBR Polymers
View Description Hide DescriptionThe low shear rate viscosity behavior of SBR random copolymers is investigated in steady and transient shear flow. The polymers studied have high enough molecular weights to make them of commercial interest. The measurements were performed on an apparatus specially designed but readily available and easy to operate. The results showed that even at very low shear rates, the polymers exhibit non‐Newtonian steady shear viscosities. A log‐log plot of zero shear rate viscosity vs weight‐average molecular weight yields a straight line of slope 3.5. The transient shear data show no stress overshoot at shear rates when the viscosity is non‐Newtonian. A theoretical discussion of the independence of these two nonlinear effects is provided. The discussion is based on some popular single‐integral constitutive equations. It is shown that a recent modification by Carreau to the Lodge elastic liquid model is very realistic. That is, Carreau's model allows one to obtain separately transient shear stress overshoot and non‐Newtonian steady shear viscosity.

Stress Relaxation of Starch Xanthide Reinforced Vulcanizates
View Description Hide DescriptionStress relaxation of a reinforced vulcanized styrene‐butadiene (SBR) elastomer after simple elongation has been investigated over a range of strains and at several filler levels. Carbon blacks and starch xanthide were the reinforcing agents studied. Double logarithmic plots of load versus time at constant strain were linear over five decades in time, the slope being relatively insensitive to either filler type or loading level, except at low extensions or near the ultimate elongation level. The apparent relaxation time, given as the ratio of a viscosity, η, to a modulus, E, is thus independent of filler. Ratios and where the subscripts f and u refer to filled and unfilled material, respectively, must show the same functional dependence on filler loading level. The usual two constant Mooney plots of versus where λ is the extension ratio, were highly nonlinear, rising steeply as approached unity, particularly for starch xanthide reinforced elastomers. Modulus ratio versus volume fraction plots suggest that the rigid phase, mechanically, is the continuous phase in starch xanthide reinforced elastomers.

Numerical Calculations of the Viscoelastic Properties of Dilute Solutions of Comb‐Shaped Branched Polymers
View Description Hide DescriptionThe viscoelastic properties of dilute solutions of comb‐shaped branched polymers have been calculated from the bead‐spring model, following the Zimm and Zimm‐Kilb theories, with exact numerical evaluation of eigenvalues by the method of Lodge and Wu. Eigenvalues,relaxation times, and frequency dependence of the reduced intrinsic shear moduli and have been obtained for various combinations of number of branch points 1 to 10, beads per branch 1 to 37, backbone beads between branches 1 to 22, and the reduced hydrodynamic interaction parameter 0 to 0.25. Since the total number of beads is restricted to an unrealistically small value of 111 by computer limitations, attention is focused on the low‐frequency behavior where this restriction will have the least influence. Here, the behavior is characterized by the reduced steady‐state shear compliance. This quantity is quite sensitive to f when the mass backbone fraction λ is small (approaching starshaped geometry); and for larger λ, it can detect the presence of a small number of branches.

Stress Propagation in a Frequency‐Dependent Clay Soil
View Description Hide DescriptionReported herein are a theoretical treatment and an experimental investigation that deal with the interpretation of data from a pulse propagation test on a frequency‐dependent clay soil. A transfer function, which considers the superposition of an instantaneous response and the various modes of vibration, is obtained to relate the stress at the fixed end of a specimen to that at the input end, and the modulus of elasticity and viscosity are deduced from analyses of the fundamental resonant frequency of the specimen. Experimental data from shock tube tests on a clay soil provide a means for comparing the analytical predictions with the actual response. It is shown that use of the intuitively defined arrival time of a pulse yields values far too high for the modulus of elasticity, and higher values of damping and shorter lengths of specimen both contribute to making the results more unpredictable. Both the modulus of elasticity and the viscosity of the clay are found to be strongly dependent on frequency, the former increasing and the latter decreasing with increasing frequency.

Flow Instabilities in a Capillary Rheometer for an Elastic Polymer Solution
View Description Hide DescriptionA modified capillary rheometer and a motion‐picture camera are used to simultaneously record the pressure at the inlet to the tube, the flow rate through the tube, and the flow patterns in the barrel prior to the entry to the tube. Measured flow curves, employing tubes in the range for a medicinal grade liquid paraffin in the range and a highly elastic solution of Separan AP 30 in the range agreed well with the data obtained using a Haake Rotovisco cup and bob viscometer. Motion pictures of the flow patterns in the barrel for the Separan solution showed that the stable converging flow field at low flow rates developed a spiraling instability whose intensity increased with increasing flow rates until a complete breakdown of the flow field occurred at high flow rates prior to a second stage stability. Representative flow patterns in the range are presented for which show the behavior over the entire spectrum of shear rates including the second‐stage stability. The similarities of the flow patterns to those observed for polymer melts during extrusion are discussed in detail.

Shear Flow Behavior of Complex Asbestos Fibril Dispersions
View Description Hide DescriptionThe viscosity behavior of colloidal asbestos fibrildispersions, in the presence of a polystyrene copolymer latex, was investigated over a range of shear rates using a Ferranti‐Shirely cone‐and‐plate viscometer. Flow of the asbestos suspensions was highly dependent on shear rate and time; the apparent viscosity was reduced when aluminum trichloride, an effective agent for separating the fibrils, was added. This effect was not seen when poly(acrylic acid) (PAA) was added instead. The complex dispersions containing a relatively low fraction of latex had a high apparent viscosity and were markedly thixotropic. As the fraction of latex increased, the behavior approached that of the unmodified latex. This had a small yield stress, but was otherwise nearly Newtonian. At high shear rates, the increase in viscosity due to addition of asbestos fibrils to the latex was relatively small.

An Experimental Study of Rheological Properties of Polymer Melts in Laminar Shear Flow and of Interface Deformation and Its Mechanisms in Two‐Phase Stratified Flow
View Description Hide DescriptionThe stress state of four rheologically characterized polymer melts—low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polystyrene (PS), and poly(methyl methacrylate) (PMMA)—in laminar shearing flow was completely determined by measuring the non‐Newtonian viscosity μ and the first and second normal stress differences and The mean function was negative and about 0.1–0.3 the value of The measurements were made in a Weissenberg rheogoniometer using cone‐ and parallel‐plate geometries. Additional viscosity measurements were made in a capillary rheometer. An experimental study of interface distortion in the stratified two‐phase flow has been carried out using these melts. It was found in the stratified flow experiments that the lower viscosity melts exhibited concave interfaces and encapsulated the higher viscosity melts irrespective of the relative values of and The rate of interface distortion and encapsulation increases with increasing viscosity differences. The pressure losses for stratified flow tended to be close to the values for the lower viscosity phase, especially for long dies. The problem of instabilities at the interface between the two melts is briefly discussed.