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Volume 16, Issue 4, December 1972

The Limit of Linear Viscoelastic Response in Polymer Melts as Measured in the Maxwell Orthogonal Rheometer
View Description Hide DescriptionThe Maxwell orthogonal rheometer was used to measure the limit of linear viscoelastic response (LLVER) as a function of frequency for three linear polyethylenes at 170°C, for six atactic polystyrenes at 170°C, and for Phenoxy A at 212°C. For the elastic component of the stress, linear viscoelastic response was found to exist in all cases up to finite strains of approximately 50%. The viscous component of the stress exhibited linear viscoelastic response up to approximately 100% strain and sometimes as high as 120%, the maximum strain tested. Two constitutive equations (Bird and Carreau's theory with Gordon and Schowalter's generalization and Tanner's network rupture theory) are noted for the dependence they predict of the strain LLVER as a function of frequency. Bird's theory, with Gordon and Schowalter's generalization, predicts that the elastic strain limit times the frequency will be a constant as the frequency is varied; Tanner's theory predicts that the elastic strain limit will be a constant with varying frequency. Data are shown to support Tanner's theory. Although the theories predict similar relations for the viscous strain limit, since no viscous limit is found up to 120% strain, this portion of the theories could not be checked. Plots of the reduced in‐phase modulus, and the reduced in‐phase viscosity, versus strain, γ, ( and are the modulus and viscosity below the limit) yield very similar curves for all the polymers. This is in agreement with the limited data from MacDonald, Marsh, and Ashare. The reduced in‐phase modulus is constant as the strain is increased up to the elastic LLVER. A gradual decrease then occurs for all of the polymers; at 120% strain, the reduced modulus has decreased between 20 and 30%.

Restrictions Upon Viscoelastic Relaxation Functions and Complex Moduli
View Description Hide DescriptionThe requirements of nonnegative stored energy, nonnegative rate of dissipation of energy, and fading memory are used to derive restrictions upon the forms of the isotropic relaxation functions and the complex moduli of the linear theory of viscoelasticity. The results suggest some new means of displaying and interpreting mechanical properties.

Experimental Investigation of Nonlinear Viscoelasticity in Combined Finite Torsion‐Tension
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Time Dependent Viscoelastic Properties of Concentrated Polymer Solutions
View Description Hide DescriptionMeasurements of stress growth and stress relaxation after onset and cessation of steady simple shear flow in concentrated polymer solutions were carried out with a Weissenberg rheogoniometer R‐17 having a gap servo system. By using monodisperse polymers and their blends, the effect of molecular weight distribution on those transient phenomena is discussed. The so‐called stress‐overshoot was observed in both experiments of shear and normal stress growths. Ratio of the time of the maximum normal stress difference and that of the maximum shear stress is close to 2 at the limit of low shear rate for both monodisperse and polydisperse polymers. In the range of finite shear rate, the ratio is remarkably dependent on shear rate for polydisperse samples, whereas it is almost independent of shear rate for monodisperse polymers. Shear rate dependence of the ratio of the apparent relaxation time of normal stress difference and that of shear stress in stress relaxation experiments is also found to be remarkably affected by molecular weight distribution. From a comparison between these experiments and theories so far published, it is concluded that these transient phenomena may be explained by assuming that the relaxation spectrum is a function of shear rate at least if the shear rates are not too high. The comparison between theory and experiments is carried out without assuming explicit forms for relaxation spectrum.

Internal Viscosity Effects on Transient Elongational Behavior of Dilute Polymer Solutions (Elastic dumbbell model)
View Description Hide DescriptionThe transient elongational viscosity of dumbbell suspensions is calculated accounting for the effect of an internal viscosity in the dumbbell. The calculations are relative to conditions of sufficiently large stretching rates for the effect of Brownian motions to be neglibible. Large extensions of the dumbbell are considered and the resulting nonlinear elastic behavior is accounted for. Both numerical and approximate analytical solutions are provided.

An Evaluation of Expressions Predicting Die Swell
View Description Hide DescriptionDie swell measurements for polystyrene samples of narrow molecular weight distribution and their blends have been made using a capillary viscometer. For the capillaries studied, the swelling ratios were nearly independent of (length/diameter) but strongly dependent on the distribution of molecular weights. The broader the distribution, the larger the swelling ratio for the same extrusion pressure. The recoverable shear at the wall, which is defined to be half the ratio of the first normal stress difference over the shear stress, was estimated using Graessley's correlation between experimental and Rouse shear compliance. The results were compared to predictions from the theories of Nakajima and Shida, Bagley and Duffey, Graessley et al., and Tanner.

A Kinematic Calculation of Intrinsic Errors in Pressure Measurements Made with Holes
View Description Hide DescriptionIn measuring the normal stress exerted by a fluid on a surface it is often convenient to puncture the surface with a ‘small’ hole leading to a larger cavity. An estimate of the stress is then made by measuring the hydrostaticpressure at the bottom of this cavity with a pressuretransducer. Such a procedure, expedient though it is in practice, can result in large systematic errors in the estimate of the stress exerted on the surface, as has been shown experimentally by Kaye, Lodge, and Vale. The present paper gives a discussion of these errors based on kinematic considerations. The value of an approach of this kind is that it gives a physical understanding of the source of the error and suggests how such errors may arise even with rather complicated fluids. Three different configurations are examined. In the first example we consider a shear flow past a deep two‐dimensional slot normal to the flow; for the particular case of a second‐order fluid the intrinsic error is a quarter of the primary normal‐stress difference, in agreement with the previous calculation of Tanner and Pipkin. In the second case, the rectilinear motion along a slot aligned with the flow is considered, and the result obtained by Kearsley is recovered. However, the present analysis is applicable to the rectilinear motion of any material along a slot and, accordingly, a new method is suggested by which direct measurements of the secondary normal‐stress difference might be made. The third configuration comprises a shear flow past a circular hole and it is suggested, in this case, that the intrinsic error is approximately a sixth of the difference between the primary and the secondary normal‐stress differences of the material.

The Drainage of Non‐Newtonian Liquids Entrained on a Vertical Surface
View Description Hide DescriptionThe drainage behavior of a wide variety of non‐Newtonian liquids has been studied under circumstances when “free‐drainage” conditions apply. Experimental values for the time‐variant film thicknesses were obtained while drainage proceeded using a light absorption technique, and an analytic expression relating film thickness to drainage time was derived for fluids described by the Ellis model. Deviations between the experimental and theoretical results are interpreted in light of the Ellis model's inability to describe the elastic properties of the liquids studied.

Finite Amplitude Dynamic Motion of Viscoelastic Materials
View Description Hide DescriptionThe BKZ theory is applied to finite amplitude dynamic motion of polymer solutions. Material parameters are obtained by fitting steady shearing and small amplitude oscillatory data. Predictions of and are shown to be quite good. The second normal stress predictions are also in agreement with the currently accepted sign and magnitude.

Secondary and Primary Normal Stresses, Hole Error, and Reservoir Edge Effects in Cone‐and‐Plate Flow of Polymer Solutions
View Description Hide DescriptionPressure profiles were obtained for several polymer solutions in a cone‐and‐plate device ( ) over a shear rate range Measurements were made with a single transducer mounted flush with a movable plate; the transducer could also be lowered to simulate the effect of holes. Normal stress functions and were calculated by four different methods, representing varying approximations to the real distribution. For polyethylene oxide (PEO) in water/glycerin and polystyrene (PS) in Aroclor, was found to be negative and greater in magnitude for the latter system. The function for PEO appeared nearly constant over most of the shear range, although possibly increasing below Values for PS did not achieve this asymptotic condition, but were consistent with such behavior. Magnitude of the asymptote for PEO was 0.1–0.2, depending on the method of calculation. Simulated pressure tap holes caused lower leading to values reduced by as much as 30% and totally misleading The holes are thus shown to be responsible for the commonly reported positive values of

Extrusion Rheology of Lubricated Polytetrafluoroethylene
View Description Hide DescriptionPolytetrafluoroethylene is probably the only polymer which is commercially extruded in solid state. The polymer is provided in powder form which is lubricated by an oil. The samples of this study were powder of about 500 μ size, coagulated from latex particles of average .2–.4 μ. Naphtha was used as the lubricant at 16.5 weight percent of the composition. The pressure‐output rate relation was examined with two types of capillary rheometers. A constant pressure rheometer was used to characterize the pressure range of 1000 3000 psi. The output rate at a given pressure decreased with time. A constant drive speed rheometer was used in the pressure range of 4000–14,000 psi. The recording of the force was very irregular but had an oscillating pattern. With both rheometers the extrudate diameters were equal or smaller than the die diameter. The compression experiment showed that the material behavior was dependent on not only the available free volume but the nature of powder itself. The compressive stress relaxation, however, depended on the free volume only. Recovery from compression was almost perfect.