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Dec 1969

Volume 13, Issue 4, pp. 411-546


Drop Shapes in Shear from a Second‐Order Theory

Brian M. Turner and Charles E. Chaffey

Trans. Soc. Rheol. 13, 411 (1969); http://dx.doi.org/10.1122/1.549145 (17 pages)

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The recent second‐order theory of Chaffey and Brenner for the deformation of a drop suspended in an immiscible liquid undergoing slow steady shear flow has a narrow range of validity. The deformation parameter DI (proportional to the product of the velocity gradient, the drop radius, the suspending liquid’s viscosity and the reciprocal of the interfacial tension) must be less than 0.24 if the predicted deformation of drops of low viscosity in Couette flow is to be realistic; for highly viscous drops DI must not exceed 0.1. For all drops in hyperbolic flow and hyperbolic‐radial flow DI must be less than 0.22 and 0.24, respectively. The second‐order approximation, DII, to the observable deformation ratio D (the difference between the drop’s length and width, divided by their sum) exceeds DI for viscous drops in Couette flow but is slightly smaller than DI for drops of low viscosity. Calculated values of DII deviate from experimental data on D. The second‐order theory does predict the lengthening in hyperbolic flow of one drop axis and the shortening of the other two. A new first‐order theory by Cox has a much wider range of validity but does not conflict with the second‐order theory.
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83.50.-v Deformation and flow
83.50.Ax Steady shear flows, viscometric flow
47.55.D- Drops and bubbles

Measurement of Stresses Developed in Steady Laminar Shearing Flows of Viscoelastic Media

R. F. Ginn and A. B. Metzner

Trans. Soc. Rheol. 13, 429 (1969); http://dx.doi.org/10.1122/1.549138 (25 pages)

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The shearing stress and both normal stress differences are reported for three solutions of polyisobutylene in decalin. The ratio of the second normal stress difference to the first, (P22−P33)/(P11−P22), is seen to be negative and to vary between −0.1 and −0.4 under the conditions studied for these media. The statistical significance and the precision of these data is considered in some detail; the results are believed to be definitive at the error levels specified. Previous measurements of this normal stress ratio, which may be shown to be free of all the major known errors, are seen to have yielded the same sign as obtained herein, for similar fluids.
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83.60.Bc Linear viscoelasticity
83.50.Ax Steady shear flows, viscometric flow
83.85.Cg Rheological measurements—rheometry

Measurement of the Axial Pressure Distribution of Molten Polymers in Flow Through a Circular Tube

C. D. Han, M. Charles, and W. Philippoff

Trans. Soc. Rheol. 13, 455 (1969); http://dx.doi.org/10.1122/1.549146 (12 pages)

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Axial pressure distributions for the flow of molten polyethylene and polystyrene has been obtained at shear rates of from 100 to 500 sec−1. In the case of polyethylene, fully developed flow was obtained within a length equivalent to one tube diameter (⅛ in.). The extrapolation of the polyethylene pressure profile revealed a normal stress (radial) at the exit which was greater than zero for all shear rates investigated. These extrapolated values of “exit pressure” were used to calculate values of the primary normal stress difference at the shear rates considered. The differences so calculated were found to correlate well with shear rate.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Cg Rheological measurements—rheometry
47.60.-i Flow phenomena in quasi-one-dimensional systems

Historical Comments on Stress Relaxation Following Steady Flows Through a Duct or Orifice

A. B. Metzner

Trans. Soc. Rheol. 13, 467 (1969); http://dx.doi.org/10.1122/1.549139 (4 pages)

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The early scientific literature relating to the geometry of a jet of fluid as it emerges from a duct or orifice is considered. This stress‐relaxation problem has become variously known as the “Barus effect” or “Merrington phenomenon”. Both of these designations are seen to be incorrect historically and their discontinuance is recommended in favor of a phrase description of the material behavior, such as “extrudate expansion.”
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83.50.Ax Steady shear flows, viscometric flow
83.10.Gr Constitutive relations
47.60.-i Flow phenomena in quasi-one-dimensional systems

Intrinsic Errors in Pressure‐Hole Measurements

R. I. Tanner and A. C. Pipkin

Trans. Soc. Rheol. 13, 471 (1969); http://dx.doi.org/10.1122/1.549147 (14 pages)

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A convenient way of measuring normal thrusts on fluid‐immersed surfaces is by use of a pressure gauge attached to a hole in the surface. With viscoelastic fluids exhibiting normal stress effects, it is shown that a systematic error exists, independent of hole size, but dependent on wall shear stress. Experiments were made in an open channel with various holes from math in. to ¼ in. diameter, and also with an ⅛ in. wide slot. Errors were small with 30P silicone fluid, but with two viscoelastic solutions errors were always negative and of the order of 25% of the first normal stress difference. No significant difference has been seen yet between sharp‐edged holes of different sizes or between holes and slots. A theoretical treatment for plane creeping flow over a deep slot predicts that the error is negative, independent of slot width, and 25% of the first normal stress difference. Some implications for normal stress measurements are considered.
Show PACS
83.85.Lq Normal stress difference measurements
83.60.Bc Linear viscoelasticity
83.50.Lh Slip boundary effects (interfacial and free surface flows)

The Visco‐elastic Behavior of Confined Thin Films of Bitumen in Tension Compression

E. J. Dickinson and H. P. Witt

Trans. Soc. Rheol. 13, 485 (1969); http://dx.doi.org/10.1122/1.549148 (27 pages)

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The behavior of confined thin films of a bitumen under sinusoidal loading both in shear and in a direction normal to the plane of the film (tension∕compression) has been investigated. For small strains, behavior in tension∕compression like that in shear, is linear and thermorheologically simple and the temperature dependence of the rheological parameters is the same in each case. In tension∕compression, the degree of confinement can be defined by the ratio of the radius of the confining plates (r) to the thickness of the film (d). For confinement ratios greater than about one, the longitudinal complex modulus ∣M∗∣ was found to be greater than three times the complex shear modulus 3∣G∗∣ (the value expected for shear behavior). The complex modulus ratio ∣M∗∣/3∣G∗∣, where ∣M∗∣ and ∣G∗∣ are measured at the same frequency and temperature, was found to be approximately proportional to the square of the confinement ratio over the confinement ratio range 4.5 to 45. This relationship should be predicted by the theory of the purely elastic situation. The energy loss factor under sinusoidal loading, π/2 tan ϕ (where ϕ is the angular phase difference between stress and strain), was found to be different in tension∕compression from that in shear. As the confinement ratio increases, the energy loss factor decreases more rapidly with frequency than for shear conditions. To indicate the temperature∕frequency region for this decrease, the behavior where tan ϕ = 1 was evaluated and found to correspond to an ∣M∗∣ value of about 8×108 dynes/cm (the same value is obtained in shear for tan ϕ = 1). The particular relationship (for the bitumen tested) between the temperature, the frequency, and the confinement ratio when tan ϕ = 1 was determined for the range of frequencies and temperatures covered experimentally. The theoretical implications of the results and their relation to the deformation, fracture, and fatigue behavior of bitumen bonded road surfacing materials are briefly discussed.
Show PACS
83.80.Va Elastomeric polymers
83.85.Lq Normal stress difference measurements
83.60.Bc Linear viscoelasticity

On the Properties of the Motion With Constant Stretch History Occurring in the Maxwell Rheometer

R. R. Huilgol

Trans. Soc. Rheol. 13, 513 (1969); http://dx.doi.org/10.1122/1.549140 (14 pages)

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The motion in the Maxwell orthogonal rheometer has been treated by several authors recently. The original purpose of this instrument was to measure the normal and shear stresses in a polymer melt being subjected to a shearing in three directions simultaneously. Later on, attempts were made to relate the experiment to the material constants of a nonlinear Maxwell model and an empirical model. The purpose of this article is two fold: to show that the steady motion in this rheometer is a motion with constant stretch history, and then to determine the five material functions for the general simple fluid if it were used in the rheometer. It is found that a close relation exists between these five material functions and the viscometric functions. The BKZ model is used to compute the stresses for this flow. The relation between the measured forces in the rheometer and the material functions is pointed out, and it is shown that this rheometer can be used to determine whether the fluid being sheared is a simple fluid with fading memory or not. In the Appendix it is shown that for the BKZ model, the memory functions determined from viscometric flows can be used to calculate the present five functions at low shear rates.
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83.80.Va Elastomeric polymers
83.85.Cg Rheological measurements—rheometry
83.60.Bc Linear viscoelasticity

Relaxation in Polyurethanes in the Glass Transition Region

T. Kajiyama and W. J. MacKnight

Trans. Soc. Rheol. 13, 527 (1969); http://dx.doi.org/10.1122/1.549149 (20 pages)

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A study has been made of the relaxation phenomena in three series of polyurethanes in the neighborhood of their glass transition temperatures and above. The technique of dynamic mechanical relaxation was used in the investigation at various frequencies up to 110 Hz. Differential Scanning Calorimetry (DSC) was also used as a supplement to the mechanical measurements. The series are: (1) H series based on polymerization of hexamethylene diisocyanate and various diols, (2) DP series based on polymerization of 4,4′ diphenylmethane diisocyanate and various diols, and (3) 4M series based on polymerization of 4‐methyl meta phenylene diisocyanate and various diols. Four relaxation regions are discernible in the temperature range investigated and these are labelled β, α, αt and αc in order of increasing temperature. The following molecular mechanisms are associated with these relaxations: (1) The β relaxation (DP and 4M series only) arises from phenyl group motion in the chain backbone, (2) the α relaxation (all series) arises from microbrownian segmental motion associated with the glass transition, (3) the αt relaxation (H series only) is associated with a solid‐solid phase transition involving the change from one crystalline modification to another, (4) the αc relaxation (H and DP series only) involves rotational or translational motion of the chains in the crystalline phase.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.85.Cg Rheological measurements—rheometry
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