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The Flow of Moderately Concentrated Polymer Solutions in Water

F. Rodriguez and L. A. Goettler

Trans. Soc. Rheol. 8, 3 (1964); http://dx.doi.org/10.1122/1.548976 (15 pages)

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The flow curves for four water‐soluble, non‐ionic polymer types have been characterized using rotational viscometers primarily. Molecular weight and solution concentration variations gave a total of twenty‐five curves. Polyacrylamide, poly(ethylene oxide), hydroxyethyl cellulose, and methyl cellulose were studied. A two‐parameter model that gives a good fit to the data over five decades of shear‐rate is: log (η_r)∕log (η_r)₀=0.68−0.32 erf {[log (τ math

)−log B]∕2.27 math

} In this equation, η_r is the relative viscosity; (η_r)₀, the same at zero shear‐rate, erf, the error function; (τ math

), the rate of energy dissipation; and, B, the value of (τ math

) at the inflection point of the flow curve. Furthermore, B is independent of concentration.

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83.80.Rs	Polymer solutions
83.80.Sg	Polymer melts
83.50.Ax	Steady shear flows, viscometric flow

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Analysis and Interrelation of Stress‐Strain‐Time Data for Asphalt Concrete

Kenneth E. Secor and Carl L. Monismith

Trans. Soc. Rheol. 8, 19 (1964); http://dx.doi.org/10.1122/1.548967 (14 pages)

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Test data are presented for an asphalt concrete subjected to creep and stress‐relaxation in compression at 40°F. Because of the large initial stresses developed in the relaxation tests, perfect step‐function inputs of strain as a function of time were not obtained, and it was thus necessary to utilize data exhibiting some variation of strain with time. The relaxation modulus‐time relationship was obtained from these results by means of a numerical application of the superposition principle. The mathematical development of the numerical solution from the superposition equation is included. Another numerical procedure was utilized to interconvert test values for creep compliance vs. time to a second relaxation modulus‐time relationship. Both solutions were accomplished with the aid of an IBM 7090 computer. Comparison of the results for the relaxation modulus vs. time derived from the two tests showed a comparison sufficiently satisfying to warrant further study along such lines.

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83.10.Gr	Constitutive relations
83.80.Fg	Granular solids

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The Recursive Theory of Slow Viscoelastic Flow Applied to Three Basic Problems of Hydrodynamics

W. E. Langlois

Trans. Soc. Rheol. 8, 33 (1964); http://dx.doi.org/10.1122/1.548968 (28 pages)

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The flow‐field and stresses, correct to the third order, are calculated for three basic problems of viscoelastic flow: the Poiseuille problem; helical flow in an annulus, and torsional flow between discs. The slow flow equations are set out in general tensor notation, then specialized to cylindrical polar coordinates and to spherical polar coordinates.

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47.50.-d	Non-Newtonian fluid flows
83.60.Df	Nonlinear viscoelasticity

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Tensile Creep of Polystyrene at Elevated Temperatures. Part I.

Henry J. Karam and John C. Bellinger

Trans. Soc. Rheol. 8, 61 (1964); http://dx.doi.org/10.1122/1.548969 (12 pages)

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The tensile creep behavior of polystyrene was studied at elevated temperature of 70 to 240°C. This paper will describe in detail experimental techniques and apparatus to obtain the zero shear viscosity of the polymer in this temperature range. Data will be compared with similar information obtained by other experimental techniques. Possible explanations for the discrepancies in the two sets of data are discussed. The paper will indicate, however will not discuss in detail how one can obtain melt elasticity, creep function, and compliance function of an amorphous polymer in the temperature range of 70 to 240°C, by creep experiments.

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83.10.Gr	Constitutive relations
83.80.-k	Material type

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Flow of Gelling Materials in a Uniform Layer on a Vertical Plane

F. J. Fischer and P. R. Paslay

Trans. Soc. Rheol. 8, 73 (1964); http://dx.doi.org/10.1122/1.548970 (11 pages)

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The motion of a general class of gelling materials was investigated under a particular physical configuration. The gelling material was hypothesized to be a Bingham type body of constant viscosity and variable yield stress. The form of the time‐past deformation dependent yield stress has been proposed by Slibar and Paslay and incorporates an exponential memory function, which “weights” current deformation rates more heavily than those occurring at a previous time. The general constitutive equations used in this study were proposed earlier by Slibar and Paslay and in essence infer that no motion within the body is permissible for values of the square root of the quadratic invariant of the reduced stress tensor less than the yield stress. The physical configuration treated is that of a uniform layer of the proposed material extending over an infinite vertical plane. Hence, the stress field is a function of the material density and layer thickness only. The steady‐state solution was found for incipient flow and the necessary and sufficient criterion for solidification of the flow was determined. A numerical technique was used to obtain the time elapsed and total vertical displacement during the interim of relative motion, for various material parameters, felt by the authors to be in the practical range of interest. The results were found to meet all physically motivated anticipations; however, many different mechanisms are active in various gelling materials and the applicability of the proposed constitutive equations has to be verified in each case of a different material.

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83.60.Pq	Time-dependent structure (thixotropy, rheopexy)
83.80.Hj	Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz	Emulsions and foams

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Stretching of Elastic Tubes over Rotationally Symmetric Mandrels

R. A. Wessling and T. Alfrey, Jr.

Trans. Soc. Rheol. 8, 85 (1964); http://dx.doi.org/10.1122/1.548974 (16 pages)

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The pattern of biaxial stretching which occurs when a thin‐walled elastic tube is drawn slowly over a rotationally symmetric mandrel is analyzed. Acceleration terms are neglected in the balance of forces and the friction is assumed to be simple Coulombic. The particular case of the conical mandrel is treated in detail. Solutions are obtained for both Mooney‐Rivlin and Hookean elastic material properties and the results are compared with experiment.

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83.10.Bb	Kinematics of deformation and flow
83.50.-v	Deformation and flow
83.80.Va	Elastomeric polymers

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Biharmonic Solutions of Certain Integro‐Differential Equations of Linear Viscoelasticity

Alexander S. Elder

Trans. Soc. Rheol. 8, 101 (1964); http://dx.doi.org/10.1122/1.548971 (15 pages)

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A stress function theory for linearly viscoelastic solids is developed in this paper. If body forces and inertial forces are neglected, the stresses, strains, and displacements are biharmonic functions of the space variables. The displacements are expressed in terms of harmonic functions by an extension of the Neuber‐Papkovitch theory. Axially symmetric stresses and strains are given in terms of a single biharmonic function. As the analysis does not involve boundary conditions, it is valid for problems involving moving leads and moving boundaries. The theory may be used to formulate stress analysis problems in terms of Volterra integral equations, using creep or relaxation functions as the kernel. The integral equations governing the stresses in a viscoelastic propellant grain subjected to the combined effects of internal pressure and erosion are derived.

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83.10.Ff	Continuum mechanics
83.60.Bc	Linear viscoelasticity

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Dynamic Investigations of Polymer Solutions in an Extended Range of Frequencies

W. Philippoff

Trans. Soc. Rheol. 8, 117 (1964); http://dx.doi.org/10.1122/1.548975 (19 pages)

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Investigations of the dynamic properties of several polystyrene solutions in the viscous solvent Aroclor 1248 were made, comparing the lower frequency results obtained with the Birnboim instrument with the higher ones in the ultrasonic range using the torsional crystal of Mason. Both sets of values merge well in the overlapping range of reduced frequencies, giving a considerably larger combined range. The viscosity η₁ of all the solutions at higher frequencies did not approach that of the solvent but reached a higher asymptotic value, not predicted by theory. This causes cot δ (with δ the “loss angle”) to have a maximum at intermediate frequencies and explains former ultrasonic results. The influence of the polydispersity on the dynamic properties is not large for the loss modulus G″, but is much larger, as theoretically predicted, for the storage modulus G′.

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83.10.Gr	Constitutive relations
83.80.Rs	Polymer solutions
83.80.Sg	Polymer melts

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Velocity Profiles in Tube Flow

J. E. Gerrard

Trans. Soc. Rheol. 8, 137 (1964); http://dx.doi.org/10.1122/1.548972 (10 pages)

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The terminal velocity profile of a liquid flowing in a capillary (tube) can be determined quite accurately from a simultaneous measurement of the mass flux (throughput) and momentum flux (thrust). The flow may be of almost any type, i.e., laminar, transitional, turbulent, most shear‐sensitive, and most non‐isothermal cases. The assumptions embodied appear to be quite logical and exclude very few types of flow systems.

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