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Sep 1966

Volume 10, Issue 2, pp. 449-653


Dynamical Aspects of Viscoelasticity

Julian L. Davis

Trans. Soc. Rheol. 10, 449 (1966); http://dx.doi.org/10.1122/1.549032 (17 pages)

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This paper is concerned with some aspects of the dynamic response of a three‐dimensional linear viscoelastic medium to prescribed boundary conditions. The constitutive equations, expressed in operator form, are applied to a three‐dimensional continuum and are combined with the equations of motion to yield a system of linear partial differential equations. This system may be expressed in terms of a scalar and vector potential and parameters called “generalized velocities c1∗ and c2∗” (operators describing the properties of the medium). The free radial vibrations of a viscoelastic sphere and spherical shell are worked out for the prescribed boundary conditions. In particular the phase velocity is obtained as a function of the wave number and a complex frequency. The wave number is obtained from the roots of a transcendental equation. The free longitudinal vibrations of a viscoelastic cylinder are determined by solving the equations for the scalar and vector potentials with the appropriate boundary conditions. The phase velocity is obtained for the Voigt and Maxwell models. In addition, asymptotic results are obtained which reduce to either the thin rod or the Pochhammer approximation.
Show PACS
83.60.Bc Linear viscoelasticity
83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.10.Ff Continuum mechanics

Correlation of the Weissenberg Rheogoniometer with Other Methods

W. Philippoff and R. A. Stratton

Trans. Soc. Rheol. 10, 467 (1966); http://dx.doi.org/10.1122/1.549060 (21 pages)

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Measurements of the recoverable shear, s using three different methods, recoil, Weissenberg rheogoniometer, and flow birefringence, have been made on solutions of polyisobutylene in oil and polystyrene in Aroclor. All three methods, within their applicability limits, gave consistent results, calculating the recoil values from the rheogoniometer without the factor of ½ required by the theories using constitutive equations for viscoelastic liquids. Especially, these experiments with “matching solvents” gave a very good agreement on s measured in the rheogoniometer and flow birefringence.
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83.60.Hc Normal stress differences and their effects (e.g. rod climbing)
83.85.Cg Rheological measurements—rheometry
83.80.Rs Polymer solutions
83.80.Sg Polymer melts

Effect of Degradation by Pumping on Normal Stresses in Polyisobutylene Solutions

Gary K. Patterson, Harry C. Hershey, Charles D. Green, and Jacques L. Zakin

Trans. Soc. Rheol. 10, 489 (1966); http://dx.doi.org/10.1122/1.549033 (12 pages)

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Normal stress measurements were made on dilute solutions of polyisobutylene in three low‐viscosity solvents at high shear rates with a jet thrust apparatus in which the thrust tube was mounted on the frame of an analytical balance. Thrust measurements could be easily read to 0.01 g and replicate measurements agreed closely with the original ones. Mechanical degradation of polyisobutylene in cyclohexane and toluene caused significant reductions in (P11−P22)w values at high shear rates and in the amount of drag reduction in turbulent flow. Molecular weight distribution curves and estimates of viscosity‐average molecular weights of the fresh and degraded solutions in toluene indicate that these effects noted in this solvent are caused by the breakdown of small amounts of high molecular weight polymer, with only a small change in the viscosity‐average molecular weight.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Lq Normal stress difference measurements
83.10.Gr Constitutive relations

Time‐Temperature Strain and Molecular Weight Effects in the Environmental Stress Cracking of 0.95 Density Polyethylene

Glenn E. Fulmer

Trans. Soc. Rheol. 10, 501 (1966); http://dx.doi.org/10.1122/1.549063 (12 pages)

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Reduced variables of time‐temperature and molecular weight are used to describe the stress relaxation failure of 0.95 density polyethylene in a stress cracking agent, Igepal CO‐630. This method was previously shown to work for 0.96 density linear polyethylene. The 0.95 density polyethylene has an apparent activation energy of 38 kcal for stress cracking. This is appreciably higher than the 22 kcal found for 0.96 density linear polyethylene. A much higher dependence on molecular weight was also found. The 0.95 density polyethylene has a lifetime that is proportional to Mv5.8 while the 0.96 density polyethylene has a lifetime proportional to Mv3.4. Some data are also shown which indicate a difference in the sensitivity to strain for the two materials. This can lead to appreciably longer lifetimes for the 0.95 density polyethylene at low strain.
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83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.85.Lq Normal stress difference measurements

Linear Free Energy Effects in Poly(vinyl Chloride)‐Ester Systems from Tensile Creep Compliance, Melt, and Solution Viscosity Techniques

R. J. Hammond and E. M. Smoley

Trans. Soc. Rheol. 10, 513 (1966); http://dx.doi.org/10.1122/1.549064 (16 pages)

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Current literature indicates that considerable effort is being made to relate rheological behavior of various materials to molecular mechanisms of flow. Implicit in viscoelastic spectra are the molecular motions and configurations that give shape to the stress relaxation or creep compliance curves. In dilute solutions or concentrated melts at higher temperatures, flow curves give indications of molecular arrangements present which cause deviation from some previously defined standard. Both qualitative and quantitative descriptions of solution and flow mechanisms recognize the importance of intermolecular forces. While these treatments can be used with confidence in systems of low polarity, highly polar solvent‐solute mixtures are not adequately described by these relations. Our primary considerations here are directed at understanding the nature of the interaction of 2‐ethylhexyl carboxylates with poly(vinyl chloride) and its model 1,3‐dichloropropane. The method employed represents a departure from conventional thought in that rheological behavior, from tensile creep compliance, dilute solution, and melt viscosity, has been successfully correlated to both Hammett and Taft substituent constants as implied in Eyring's concept of absolute reaction rates. While changes in interaction free energies between solvent and ester evolve simply and naturally from this technique, the significant conclusion obtained from these data is that the generally accepted “hydrogen‐bonding” interaction hypothesis of poly(vinyl chloride) with esters is clearly absent.
Show PACS
83.60.Bc Linear viscoelasticity
83.10.Gr Constitutive relations
83.80.Rs Polymer solutions
83.80.Sg Polymer melts

Analog Study of the Dynamics of a Nonlinear Maxwell Model Material

I. J. Gruntfest and G. E. Mueller

Trans. Soc. Rheol. 10, 529 (1966); http://dx.doi.org/10.1122/1.549034 (15 pages)

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As part of a continuing study of the mechanical behavior of materials which have temperature‐dependent properties, electric analog experiments on a nonlinear Maxwell Model Material are described. The circuit that is used contains thermistor elements which simulate the temperature‐dependent viscosity of the mechanical model. The inertial and elastic elements are simulated by electronic integrators instead of inductors and capacitors which assures the ideality of the elements and increases the versatility of the analog. The work leads to the identification of a natural “property” of the material which has advantages over the use of the viscosity coefficients and elastic moduli alone. The results show how, because of heating, the responses of the model change from elastic to viscous as the severity or duration of the excitation increases. The heating also leads to stress reduction in the trailing part of the disturbance. Since elements of the analog may be identified with elements of atomic scale models of material, the work relates to material development programs as well as to mechanical design studies.
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83.60.Df Nonlinear viscoelasticity
83.60.Np Effects of electric and magnetic fields
83.10.Kn Reptation and tube theories
83.10.Mj Molecular dynamics, Brownian dynamics

Flow Behavior of Low Molecular Weight Polybutadiene, Carboxyl‐Polybutadiene, and Butadiene‐Acrylonitrile Copolymers

Richard J. Boyce, Walter H. Bauer, and Edward A. Collins

Trans. Soc. Rheol. 10, 545 (1966); http://dx.doi.org/10.1122/1.549065 (26 pages)

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The flow behavior of some low molecular weight polymers was studied as a function of shear rate, shear stress, and temperature. The polymers included polybutadienes, random carboxyl and carboxyl‐terminated polybutadienes, carboxyl‐terminated butadiene‐acrylonitrile, and acrylonitrile‐butadiene copolymers. Measurements were made in the temperature range 3.8–73°C. A cone and plate viscometer and pressure capillary viscometer were used to cover the shear rate range 1−105 sec−1. Measurements were carried out with various capillary radius to length ratios. mathw and mathn values were calculated from molecular weight distribution data obtained by gel permeation chromatography. Limiting viscosity numbers were also determined. In the range of shear rates studied, all polymers showed a limiting viscosity at low rates of shear and a region of shear rate thinning. The log viscosity‐log shear rate flow curves for each sample at the various temperatures were superimposable by linear shifts. Energies of activation calculated according to the method of Fox and Loshaek were found to have values characteristic of the molecular structure. Normal stresses developed in capillary flow as measured by entrance effects showed some dependence on structure. Flow results were compared with the Bueche‐Harding experimental standard curve and the Bueche theoretical curve. The presence of polar groups in the polymer chain increased the energy of activation and the relative magnitude of the viscosity. The log viscosity‐log shear rate flow curves for all the samples at any constant temperature were superimposable by linear shifts in two distinct classes according to differences in molecular weight distribution.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.85.Cg Rheological measurements—rheometry
83.50.Ax Steady shear flows, viscometric flow

Particle Motions in Sheared Suspensions. XIX. Viscoelastic Media

A. Karnis and S. G. Mason

Trans. Soc. Rheol. 10, 571 (1966); http://dx.doi.org/10.1122/1.549066 (22 pages)

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The behavior of rigid and deformable particles suspended in viscoelastic fluids undergoing slow Couette and Poiseuille flows was studied experimentally. In tube flow, the particles migrated from the wall to a limiting radial position at which the velocity gradient was effectively zero; in Couette flow between concentric rotating cylinders, migration occurred towards the outer cylinder wall. The rotations of rigid rods and disks were similar to those in Newtonian liquids, except for a steady drift in orbit constant to asymptotic values which in Newtonian liquids correspond to minimum energy dissipation. Two‐body collisions of rigid uniform spheres were unsymmetrical and irreversible. The deformation and burst of Newtonian liquid drops were as in Newtonian suspending liquids of comparable suspending phase viscosity, except for the alignment angle of the drop at zero deformation.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.10.Pp Particle dynamics
83.85.Jn Viscosity measurements

A Critical Evaluation of the Effect of Thermal Feedback in Liquid Flow

John G. Brodnyan

Trans. Soc. Rheol. 10, 593 (1966); http://dx.doi.org/10.1122/1.549035 (9 pages)

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In a recent series of articles Gruntfest has obtained numerical solutions of the equations relating the effects of a dissipative process like viscous flow on the observable flow patterns of a heat‐sensitive material. Gruntfest has implied that non‐Newtonian flow is at least partially due to this thermal feedback, and he has demonstrated its significance in the flow of polymer‐modified oils reported on by Philippoff. This raises the question of how important these effects are in general, i.e., is non‐Newtonian flow an experimental artifact. In this paper the qualitative and quantitative predictions of Grantfest's analysis are examined. These predictions are then compared to some experimental data obtained with simple fluids, polymer solutions, polymer melts, and colloidal dispersions. It is shown that non‐Newtonian flow usually appears well before the rates of shear at which thermal effects would be noticed. Hence, non‐Newtonian flow is not an experimental artifact brought about by the inability to transfer thermal energy away from heat‐sensitive materials.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
47.50.-d Non-Newtonian fluid flows

A Capillary Model for Non‐Darcy Flow through Porous Media

Y. Klausner and R. Kraft

Trans. Soc. Rheol. 10, 603 (1966); http://dx.doi.org/10.1122/1.549036 (17 pages)

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A parallel capillary porous flow model is constructed from capillaries with “wall forces.” The model exhibits critical pressure gradients and nonlinear discharge velocity at low pressure gradients, while for high gradients the discharge velocity is linear.
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83.80.Fg Granular solids
83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.50.-v Deformation and flow

A Relationship between Molecular Weight Distribution and Non‐Newtonian Flow for Polyisobutenes

Roger S. Porter, Manfred J. R. Cantow, and Julian F. Johnson

Trans. Soc. Rheol. 10, 621 (1966); http://dx.doi.org/10.1122/1.549067 (6 pages)

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In recent years it has been demonstrated widely that relationships do exist between molecular weight distribution and the non‐Newtonian flow of linear amorphous polymers. Variations in distribution cause marked deviations from general reduced variable curves for non‐Newtonian flow. This conclusion means that reduced variables must involve more than a single molecular weight average. This complexity has been evaluated in this study by equating shear relaxation spectra for polymer solutions to their respective molecular weight distributions. Molecular weight distributions have been generated by column fractionation, measured by gel permeation chromatography, and expressed in terms of their standard deviations. The distributions, expressed in the common form of Mw/Mn, ranged from 3.07 to 1.01. The procedure has been successfully applied to non‐Newtonian flow curves for concentrated solutions of polyisobutenes. This new relationship may be suitable for expressing the non‐Newtonian flow of other linear amorphous polymers. A general approach of this type is of value for predicting and tailoring the flow properties of polymers.
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83.80.Va Elastomeric polymers
47.50.-d Non-Newtonian fluid flows
83.50.Ax Steady shear flows, viscometric flow

Rheological Study on Cold and Warm Processings of Polycarbonate

Shoichi Ueno, Hiroaki Yamazaki, Takeshi Oue, Katsuhiko Ito, and Makoto Tsutsui

Trans. Soc. Rheol. 10, 627 (1966); http://dx.doi.org/10.1122/1.549037 (26 pages)

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The retentivity of shape in uniaxial compression of polycarbonate resin when processing in the cold and warm processing temperature range was investigated experimentally. Iupilon, a polycarbonate resin manufactured by the solvent process, was used as the sample. Strain recovery of test specimens, which were processed by compression at various temperatures, was measured after free annealing by raising the temperature gradually to a temperature higher than the processing temperature. Polycarbonate has superior processability in the vicinity of room temperature and has good strain‐freezing properties at temperatures below the glass transition temperature; however, strain is recovered completely at temperatures above the glass transition point. A new Erichsen testing apparatus was developed for measuring the temperature dependence of processability of sheet in the cold and warm temperature range. A punch is pushed into the sheet whose temperature has been made uniform in a constant temperature apparatus at a fixed stroke speed; the Erichsen depth at fracture at the various temperatures is measured. Results indicated that processability of polycarbonate sheet (thickness, 1 mm) improves gradually with temperature rise as high as the glass transition point. Experiments on strain recovery of an Erichsen test specimen were carried out in the same manner as in the case of uniaxial compression. The results for combined stresses, such as in Erichsen bulging, were similar to those of uniaxial compression. An attempt is being made to utilize such Erichsen bulging test specimens for environmental stress cracking tests of polycarbonate.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Cg Rheological measurements—rheometry
83.50.Ax Steady shear flows, viscometric flow

Erratum: An Experimental Appraisal of Viscoelastic Models

Thomas W. Spriggs, John D. Huppler, and R. Byron Bird

Trans. Soc. Rheol. 10, 653 (1966); http://dx.doi.org/10.1122/1.549038 (1 page)

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Abstract Unavailable
Show PACS
83.60.Bc Linear viscoelasticity
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
47.50.-d Non-Newtonian fluid flows
99.10.Cd Errata
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