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Dec 1985

Volume 29, Issue 6, pp. 605-1039


Explanation for Slip‐Stick Melt Fracture in Terms of Molecular Dynamics in Polymer Melts

Y.‐H. Lin

J. Rheol. 29, 605 (1985); http://dx.doi.org/10.1122/1.549804 (33 pages) | Cited 1 time

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A general constitutive equation, which includes both reptational motion and chain tension relaxation, has been obtained from modifying Doi's theory. Based on the constitutive equation, a dip on the flow curve can occur as the two relaxation processes separate apart with increasing molecular weight (MW). Theoretically, the maximum on the flow curve is an instability point. Experimentally, we have measured the flow curves of a series of nearly monodisperse polyisoprene and polystyrene samples and a commercial polyethylene sample and shown that slip‐stick melt fracture occurs as the shear rate reaches the dip, where the stress‐vs‐rate curve has a negative slope. In the case of polystyrene samples, the linear viscoelastic data were analyzed in terms of the proposed general linear viscoelastic theory. The analyzed results were then used in the constitutive equation to calculate their flow curves. In the reptational region, the agreement between theory and experiment is very good. Despite some quantitative difference between theory and experiment in the high rate region, the present theory correctly show the effect of the relaxation rates of the reptational motion and chain tension relaxation relative to each other. The extrudates of the polyisoprene, polystyrene and polyethylene samples were examined and compared. We have also shown from numerical calculations that the dip can be eliminated by the broadening of the molecular weight distribution (MWD). We conclude that slip‐stick melt fracture is a general phenomenon of linear flexible polymers and that it will occur when MW is high enough and MWD is narrow enough.
Show PACS
83.10.Kn Reptation and tube theories
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.60.Uv Wave propagation, fracture, and crack healing

Anomalous Migration of a Rigid Sphere in Torsional Flow of a Viscoelastic Fluid. II: Effect of Shear Rate

D. C. Prieve, M. S. Jhon, and T. L. Koenig

J. Rheol. 29, 639 (1985); http://dx.doi.org/10.1122/1.549820 (16 pages) | Cited 1 time

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A single particle (365–640 μm) is injected into a 0.1% w/w solution of polyisobutylene (Mv=1.5×106), dissolved in polybutene (Mn=800), held between a plate and a 21‐cm disc. When rotation of the disc is begun at 4–9 rpm, with a disc‐plate separation of 3.6–6.6 mm, an anomalous discontinuity in the direction of lateral migration is observed at an initial radial location r=rcr: for r<rcr, the particle migrates radially inward and vertically downward; whereas, for r>rcr, the particle migrates radially outward and vertically toward a plane midway between the disc and plate. By improving the apparatus used in Part I [J. Rheol. 28, 381 (1984)], more reproducible measurements of rcr are obtained. rcr is found to be inversely proportional to rotation speed, directly proportional to disc‐plate separation, and independent of particle radius. The proportionality constant, 6.3/s, represents a critical shear rate for the direction of lateral migration in this fluid and this geometry. A qualitative interpretation for this anomalous behavior is presented in which this critical shear rate is associated with the relaxation time for the polymer molecules.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.60.Bc Linear viscoelasticity
83.50.Uv Material processing (extension, molding, etc.)

Flow Past a Radially Oriented Cylinder in a Converging Flow Channel

M. E. Mackay and A. J. McHugh

J. Rheol. 29, 655 (1985); http://dx.doi.org/10.1122/1.549805 (16 pages)

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An experimental analysis has been carried out for the kinematics of a Newtonian (glycerin solution) and a non‐Newtonian (polyacrylamide solution) fluid undergoing flow past a radially oriented cylinder in a two‐dimensional, converging channel. The macroscopic or free stream fields are found to follow Newtonian and power‐law behavior for the glycerin and polyacrylamide solutions, respectively. In both cases the lubrication approximation describes the data well. The local flow kinematics near the cylinder surface are, however, found to be the same for both fluids and are well described by the solution to the Stokes equations for constant free stream flow past a prolate ellipsoid. Extension rates in the vicinity of the cylinder axis are significantly enhanced over those in the mainstream, and, in a region within about two diameters downstream of the cylinder tip, the kinematics can be classified as “strong” becoming “weak” thereafter.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Jf Extensional flow and combined shear and extension
47.50.-d Non-Newtonian fluid flows

Uniaxial Compression of Bonded and Lubricated Gels

D. D. Christianson, E. M. Casiraghi, and E. B. Bagley

J. Rheol. 29, 671 (1985); http://dx.doi.org/10.1122/1.549821 (14 pages)

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Experimental measurements of the response of starch gels in uniaxial compression, under both lubricated and bonded conditions, are reported. With samples of initial height h0 it was found for lubricated compression that true stress σ versus strain plots (strain being defined as ϵ=(h0−h)∕h) were independent of h0. The curves of true stress versus strain, for uniaxial compression of gels bonded to the instrument platens, lay well above the curve obtained in lubricated compression; and furthermore, the results in bonded compression were strongly dependent on h0. To a good approximation the results in bonded compression could be brought into agreement with the lubricated compression data by correcting true stress for bonded compression by a factor (1+R02/2h2)−1, a modification of a result originally reported by Gent and Lindley. The corrected curves for bonded compression were independent of h0 and agreed with the response of the lubricated samples until near the failure point. Corrected stress for bonded compression at fracture increased with increasing h0, while for lubricated compression, stress at fracture was constant or decreased with increasing h0.
Show PACS
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.85.Cg Rheological measurements—rheometry
83.60.La Viscoplasticity; yield stress

The Viscoelastic Behavior of Heat‐Set Ovalbumin Gels Explained in Terms of a Transient‐Network Model

H. Kamphuis and R. J. J. Jongschaap

J. Rheol. 29, 685 (1985); http://dx.doi.org/10.1122/1.549806 (24 pages)

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The transient network model for concentrated dispersions, presented in a previous paper, is used for the interpretation of the viscoelastic behavior of heat‐set ovalbumin gels. The gels consist of a water phase and a network‐shaped phase of denatured ovalbumin molecules, which are crosslinked and entangled by sulphur bridges, hydrogen bridges, and hydrophobic bonds. The local stresses inside the dispersed phase are calculated from the local deformation and a modified Maxwell‐type constitutive equation that is used for the description of the rheological behavior of this phase. Subsequently, the macroscopic stress tensor is calculated making use of the concepts of the transient network model. Some remarkable model stress predictions are presented and interpreted. Linear viscoelastic measurements on the ovalbumin gels are used to quantify model parameters. Subsequently, the sample's behavior in simple shear and uniaxial compression experiments, including stress relaxation, are compared with model predictions. The model is thus found to satisfactorily describe the system's rheological behavior.
Show PACS
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Ha Flow in channels
83.60.Df Nonlinear viscoelasticity

Stress Relaxation in Guayule Rubber

L. F. Ramos‐De Valle and S. Sánchez‐López

J. Rheol. 29, 709 (1985); http://dx.doi.org/10.1122/1.549822 (16 pages)

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The modulus E(t) variations were determined for natural Guayule rubber, natural Hevea rubber, and synthetic polyisoprene. This was done with unvulcanized samples, with and without carbon black; and with vulcanized samples, with and without carbon black. Using the time‐temperature superposition principle, the corresponding master curves were obtained. Using the procedure by Tobolsky and Murakami, a generalized Maxwell model was adjusted to each master curve. Finally, using the approximations due to Ferry and Williams and to Alfrey, the storage and loss modulus were obtained for each sample. It is shown that when unvulcanized Guayule rubber behaves very similar to synthetic polyisoprene; but having lower modulus, lower relaxation time, and lower storage modulus than Hevea. Vulcanized Guayule rubber can behave either very similar to Hevea rubber or present lower modulus, lower relaxation time, lower storage modulus, and higher loss modulus than Hevea; depending on the Guayule rubber vulcanizing system.
Show PACS
83.80.Tc Polymer blends
83.10.Gr Constitutive relations
83.60.Bc Linear viscoelasticity

Model Analysis of Shear‐Flow Behavior of Linear Low‐Density Polyethylene (LLDPE) Using a Simple Integral Constitutive Equation

L. M. Quinzani and E. M. Vallés

J. Rheol. 29, 726 (1985); http://dx.doi.org/10.1122/1.549807 (13 pages)

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A modification of Lodge's rubberlike‐liquid theory postulated by M. H. Wagner has been used to model the rheological behavior of commercial linear low‐density polyethylene (LLDPE). Experimental results from steady and start‐up shear deformation, and sinusoidal dynamic oscillations have been obtained at several temperatures from 150 to 220 °C. It was found that Wagner's equation gives an excellent fit to the LLDPE melt material properties on the whole range of times and deformations covered by this work.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.85.Cg Rheological measurements—rheometry

Rheology of Suspensions in Polymeric Liquids

A. B. Metzner

J. Rheol. 29, 739 (1985); http://dx.doi.org/10.1122/1.549808 (37 pages) | Cited 14 times

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This paper reviews the flow behavior of concentrated suspensions as may be of interest in the processing of composites and similar polymeric materials. Succinct synopses are arranged at the end of each section. In general, the state of the art is a good one: a small number of experiments on a new formulation frequently suffice for a general prediction of flow behavior when solids are suspended in viscous molten polymers, and in many instances, even a priori predictions of the viscosity are possible. Less viscous systems are much more difficult; several remaining problems and research areas are identified.
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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
83.85.Cg Rheological measurements—rheometry

Rheology: in the Beginning

Hershel Markovitz

J. Rheol. 29, 777 (1985); http://dx.doi.org/10.1122/1.549809 (22 pages)

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Abstract Unavailable
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83.10.Ff Continuum mechanics
47.50.-d Non-Newtonian fluid flows
83.10.Gr Constitutive relations

Abstracts: Cahiers du Groupe Francais de Rheologie

J. Rheol. 29, 799 (1985); http://dx.doi.org/10.1122/1.549844 (6 pages)

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Abstract Unavailable
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83.00.00 Rheology

Abstracts from the Journal of the Society of Rheology, Japan

J. Rheol. 29, 805 (1985); http://dx.doi.org/10.1122/1.549840 (4 pages)

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Abstract Unavailable
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83.00.00 Rheology

Abstracts: Third National Conference on Rheology–British Society of Rheology Australian Branch

J. Rheol. 29, 809 (1985); http://dx.doi.org/10.1122/1.549841 (1 page)

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Abstract Unavailable
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83.00.00 Rheology

Nonlinear Shear Relaxation Modulus for a Linear Low‐Density Polyethylene

R. G. Larson

J. Rheol. 29, 823 (1985); http://dx.doi.org/10.1122/1.549827 (9 pages) | Cited 5 times

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The response of a polydisperse linear low‐density polyethylene to imposed step shear strains up to strains of 10 were measured. The measured stress is approximately factorable into a product of a time‐dependent term, which is just the linear relaxation modulus, and a strain‐dependent term, the damping function. The damping function can be fit by a simple analytic function derived from a molecular theory with a single ad hoc parameter ξ′; a larger value of ξ′ corresponds to more softening of the nonlinear modulus. A tabulation of ξ′ values from fits to experimental shear damping functions given here and published elsewhere indicates that ξ′ is decreased both by polydispersity and by long chain branching.
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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

A Rheometer for Characterizing Polymer Melts and Suspensions in Shear Creep and Recovery Experiments

A. J. P. Franck

J. Rheol. 29, 833 (1985); http://dx.doi.org/10.1122/1.549833 (18 pages)

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A rheometer capable of performing shear creep and recovery experiments has been developed by Rheometrics, Inc. The test geometry can be parallel plates, cone‐plate, or concentric cylinders. The torque is transmitted to the upper plate by a drag cup motor with low inertia and extremely smooth torque output. The driven shaft is supported both axially and radially by an air bearing of low friction assuring that all the torque is transmitted to the sample. Measurements of the angular displacement with a resolution of 10−5 rad over a complete revolution provide the output of strain. The lower torque limit after compensation for residual torques of the air bearing is ≃1 dyne cm. Results of creep and recovery experiments on polymer melts are presented. The viscosity and the steady‐state compliance, which are sensitive to small changes in molecular weight and molecular weight distribution, can easily be determined, thus making the rheometer a very suitable instrument for characterizing polymer melts. Finally, results on suspensions which exhibit yield stresses and thixotropic behavior are discussed, showing the potential of the creep and recovery experiments in characterizing coatings, inks, foods, etc.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.60.La Viscoplasticity; yield stress

Fractional Rates of Deformation

William E. VanArsdale

J. Rheol. 29, 851 (1985); http://dx.doi.org/10.1122/1.549832 (7 pages) | Cited 2 times

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An objective measure of fractional deformation rate is obtained by generalizing the order of the Rivlin‐Ericksen tensors from integer to real values. These extended measures of deformation rate are used to formulate a simple constitutive model for incompressible fluids. This model predicts a time‐dependent viscosity characteristic of antithixotropic fluids in steady shear flow. The constitutive model is contained in a theory for dissipative materials described by Goddard.
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83.50.Ax Steady shear flows, viscometric flow
83.60.Bc Linear viscoelasticity
83.60.Pq Time-dependent structure (thixotropy, rheopexy)

Wall Effects for Dilute Polymer Solutions in Arbitrary Unidirectional Flows

P. O. Brunn

J. Rheol. 29, 859 (1985); http://dx.doi.org/10.1122/1.549824 (28 pages) | Cited 1 time

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General rheological results for a dilute solution of dumbbell model macromolecules in general unidirectional flows in the presence of plane walls (z=±d) are obtained. Quite generally, we show that all three normal stresses are unequal and that the second normal stress is independent of transverse position z. For simple shear flow a shear viscosity and a first normal stress coefficient result, which are independent of the strength of the flow. For channel flow within a narrow channel a first normal stress coefficient cannot be defined, the reason being that a nonzero flow‐induced first normal stress prevails at the channel axis, where the local shear rate is zero. The results are valid no matter what v(0), the actual center line velocity, is. This implies that, as in the shear flow case, the thickness of wall layers is independent of the strengths of the flow field.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
47.11.-j Computational methods in fluid dynamics
83.10.Gr Constitutive relations

Constant Viscosity Elastic Liquids

R. J. Binnington and D. V. Boger

J. Rheol. 29, 887 (1985); http://dx.doi.org/10.1122/1.549825 (18 pages) | Cited 4 times

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The rheology of non‐shear thinning elastic fluids is re‐examined to clarify some of the misconceptions that exist in regard to their behavior. It is demonstrated that these fluids are no more than dilute solutions, constructed by dissolving a high molecular weight polymer solute in a highly viscous Newtonian solvent. Organic and inorganic systems can be constructed and there is no magic recipe. The highly elastic non‐shear thinning fluid systems represent a class of real fluid behavior entirely consistent with molecular theory for dilute solutions and with the Oldroyd B constitutive equation. It is shown that the Oldroyd B constitutive equation is far superior to the convected Maxwell model for predicting the dynamic and steady shear properties of these materials. However the Oldroyd B model fails at higher shear rates and may be completely inadequate for representing the extensional properties of such materials. The paper concludes with some squeeze film flow experimental data for constant viscosity elastic fluids in comparison to a theoretical prediction for Oldroyd B fluids by N. Phan‐Thien in this geometry. The predicted load reduction from Newtonian behavior as a result of fluid elasticity is confirmed by the experimental observations.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.60.Bc Linear viscoelasticity
47.50.-d Non-Newtonian fluid flows

Shear Flow Properties of Semiconcentrated Fiber Suspensions

Miguel A. Bibbo, Steven M. Dinh, and Robert C. Armstrong

J. Rheol. 29, 905 (1985); http://dx.doi.org/10.1122/1.549836 (25 pages) | Cited 1 time

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Measurements are reported for the shear stress of a semiconcentrated suspension of rigid fibers in a Newtonian solvent in the startup of steady shear flow. There are n fibers each of length L per unit volume. A variety of different volume fractions of fibers was used; the fiber aspect ratio was varied as well. It is found that the viscous resistance of a randomly oriented fiber suspension is roughly (nL3) times the resistance observed when the particles lie in the planes of shear. The transient shear stress measurements show the rheological properties depend on the total strain and not on shear rate or time separately. Experiments were done in torsional flow between parallel plates separated by distance H to determine the effect of H/L on the measured properties. It is found that there is no effect for H/L>1. Two different models are presented to account for wall effects for H/L<1. Good agreement is found between computed and measured values.
Show PACS
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.85.Cg Rheological measurements—rheometry
83.85.Lq Normal stress difference measurements

Transient Flow Viscometry

E. Ganani and R. L. Powell

J. Rheol. 29, 931 (1985); http://dx.doi.org/10.1122/1.549826 (11 pages)

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Theoretical relations are derived between material properties and the torque measured in transient flow experiments using the parallel‐plate and the cone‐and‐plate geometries. The formulas are similar to well‐known expressions from viscometric flow theory, except in the parallel‐plate case where the differentiation with respect to edge shear rate is taken at a fixed time. Shear stress growth σ+ and shear stress relaxation σ− functions were measured for two aqueous polyethylene oxide solutions and the NBS fluid 40 using both geometries attached to a Weissenberg rheogoniometer fitted with a piezoelectric load cell and interfaced to a microcomputer. The results show that σ+ and σ− can be measured in the parallel‐plate geometry if the appropriate formulas are used to transform measured torques to material properties. Data from both geometries clearly indicate the existence of primary overshoot and undershoot and that the strain at which the primary overshoot maximum is obtained is the same for all three fluids over the range of shear rates studied.
Show PACS
83.10.Gr Constitutive relations
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Cg Rheological measurements—rheometry

Rheo‐Optical Studies of Polyelectrolyte Solutions in Simple Shear Flow

B. E. Zebrowski and G. G. Fuller

J. Rheol. 29, 943 (1985); http://dx.doi.org/10.1122/1.549823 (12 pages)

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The birefringence and orientation angle of sodium polystyrene sulfonate in aqueous solvents containing 95% glycerol by volume were measured in steady shear and on the inception and cessation of steady shear using the two‐color flow birefringence technique. Polyelectrolyte concentrations ranged from 1 to 9 mg/ml and NaCl concentrations ranged from 0 to 0.1 M. With increased ionic strength from increased NaCl and polyion concentrations, the steady‐state birefringence decreased, and the average orientation angle with respect to the flow direction increased. The more extended conformations of the no‐salt solutions resulted in larger overshoots on the inception of shear and longer relaxation times on the cessation of shear. Rheological effects of increased Na+ concentration with polyelectrolyte concentration were at least partially offset by entanglements.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Ax Steady shear flows, viscometric flow
83.85.Cg Rheological measurements—rheometry

Oscillatory Shear Measurements on Concentrated Dextran Solutions: Comparison with Doi and Edwards' Theory of Reptation

R. R. Rahalkar, C. Javanaud, P. Richmond, I. Melville, and R. A. Pethrick

J. Rheol. 29, 955 (1985); http://dx.doi.org/10.1122/1.549835 (16 pages)

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The Doi and Edwards' theory of reptation was tested in the linear region on the basis of oscillatory shear measurements for dextran solutions. Storage and loss moduli were measured as functions of frequency over the range 0.06–35 Hz and at 35.7 kHz, and polydispersity was measured using gel permeation chromatography. A modification of Doi and Edwards' theory, which takes into account the effects of molecular weight distribution, was used for comparison. Theoretical values assuming monodisperse polymer differed from the experimental values by more than 100%. The experimental results were found to be in good agreement with the modified theory. It was found possible to represent the results for both the solutions studied on one masterplot in terms of reduced variables.
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Ax Steady shear flows, viscometric flow
83.10.Kn Reptation and tube theories

Abstracts: 56th Annual Meeting, Society of Rheology, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

J. Rheol. 29, 971 (1985); http://dx.doi.org/10.1122/1.549842 (54 pages)

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Abstract Unavailable
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83.00.00 Rheology

Abstracts: Abstracts from the Journal of the Society of Rheology, Japan, Volume 12, Number 4, 1984

J. Rheol. 29, 1025 (1985); http://dx.doi.org/10.1122/1.549843 (2 pages)

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Abstract Unavailable
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83.00.00 Rheology

Notes: Excess Pressure Losses in a Sudden Contraction

N. D. Sylvester and Hung‐Lung Chen

J. Rheol. 29, 1027 (1985); http://dx.doi.org/10.1122/1.549834 (7 pages) | Cited 1 time

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Abstract Unavailable
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.50.Lh Slip boundary effects (interfacial and free surface flows)

Comment on the Impulse Approach to Measuring the Equilibrium Modulus of an Evolving Viscoelastic Solid

C. P. Buckley

J. Rheol. 29, 1035 (1985); http://dx.doi.org/10.1122/1.549829 (5 pages)

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Abstract Unavailable
Show PACS
83.50.-v Deformation and flow
83.60.Bc Linear viscoelasticity
83.85.Cg Rheological measurements—rheometry
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