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Jun 1985

Volume 29, Issue 3, pp. 245-368


Relations Between Creep and Relaxation Functions in Nonlinear Viscoelasticity with or Without Aging

C. Huet

J. Rheol. 29, 245 (1985); http://dx.doi.org/10.1122/1.549789 (13 pages)

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Generalized creep and relaxation functions, appearing as kernels in the Fréchet‐Green‐Rivlin multiple integral developments of the response functionals, are related by a system of linear Volterra equations of the first order. The general form of these relations is given explicitly in the one‐dimensional case. The kernels of the Volterra equations obtained are the same for every order. They have hence the same resolvent kernel, derived simply from the relaxation function of order one. Furthermore, the relaxation function of order one depends only on the creep function of order one, through an equation identical to that obtained in linear viscoelasticity. The resolution of this last equation (by standard methods used in linear viscoelasticity) gives the solution for higher orders by quadratures. In the case without aging, the usual Carson‐Laplace transform method can be used to solve the first equation and perform the quadratures. These results have been obtained by direct calculations which are a little tedious and are not given here. However, an explicit derivation of the system of Volterra equations is given in the Appendix, for the nonaging case. This derivation is made by use of the Hn transform, which is based on the multidimensional Carson‐Laplace transform.
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83.60.Df Nonlinear viscoelasticity
83.10.Gr Constitutive relations
47.11.-j Computational methods in fluid dynamics

Viscosity Rise during Free Radical Crosslinking Polymerization with Inhibition

Victor M. González‐Romero and Christopher W. Macosko

J. Rheol. 29, 259 (1985); http://dx.doi.org/10.1122/1.549790 (14 pages)

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A study of the viscosity rise during free radical crosslinking polymerization is presented. Techniques were developed for monitoring isothermal viscosity rise during fast polymerization reactions. The chemical system used was composed of a dimethacrylate resin in styrene monomer, t‐butyl perbenzoate initiator, and hydroquinone as the inhibitor. When reduced viscosity is plotted versus conversion, data at all temperatures collapsed into a single curve. A theoretical equation is suggested for the time required to reach the gel point in free radical crosslinking polymerization with inhibition. This equation showed good agreement with experimental observations.
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81.05.Lg Polymers and plastics; rubber; synthetic and natural fibers; organometallic and organic materials
47.11.-j Computational methods in fluid dynamics
83.60.Bc Linear viscoelasticity

Stress Relaxation and Differential Dynamic Modulus of Polyisobutylene in Large Shearing Deformations

Yoshinobu Isono and John D. Ferry

J. Rheol. 29, 273 (1985); http://dx.doi.org/10.1122/1.549791 (8 pages) | Cited 1 time

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Stress relaxation in shear has been measured at 25°C for a polyisobutylene sample with viscosity average molecular weight 7.7×105, at shear strains γ from 0.2 to 0.5, over a time scale from 102 to 104.5 s. In this range, the relaxation modulus G(γ;t) could be expressed by the product G(0;t)h(γ); at γ=0.5, h=0.76. Simultaneous measurements of the differential storage and loss shear moduli, G′(ω,γ;t) and G″(ω,γ;t) were made throughout the relaxation process by intermittently superposing small oscillating deformations with a maximum additional strain of 0.01, at a frequency of about 0.33 Hz, which falls in the middle of the plateau zone of the polymer. For γ=0.2, G′ and G″ remained unchanged from their values at zero static strain, G′(ω,0) and G″(ω,0) respectively, confirming that the density of entanglements (or topological obstacles, or temporary network junctions), remains constant throughout the relaxation process at small strains. At higher strains, G″ was nearly constant, but G′ was somewhat smaller at the first measurement after imposition of static strain and slowly recovered to its original zero‐strain value. The behavior could be qualitatively interpreted by the Doi theory which includes both an equilibration process characterized by a time τe and a disengagement process characterized by a time τd; the decrease in G′ would correspond to loss of entanglements by the contraction of stretched molecules during equilibration and the subsequent increase to reestablishment of new entanglements by reptation during disengagement.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.60.Bc Linear viscoelasticity

On the Origin of Negative Normal Stresses in Sheared or Lyotropic Liquid Crystals

Charles E. Chaffey and Roger S. Porter

J. Rheol. 29, 281 (1985); http://dx.doi.org/10.1122/1.549792 (25 pages) | Cited 1 time

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In steady shear flow, sustained negative primary normal‐stress differences have been reported for several liquid crystalline systems, in most detail for m‐cresol solutions of helicoidal polypeptides and for copolyesters. A theoretical model is herewith proposed in which “dumbbell” molecules are constrained from rotating freely in the shear flow by the intermolecular potential that produces liquid crystalline order. In steady state, the molecules are imperfectly aligned, corresponding to a shortening or buckling of molecular layers. The tendency for the layers to straighten toward perfect order causes a compressive force along the streamlines, corresponding to a negative normal stress. For this actually to occur, a dimensionless group (containing the molecular axial ratio, shear rate, solute volume fraction and intermolecular potential) is predicted to be within a restricted range. The experimentally observed range for the polypeptide solutions is wider, probably because of polydispersity (imperfect monodispersity), and the theory underestimates the magnitude of observed negative normal stress. Although the copolyesters must be characterized by different independent variables, again one can identify a dimensionless group such that all the negative normal stresses occur within a restricted range. This simple model identifies dimensionless variables that will be important in any detailed microrheological theory based on calculating the distribution of molecular orientations.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Ax Steady shear flows, viscometric flow
83.85.Lq Normal stress difference measurements

Longitudinal Volume Viscosity of Poly(butylene terephthalate)

M. Sanchez‐Sancha and J. V. Aleman

J. Rheol. 29, 307 (1985); http://dx.doi.org/10.1122/1.549810 (15 pages)

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The volume flow of poly(butylene terephthalate) (PBT) of mathn=19,600, Tm=598 K and Tg=316 K, has been measured in an Instron Capillary Rheometer. The elastic modulus of the longitudinal wave, longitudinal volume viscosity, initial longitudinal volume viscosity, and retardation times are described at temperatures above the melting temperature (493 K), and compression rates of ca. 1 to 200×10−5 s−1. An increase in longitudinal volume viscosity with decreasing volume deformation, increasing compression rate, and increasing temperature has been observed. The volume flow activation energy decreases as the volume deformation increases.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Cg Rheological measurements—rheometry
83.85.Jn Viscosity measurements

Molecular Weight Dependency of Rheological Characteristics of Linear Low Density Polyethylene

D. Acierno, A. Brancaccio, D. Curto, F. P. La Mantia, and A. Valenza

J. Rheol. 29, 323 (1985); http://dx.doi.org/10.1122/1.549793 (12 pages)

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Five samples of linear low density polyethylene, polymerized with l‐butene as comonomer and having different molecular weights but similar molecular weight distributions, have been characterized in shear and nonisothermal elongational flow. From the experimental data, generalized relationships have been found for the zero shear viscosity, the shift factors of the whole viscosity curve, the critical shear rate, the melt strength and the breaking‐stretching ratio. It is then possible to predict with very good confidence values for the most important rheological characteristics of any LLDPE of similar polydispersity from the sole knowledge of the weight average molecular weight, in the range of temperature and flow conditions of industrial interest.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Jf Extensional flow and combined shear and extension
83.85.Jn Viscosity measurements

Direct Yield Stress Measurement with the Vane Method

Nguyen Q. Dzuy and D. V. Boger

J. Rheol. 29, 335 (1985); http://dx.doi.org/10.1122/1.549794 (13 pages) | Cited 16 times

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In the vane method for measuring the yield stress, the conventional analysis assumes that the stress is uniformly distributed on a cylindrical sheared surface to calculate the yield stress from the maximum torque and vane dimensions. By using two simple procedures, the present work shows that this assumption is justified at the moment of yielding. The yield stress calculated using the proposed methods compares favorably with that obtained with the conventional procedure. A comparison with the yield stress independently determined by other methods again confirms the usefulness of the vane technique as a simple but accurate method for direct yield stress measurement.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.La Viscoplasticity; yield stress
83.10.Gr Constitutive relations

Rheological and Pipeline Flow Behavior of Corn Starch Dispersions

Richard G. Griskey, D. G. Nechrebecki, P. J. Notheis, and R. T. Balmer

J. Rheol. 29, 349 (1985); http://dx.doi.org/10.1122/1.549816 (12 pages)

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The rheological and pipeline flow behavior of corn starch dispersions has been studied. It was found that the flow characteristics of these systems gave dilatant (shear thickening) behavior until a critical shear rate was attained at which point Newtonian behavior commenced. This critical shear rate, as well as the behavior of power law index and consistency index were found to be functions of percent volume concentration. Additionally, the behavior of these rheological parameters was explained on the basis of an existing theory describing shear thickening. Pipeline flow data confirmed that dilatant (shear thickening) fluids followed the Metzner‐Reed friction factor relationships in the laminar region. The range of behavior was extended to fluids having n values of 2.92 and volume concentrations of 40.0 percent. Finally, it was found that transition and turbulent flow could not be attained for dilatant (shear thickening) corn starch suspensions. This principally occurred because the critical shear rates yielding Newtonian behavior were excluded.
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83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.85.Cg Rheological measurements—rheometry
83.60.Pq Time-dependent structure (thixotropy, rheopexy)

Do Polymers Really Climb Rods?

Ole Hassager

J. Rheol. 29, 361 (1985); http://dx.doi.org/10.1122/1.549817 (4 pages) | Cited 2 times

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Abstract Unavailable
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Lh Slip boundary effects (interfacial and free surface flows)
47.50.-d Non-Newtonian fluid flows

The Response of Elastic Fluids to a Step Shear Strain

W. E. Vanarsdale

J. Rheol. 29, 365 (1985); http://dx.doi.org/10.1122/1.549795 (4 pages)

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Abstract Unavailable
Show PACS
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Ax Steady shear flows, viscometric flow
47.11.-j Computational methods in fluid dynamics
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