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Aug 1990

Volume 34, Issue 6, pp. 787-992


Laminar jets of Bingham‐plastic liquids

K. R. J. Ellwood, G. C. Georgiou, T. C. Papanastasiou, and J. O. Wilkes

J. Rheol. 34, 787 (1990); http://dx.doi.org/10.1122/1.550144 (26 pages) | Cited 3 times

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The steady and transient behavior of jets generated by circular and slit nozzles are analyzed by the Galerkin finite‐element method with free‐surface parametrization and Newton iteration. A novel constitutive equation is used to approximate Bingham liquids that is valid uniformly in yielded and unyielded domains and which approximates the ideal Bingham model and the Newtonian liquid in its two limiting behaviors. At steady state the influence of yield stress on the die swell is equivalent to that of surface tension; that is, suppression of jet diameter at low Reynolds numbers and necking at high Reynolds number. The predictions at high Reynolds numbers agree with the asymptotic behavior at infinite Reynolds number of the jet far downstream. In the transient analysis, surface tension destabilizes round jets and increases the size of satellite drops. Yield stress was found to retard jet breakup times in addition to producing smaller satellites. Shear thinning was found to result in shorter collapse times than those for Newtonian fluid; furthermore, the satellite drop size increased with increasing shear thinning. The nonlinear analysis predicts that, although round jet breakup may occur spontaneously by surface tension, an external factor, commonly air shear, must be applied to break a planar jet at Reynolds numbers below its transition to a turbulent jet.
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47.27.wg Turbulent jets

A torsional dilatometer for volume change measurements on deformed glasses: Instrument description and measurements on equilibrated glasses

Randolph S. Duran and Gregory B. McKenna

J. Rheol. 34, 813 (1990); http://dx.doi.org/10.1122/1.550150 (27 pages) | Cited 4 times

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An automated mercury dilatometer has been designed and built for the purpose of making volume change measurements on cylindrical samples subjected to torsional deformations. In its current configuration the instrument takes readings of torque, normal force, and volume change upon application of a twist at one end of the sample. Volume change sensitivity of approximately 2× 10−6cm3 makes possible relative volume change measurements of the order of ΔV/V0≂10−7 given the sample geometry. Over long times temperature stability limits this to approximately 2.5×10−5. The instrument is described and preliminary measurements are presented for epoxy glasses which have been equilibrated by annealing near to the glass transition. The results show that the volume of the sample tested at temperatures ranging from 10 K below the conventionally measured glass transition temperature Tg to Tg increases upon application of a torsional deformation. This result is contrary to results reported in the literature for samples tested well below Tg.
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06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
46.35.+z Viscoelasticity, plasticity, viscoplasticity
46.80.+j Measurement methods and techniques in continuum mechanics of solids

The vane‐in‐cup as a novel rheometer geometry for shear thinning and thixotropic materials

H. A. Barnes and J. O. Carnali

J. Rheol. 34, 841 (1990); http://dx.doi.org/10.1122/1.550103 (26 pages) | Cited 7 times

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We have addressed the question of the suitability of the vane‐in‐cup as a rheometer geometry. A numerical simulation of this geometry was conducted for a power‐law fluid and the results compared with a similar study for a conventional bob‐in‐cup geometry. The comparison indicates that for a sufficiently shear‐thinning fluid (of shear‐thinning index less than 0.5) the fluid within the periphery of the vane blades is essentially trapped there and turns with the vane as a solid body. Calculation of the shear stress at the cup wall indicates that this quantity is equal in both geometries for a given rotational rate of the spindle. Thus the torque required to turn the spindle would be the same and identical flow curves would be predicted. This prediction was tested on two fluids thought to possess a yield stress: a 5.5% sodium carboxymethylcellulose (CMC) solution and a 4.2% Veegum PRO clay suspension. Equivalent flow curves were obtained at very low stresses/shear rates but a sudden, catastrophic viscosity loss was found for both fluids with the bob at shear rates which were still quite low. Such a loss was observed with the vane as well, but at much higher shear rates. It is suggested that this phenomenon is a form of apparent slip due to the formation of a thixotropic layer at the bob/vane surface. The much flatter stress profile obtained in the vane geometry is reasoned to postpone the formation of this layer. Rheological data obtained with the vane appear to be a faithful representation of these materials and show the absence of a true yield stress.
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47.80.-v Instrumentation and measurement methods in fluid dynamics

Determining the molecular weight distribution from the stress relaxation properties of a melt

W. J. McGrory and W. H. Tuminello

J. Rheol. 34, 867 (1990); http://dx.doi.org/10.1122/1.550104 (24 pages) | Cited 1 time

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The molecular weight distributions of well‐characterized polystyrenes were determined from their stress relaxation modulus as a function of time G(t). Linear viscoelastic measurements were made in the ‘‘terminal zone’’. The weight fraction of chains as a function of molecular weight was determined by assuming that the shorter (relaxed) chains, which are the first to disentangle from the transient network of entanglements, act as diluent for the longer (unrelaxed) chains. Nearly monodisperse samples were found to have false bimodal distributions although the breadth of these distributions was clearly distinguishable from the samples with broader molecular weight distributions. The distributions determined for a broader distribution sample or ones with truly bimodal distributions were closer to the shapes determined by size exclusion chromatography. The unexpected results for the narrow distribution samples were attributed to the oversimplified dilution assumption stated above.
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36.20.Cw Molecular weights, dispersity

On the apparent relation between adhesive failure and melt fracture

Davide A. Hill, Tomiichi Hasegawa, and Morton M. Denn

J. Rheol. 34, 891 (1990); http://dx.doi.org/10.1122/1.550105 (28 pages) | Cited 17 times

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The theory of adhesive failure between elastomers and a nonpolymeric surface provides a framework for the analysis of melt fracture in polymer melts. Peeling experiments on LLDPE below the melt processing temperature are shown to predict the onset of melt extrudate surface distortion and the functional form and magnitude of subsequent wall slip in capillary flow experiments using the same polymer. The equation for the slip velocity is based only on peeling experiments and knowledge of the temperature‐ and pressure‐dependence of the viscoelastic shift factor.
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46.35.+z Viscoelasticity, plasticity, viscoplasticity
46.55.+d Tribology and mechanical contacts

Defect‐mediated transition in a nematic flow

Alejandro D. Rey

J. Rheol. 34, 919 (1990); http://dx.doi.org/10.1122/1.550106 (24 pages)

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Three numerical solutions of the Leslie–Ericksen equations for low‐molar‐mass rod‐like nematic liquid crystals are obtained for pressure‐driven radial outflow between concentric parallel disks. This radial geometry promotes the director escape from the shear plane; two dissipatively equivalent out‐of‐plane modes appear. The bulk of the flow consist of three distinct regions separated by sharp boundaries. The centerline, elongation‐dominated, region is characterized by complete azimuthal director alignment. The two neighboring regions are shear dominated, and characterized by an in‐plane flow‐aligned director field. The high elastic twist strains are relieved by the nucleation and growth of a twist disclination loop of strength ±1/2 that nucleates in the entrance hole region of the cell. The loop growth transforms the highly twisted out‐of‐plane modes into a twist‐free, flow‐aligned, in‐plane mode.
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62.60.+v Acoustical properties of liquids
61.30.Jf Defects in liquid crystals

A constitutive analysis of extensional flows of polyisobutylene

M. H. Wagner and A. Demarmels

J. Rheol. 34, 943 (1990); http://dx.doi.org/10.1122/1.550107 (16 pages) | Cited 4 times

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By analyzing uniaxial, planar, ellipsoidal, and equibiaxial extension data, a viscoelastic constitutive equation of the single integral form is derived for a polyisobutylene (PIB) melt. Within experimental limits, time and strain effects are separable. The strain dependence corresponds to a Mooney‐type combination of Finger and Cauchy tensors, modified by a damping function h(I1,I2), which depends on the strain invariants I1 and I2 of the Finger tensor. It is shown that the ratio of the second to the first normal stress difference in shear flow β can be extracted from planar extension experiments. For the PIB melt considered, β turns out to be negative and equal to β=−0.27, and to be independent of strain. The influence of β on the tensions in general extensional flow is discussed.
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46.35.+z Viscoelasticity, plasticity, viscoplasticity
62.60.+v Acoustical properties of liquids

Transient shear flow of nematic liquid crystals: Manifestations of director tumbling

Wesley R. Burghardt and Gerald G. Fuller

J. Rheol. 34, 959 (1990); http://dx.doi.org/10.1122/1.550151 (34 pages) | Cited 7 times

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Calculations of a variety of transient flow phenomena based on the Leslie–Ericksen model for nematic liquid crystals are presented. Emphasis is placed on the behavior of nematics subject to director tumbling. A wide range of complicated transient phenomena such as oscillatory responses are predicted when the Ericksen number is sufficiently high to cause significant rotation of the director at steady state. Particular attention is given to relaxation processes such as constrained elastic recoil and stress relaxation that arise from the interaction of the relaxing director profile with the viscous response of the nematic. These relaxation processes are dramatically different in tumbling and flow aligning systems, due to the saturation of the director profile at high Ericksen number for the flow aligning case. A qualitative physical model of a textured polymer liquid crystal is presented in which the dynamics on a local scale governed by the distance between defects are assumed to be similar to the macroscopic dynamics presented in these calculations. By assuming (i) director tumbling and (ii) the existence of a limiting Ericksen number in polymer systems, a wide range of published observations in lyotropic liquid crystalline polymer solutions may be qualitatively reproduced.
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62.60.+v Acoustical properties of liquids
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