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Nov 1991

Volume 35, Issue 8, pp. 1465-1699


Measurement of very low strains using a stress rheometer: A new rotation sensing transducer (RST)

A. Magnin and J. M. Piau

J. Rheol. 35, 1465 (1991); http://dx.doi.org/10.1122/1.550242 (15 pages) | Cited 1 time

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The problems posed by a controlled stress rheometer are studied in the low strain and slow strain rate domain, characteristic of the Newtonian plateau of polymers or of the yield stress vicinity for fluids with a yield stress. A drift in the rheometer strain measuring system was observed which attenuates and may even reverse the sign of the strain measured in comparison with that actually occurring. This drift may give the impression that a yield stress value is observed by inducing a constant strain in creep and hence a shear rate equal to zero. Investigations have shown that the major perturbations are introduced by the rheometer motor and drift depends on the torque level, time, and thermal conditions inside the tube where the motor and transducers are located. A new and more precise automatic measuring system, referred to as RST, has been developed. This may easily replace the existing rheometer strain measuring system. The lower limit of the shear rate that can be measured under steady conditions is reduced from about 10−4 to 10−8 s−1 and rapid transient measurements are possible.
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46.80.+j Measurement methods and techniques in continuum mechanics of solids
46.35.+z Viscoelasticity, plasticity, viscoplasticity

A new equation of the relaxation process in the nonequilibrium state: Application to creep and dynamic experiments in epoxy resins

G. Spathis, E. Kontou, and G. Bourkas

J. Rheol. 35, 1481 (1991); http://dx.doi.org/10.1122/1.550243 (17 pages)

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Following the Adam–Gibbs procedure for the calculation of the configurational entropy Sc, a Vogel–Fulcher type equation has been obtained, determined by a new structural parameter Tv. The equation obtained by this procedure in the equilibrium state reduces to a WLF form with universal constants, as expected. In the nonequilibrium state, an equation of the same form is determined with material‐dependent constants. Experimental data for three types of epoxy resins, obtained by creep and dynamic tests, were applied to evaluate this equation, and a common value of the activation energy H was found, it being constant for a wide temperature range in the glassy state.
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62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances
05.70.Ln Nonequilibrium and irreversible thermodynamics
82.40.Bj Oscillations, chaos, and bifurcations

Fiber–fiber interactions in homogeneous flows of nondilute suspensions

Sridhar Ranganathan and S. G. Advani

J. Rheol. 35, 1499 (1991); http://dx.doi.org/10.1122/1.550244 (24 pages) | Cited 6 times

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A theoretical model for calculating the average interfiber spacing in nondilute short fiber suspensions is presented. The approach adopts the Doi–Edwards theory to model spacing between rigid rod‐like polymer molecules to determine the interfiber spacing. Modifications have been introduced to the Doi–Edwards theory in order to obtain accurate estimates of interfiber spacing at all orientation states and for fibers of finite diameter. A parametric study has been conducted to explore the influence of the relevant dimensionless parameters: the fiber volume fraction, the fiber aspect ratio, and the probability distribution function of the fiber orientation state on the average spacing between the fibers. An approach has been suggested to use this spacing to characterize fiber–fiber interactions in flowing suspensions. Numerical predictions of flow‐induced fiber orientation based on this approach are presented.
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47.15.-x Laminar flows
82.70.Kj Emulsions and suspensions

The Einstein coefficient of suspensions in generalized Newtonian liquids

Jozua Laven and H. N. Stein

J. Rheol. 35, 1523 (1991); http://dx.doi.org/10.1122/1.550245 (27 pages)

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A new, theoretically more satisfactory, definition for relative viscosities of suspensions in generalized Newtonian media is presented, which according to the viscosities of suspensions and pure liquids should be compared to equal averaged squared strain rates γ̇2L in the liquid phases. Comparison of this quantity (ηLr) is made with two definitions currently in use, in which viscosities are compared either at equal macroscopic stresses τ or at equal macroscopic squared strain rates γ̇2m. Interrelations between the three different relative viscosities have been derived in the case of dilute suspensions of particles of arbitrary shape in generalized Newtonian liquids. Values for limiting viscosity number (Einstein coefficients KE) have been derived from experimental data on suspension viscosities both as obtained by the authors and as obtained from other sources. The data cover suspensions of spherical particles in liquids with power‐law exponents n between 0.07 and 1.0. According to the new definition the Einstein viscosity coefficient KE = limφ→0 (d ln η)/(dφ) is constant with a value of 2.5 over the whole range of n. According to the other definitions, KE is 2.5 only for n=1; with n decreasing to zero, KE decreases linearly to 0.75 (ηr under equal strain rate) or rises exponentially to ∞ (ηr under equal strain stress). The values of KE, as deduced from experiments, obey the theoretical interrelations derived. There are strong indications that the value of n has no influence on the inhomogeneity in rate of strain in dilute suspensions.
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66.20.-d Viscosity of liquids; diffusive momentum transport
46.80.+j Measurement methods and techniques in continuum mechanics of solids

The influence of end effects on birefringence measurements in nominally two‐dimensional channel flows

S. R. Galante and P. L. Frattini

J. Rheol. 35, 1551 (1991); http://dx.doi.org/10.1122/1.550251 (31 pages) | Cited 3 times

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We evaluate the influence of end effects in birefringence measurements made with polarization modulated methods on nominally two‐dimensional, viscometric, channel flows. The differential propagation Mueller matrix formulation is utilized to calculate the Mueller matrix and consequently the apparent retardation δ′ and extinction angle χ′ for flows of an upper‐convected Maxwell fluid. Optically isotropic boundary layers develop at the walls confining the flow along the optical path; and these layers reduce the observed retardation by reducing the effective optical pathlength relative to that of the ideal, two‐dimensional flow. Negative deviations of a few percent occur in δ′ when the flow aspect ratio is ten. Retardation errors increase with elasticity and flow rate and vary inversely with flow aspect ratio. For the three‐dimensional flow, χ′ is unchanged from the two‐dimensional flow value, provided that δ′≪2π; otherwise, large errors in χ′ can result near the positions where order transitions occur. The influence of end effects in flows of shear thinning fluids is also examined. We find that end effects decrease with decreasing power‐law exponent n such that the results for the constant‐viscosity fluids afford an upper bound for error analysis.
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42.25.Lc Birefringence
47.60.-i Flow phenomena in quasi-one-dimensional systems
62.60.+v Acoustical properties of liquids

The effect of particle size distribution on the antithixotropic and shear thickening properties of coal–water dispersions

D. S. Keller and D. V. Keller

J. Rheol. 35, 1583 (1991); http://dx.doi.org/10.1122/1.550246 (25 pages)

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The shear thickening rheology of coal–water suspensions prepared from six different naturally generated particle size distributions with mass median particle diameter d50 from 0.8 to 28 μm were investigated. Refined coal samples were thoroughly deflocculated with an anionic dispersant in water at particle concentrations from 47.7 to 56.4 vol %. The variations in flow behavior of the dispersions were observed in Couette flow as a function of shear rate in ramp tests and of time as a constant rate of shear was applied. Ramp test results indicated a decrease in the severity of shear thickening with increasing particle size distribution. Discontinuous shear thickening that occurred with the smaller particle sized samples was found to be approximated by a single function of the particle concentration reduced by the maximum packing fraction. The experimental results from constant shear rate experiments were compared in terms of the rate of antithixotropy, the extent of stress increase, and the total energy dissipated prior to shear thickening, as determined from characteristic points in the stress‐time rheograms. Significant differences in the shape of the antithixotropic curves were observed for the different particle size distributions. The magnitude of stress increase observed during the antithixotropic event was found to diminish with increasing particle size distributions which limited the detection of the antithixotropic event at the larger sizes. The extent of stress increase for the smaller particle sized samples, i.e., d50 < 3 μm, was such that the antithixotropic shear thickening appeared to dominate the flow behavior. A bimodal mixture of particles at d50 = 0.77 and 7.9 μm was also examined. An 8% increase in volumetric particle concentration was observed when compared to a monomodal suspension with equivalent d50 and average viscosity. No antithixotropic tendencies were observed with the bimodal suspension.
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82.70.Kj Emulsions and suspensions
47.15.-x Laminar flows

Technical Note: Angular compliance error in force rebalance torque transducers

M. E. Mackay and P. J. Halley

J. Rheol. 35, 1609 (1991); http://dx.doi.org/10.1122/1.550247 (6 pages) | Cited 1 time

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Abstract Unavailable
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46.80.+j Measurement methods and techniques in continuum mechanics of solids

On the viscosity‐concentration dependence of immiscible polymer blends

L. A. Utracki

J. Rheol. 35, 1615 (1991); http://dx.doi.org/10.1122/1.550248 (23 pages) | Cited 6 times

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Upon addition of small quantities of a second phase the mixture shows a droplet/matrix structure, changing into a co‐continuous one at the percolation threshold, ϕc≂0.16. The level of phase co‐continuity reaches a maximum at the phase inversion concentration, ϕ2I, where the viscosities of a system in which polymer‐1 is dispersed in polymer‐2 and the other where polymer‐2 is dispersed in polymer‐1 are equal. Thus ϕ1I can be expressed as function of viscosity ratio, λ=η1/η2, with intrinsic viscosity and maximum packing volume fraction as parameters. Next, it was postulated that in immiscible polymer blends the viscosity‐concentration dependence is determined by two mechanisms: an interlayer slip and the emulsionlike viscosity increase culminating at the inversion concentration, ϕ2I. The derived two‐parameter equation was found to describe the observed η versus ϕ dependence quite well. The parameters, calculated from the least‐squares regression fit of experimental data to the two‐parameter equation, were found to provide insight into the flow mechanism.
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61.41.+e Polymers, elastomers, and plastics
81.05.Lg Polymers and plastics; rubber; synthetic and natural fibers; organometallic and organic materials
62.60.+v Acoustical properties of liquids

A constitutive equation for the viscosity of stored red cell suspensions: Effect of hematocrit, shear rate, and suspending phase

A. L. Zydney, J. D. Oliver, and C. K. Colton

J. Rheol. 35, 1639 (1991); http://dx.doi.org/10.1122/1.550249 (42 pages) | Cited 1 time

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Despite the extensive previous work on the viscosity of red blood cell suspensions, experimental data at very high cell concentrations are limited and scattered, and available constitutive equations for the steady‐state viscosity are unsuitable for numerical calculations that require accurate well‐behaved analytical expressions valid over a wide range of shear rates and which include these very high cell concentrations. The steady‐state viscosity of suspensions of stored red blood cells in both saline and plasma were measured in a coaxial cylinder viscometer at shear rates ranging from below 1–300 s−1 and at cell volume fractions up to 0.98. Emphasis was placed on the evaluation of viscosity at very high cell concentrations because of the lack of available data in this regime and its importance in understanding and modeling cross‐flow microfiltration of red cell suspensions, the application which motivated the current study. This data base was supplemented by additional measurements previously reported in the literature for fresh blood. The data were correlated using a constitutive equation for the viscosity as a function of shear rate that has been used extensively in the development of rheological models for colloidal suspensions. The concentration dependence of the parameters in this model were then described using simple functional forms which incorporate available information on the physical principles governing the rheology of blood. The resulting constitutive equation provides a general expression for the viscosity as a function of shear rate, red cell concentration, and suspending phase viscosity. This equation agrees with available experimental data to within about ±14% for shear rates greater than 1 s−1 and to within ±9% for shear rates greater than 10 s−1, and it is well‐suited for numerical calculations of blood flow.
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87.19.rh Fluid transport and rheology

Flow‐induced anisotropy and its decay in polymeric liquid crystals

P. Moldenaers, H. Yanase, and J. Mewis

J. Rheol. 35, 1681 (1991); http://dx.doi.org/10.1122/1.550250 (19 pages) | Cited 2 times

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Flow induces anisotropy in polymeric liquid crystals. This can be demonstrated by comparing the stress transients during a sudden increase in shear rate with those during flow reversal: the damped oscillations of the shear stress resulting from these two experiments are shifted by nearly 180°. Flow‐induced anisotropy decays after the flow stops. Its evolution in time is followed by stress growth experiments in the flow direction and in the opposite one, with systematic changes in the rest period. The phase shift only disappears after several thousands of seconds. This time is much longer than the time necessary for the shear stress to relax. Other rheological characteristics, such as the variation of the dynamic moduli after stopping the flow, occur on the same time scale as the anisotropy decay. The anisotropy decay is not affected by temperature and consequently viscosity can be ruled out as a governing factor. The results agree in part with recent polydomain models.
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61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order
47.50.-d Non-Newtonian fluid flows
62.60.+v Acoustical properties of liquids
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