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Abstract

A common geometry used in rotational viscometry consists of two concentric cylinders in which the test fluid is sheared in the annulus between the cylinders. In this type of instrument the calculation of the shear stress from the measured torque is straightforward but the determination of the corresponding rate of shear is a difficult problem unless the type of fluid behavior, e.g. power law, is known a priori. The equation of motion may be solved (1) analytically for the special case of power-law behavior but a completely general analysis results in an expression for the difference in the rates of shear at the two surfaces (2).

Abbreviations

Nomenclature

CR

correction factor for non-Newtonian effects

CRa

correction factor based on constant power-law departure factor α

CRP

correction factor based on power-law approximation

Crk3

correction factor based on three-term series of Krieger and Elrod

Crk4

correction factor based on four-term series of Krieger and Elrod

f(τ)

rate of shear = dv/dr

K

consistency index

m

reciprocal of flow-behavior index = 1/n = d In Μ/ dln τ

n

flow-behavior index = dln τ/dlnΩ

N

number of terms

p

index variable

r

radial direction

s

radius ratio = r 1/r 2

v

linear velocity

α

power-law departure factor = dlnm/dlnτ

τ

shear stress

ω or Ω

angular velocity

Subscripts

r

radial direction

θ

angular direction

1

outer surface of inner cylinder

2

inner surface of outer cylinder

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References

  1. 1).
    Brodkey, R. S., Ind. Eng. Chem. 54, No. 9, 44 (1962).CrossRefGoogle Scholar
  2. 2).
    Brodkey, R. S., The Phenomena of Fluid Motions, p. 422 (Reading, Massachusetts, 1967).Google Scholar
  3. 3).
    Middleman, S., The Flow of High Polymers, p. 21 (New York 1968).Google Scholar
  4. 4).
    Coleman, B. D. and W. Noll, Arch. Ratl. Mech. Anal. 3, 289 (1959).CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5).
    Krieger, I. M. and H. Elrod, J. Appl. Phys. 24, 134 (1953).ADSCrossRefzbMATHGoogle Scholar
  6. 6).
    Krieger, I. M. and S. H. Moron, J. Appl. Phys. 25, 72 (1954).ADSCrossRefGoogle Scholar
  7. 7).
    Savins, J. G., G. C. Wallick, and W. R. Foster, Soc. Pet. Engrs. J. 2, 211 (1962).Google Scholar
  8. Savins, J. G., G. C. Wallick, and W. R. Foster, Soc. Pet. Engrs. J. 3, 14, 177 (1963).Google Scholar
  9. 8).
    Van Wazer, J.R., et al., Viscosity and Flow-Measurement, p. 68 (New York 1963).Google Scholar
  10. 9).
    Mooney, M., J. Rheol. 2, 210 (1931).ADSCrossRefGoogle Scholar
  11. 10).
    Metzner, A. B., in: Handbook of Fluid Dynamics, Chapt. 7, p.13 (New York 1961).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • R. K. Code
    • 1
  • J. D. Raal
    • 1
  1. 1.Department of Chemical EngineeringQueen’s UniversityKingstonCanada

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