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Abstract

Normally, a unique shear stress-shear rate relationship for the laminar flow of any time independent non-Newtonian substance can be obtained from the correct interpretation of viscometric data. The flow curve or pseudo flow curve so obtained can be used to scale up to a diameter of interest. The transportation of non-Newtonian substances in the laminar regime is preferred in many engineering applications because of low energy consumption. However, there are also many situations where a density difference exists between the conveying liquid and solid particles in suspension which results in the tendency of the particles to settle. In order to ensure the stability of the suspension of particles such mixtures or substances must be transported in the turbulent regime.

Nomenclature

C

volume fraction solid in suspension

D

tube diameter

f

Darcy-Weisbach friction factor

g

gravitational acceleration

Ks

proportionality constant defined by eq. [10]

L

length of tube

P

pressure

Re

Reynolds number \( \frac{{\rho _m VD}} {{\mu _m }} \)

t

exponent defined by eq. [1]

V

mean velocity

V*

volume of particles in pipe length L

W

settling velocity of particles

αm

factor defined by eq. [1]

γ ̇

shear rate

γ ̇turb,

turbulent pseudo shear rate defined by eqs. [8] and [9]

τw

wall shear stress

w)s

increment in wall shear stress due to presence of settling particles

μm

limiting viscosity at high rate of shear

ρ1

density of carrier liquid

ρm

density of mixture

ρs

density of solid

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References

  1. 1).
    Harris, J., Rheol. Acta 7, 228 (1968).CrossRefGoogle Scholar
  2. 2).
    Metzner, A.B. and J. C. Reed, Amer. Inst. Chem. Eng. J. 1, 434 (1955).CrossRefGoogle Scholar
  3. 3).
    Dodge, D. W. and A. B. Metzner, Amer. Inst. Chem. Eng. J. 5, 189 (1959).CrossRefGoogle Scholar
  4. 4).
    Bowen, Le. B. R., Chem. Eng. J., June 26, 127 (1961); July 10, 147 (1961); July 24, 143 (1961).ADSGoogle Scholar
  5. 5).
    Thomas, D. G., Ind. Eng. Chem. 55, No. 12, 27 (1963).CrossRefGoogle Scholar
  6. 6).
    Vocadlo, J. J. and M. E. Charles, Proceedings Hydrotransport 2, British Hydromechanics Research Association (1972).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • J. J. Vocadlo
    • 1
  • P. J. Wheatley
    • 1
  • M. E. Charles
    • 1
    • 2
    • 3
  1. 1.Worthington (Canada) Ltd.BrantfordCanada
  2. 2.Dept. of Chem. Engineering and Applied ChemistryUniversity of TorontoTorontoCanada
  3. 3.Chemical EngineeringUniversity of Toronto and to Worthington (Canada) Ltd.Canada

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