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.
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Abbreviations
- C :
-
volume fraction solid in suspension
- D :
-
tube diameter
- f :
-
Darcy-Weisbach friction factor
- g :
-
gravitational acceleration
- K s :
-
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
- α m :
-
factor defined by eq. [1]
- γ ̇:
-
shear rate
- γ ̇turb, :
-
turbulent pseudo shear rate defined by eqs. [8] and [9]
- τ w :
-
wall shear stress
- (τ w ) s :
-
increment in wall shear stress due to presence of settling particles
- μ m :
-
limiting viscosity at high rate of shear
- ρ1 :
-
density of carrier liquid
- ρ m :
-
density of mixture
- ρ s :
-
density of solid
References
Harris, J., Rheol. Acta 7, 228 (1968).
Metzner, A.B. and J. C. Reed, Amer. Inst. Chem. Eng. J. 1, 434 (1955).
Dodge, D. W. and A. B. Metzner, Amer. Inst. Chem. Eng. J. 5, 189 (1959).
Bowen, Le. B. R., Chem. Eng. J., June 26, 127 (1961); July 10, 147 (1961); July 24, 143 (1961).
Thomas, D. G., Ind. Eng. Chem. 55, No. 12, 27 (1963).
Vocadlo, J. J. and M. E. Charles, Proceedings Hydrotransport 2, British Hydromechanics Research Association (1972).
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© 1975 Springer-Verlag Berlin Heidelberg
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Vocadlo, J.J., Wheatley, P.J., Charles, M.E. (1975). Turbulent flow of non-Newtonian substances. In: Vallet, G., Meskat, W. (eds) Rheological Theories · Measuring Techniques in Rheology Test Methods in Rheology · Fractures Rheological Properties of Materials · Rheo-Optics · Biorheology. Steinkopff, Heidelberg. https://doi.org/10.1007/978-3-662-41458-3_202
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DOI: https://doi.org/10.1007/978-3-662-41458-3_202
Publisher Name: Steinkopff, Heidelberg
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