Summary
A new and very general expression is proposed for correlation of data for the effective viscosity of pseudoplastic and dilatant fluids as a function of the shear stress. Most of the models which have been proposed previously are shown to be special cases of this expression. A straightforward procedure is outlined for evaluation of the arbitrary constants.
Zusammenfassung
Eine neue und sehr allgemeine Formel wird für die Korrelation der Werte der effektiven Viskosität von strukturviskosen und dilatanten Flüssigkeiten in Abhängigkeit von der Schubspannung vorgeschlagen. Die meisten schon früher vorgeschlagenen Methoden werden hier als Spezialfälle dieser Gleichung gezeigt. Ein einfaches Verfahren für die Auswertung der willkürlichen Konstanten wird beschrieben.
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Abbreviations
- b :
-
arbitrary constant inSisko model (eq. [5])
- n :
-
arbitrary exponent in eq. [1]
- x :
-
independent variable
- y(x) :
-
dependent variable
- y 0(x):
-
limiting behavior of dependent variable asx → 0
- y∞(x) :
-
limiting behavior of dependent variable asx → ∞
- z :
-
original dependent variable
- α :
-
arbitrary constant inSisko model (eq. [5]) andBird-Sisko model (eq. [6])
- β :
-
arbitrary exponent in eqs. [2] and [8]
- η :
-
effective viscosity = shear stress/rate of shear
- η A :
-
effective viscosity atτ = τ A
- η B :
-
empirical constant in eqs. [2] and [8]
- η 0 :
-
limiting value of effective viscosity asτ → 0
- η 0(τ):
-
limiting behavior of effective viscosity asτ → 0
- η ∞ :
-
limiting value of effective viscosity asτ → ∞
- η ∞(τ):
-
limiting behavior of effective viscosity asτ → ∞
- \(\dot \gamma \) :
-
rate of shear
- \(\dot \gamma _0 \) :
-
arbitrary constant inBird-Sisko model (eq.[6])
- τ :
-
shear stress
- τ A :
-
arbitrary constant in eqs. [2] and [8]
- τ 0 :
-
shear stress at\(\dot \gamma \to 0\) inBingham model
- τ 1/2 :
-
shear stress atη = (η 0 + η∞)/2
References
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Frederickson, A. G. Principles and Applications of Rheology, Prentice-Hall (Englewood Cliffs, N.J. 1964).
Sisko, A. W. Ind. Eng. Chem.50, 1789–1792 (1958).
Bird, R. B. Canad. J. Chem. Eng.44, 161–168 (1965).
White, R. R. andS. W. Churchill Amer. Inst. Chem. Eng. J.5, 354–360 (1959).
Ashare, E., Ph. D. Thesis, University of Wisconsin, Madison, Wisconsin (1970).
Bird, R. B. andP. J. Carreau Chem. Eng. Sci.23, 427–434 (1968).
Spriggs, T. W. Chem. Eng. Sci.20, 931–940 (1965).
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Churchill, S.W., Churchill, R.U. A general model for the effective viscosity of pseudoplastic and dilatant fluids. Rheol Acta 14, 404–409 (1975). https://doi.org/10.1007/BF01527134
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DOI: https://doi.org/10.1007/BF01527134