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Relative viscosity and concentration

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Summary

A survey is given of the very many equations which have been proposed for describing the relation between relative viscosity and concentration of various disperse systems. The functions have been grouped in a formal array, which makes the connections clearer. It becomes evident then where further possibilities exist, where further elaboration has no use, and in which section experimental checking is needed or might be useful. The formulas have all been examined on their validity for suspensions of spheres. The very large number of equations proposed could be reduced to only 5 or even 2 or 3 really valuable functions. It is indicated that the same reduction should be sought for other types of disperse systems.

Zusammenfassung

Es wird eine Übersicht über die große Zahl der vorgeschlagenen Gleichungen zur Beschreibung der Beziehungen zwischen der relativen Viskosität und der Konzentration für die verschiedenen dispersen Systeme gegeben. Die dargestellten Funktionen sind formal so gegliedert, daß die Zusammenhänge möglichst durchsichtig werden, um deutlich die weiteren bestehenden Möglichkeiten aufzuzeigen und ebenso die Formeln zu kennzeichnen, deren experimentelle Nachprüfung notwendig bzw. zweckmäßig erscheint. Alle Gleichungen sind in bezug auf ihre Gültigkeit für Suspensionen kugelförmiger Teilchen untersucht worden. Dabei konnte die angegebene sehr große Zahl der Beziehungen auf 5 oder sogar auf 2 bzw. 3 reduziert werden. Es wird angedeutet, daß eine vergleichbare Einschränkung der notwendigen Zahl der Gleichungen auch für die anderen Typen der dispersen Systeme gesucht werden sollte.

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Abbreviations

A, a :

Interaction factors

B, b :

Correction factors

c :

Concentration, volume fraction; other expressions of concentration mentioned in the text

c m :

Maximal concentration for infinite viscosity

c R :

Reduced concentration

D :

Rate of shear

f :

Factor or function

G :

Shear modulus

h :

Solvation factor

h 0 :

Solvation factor at infinite dilution

k :

Intrinsic viscosity = [η]

k 1 :

Modifications ofk

M :

Molecular weight

n :

Power

p :

Axial ratio of ellipsoids

r :

Sphere radius

R :

Distance of sphere centers

s :

Self crowding or sedimentation factor

v :

Linear velocity in fluidized beds

Z :

Reduced viscosity

Z w :

Weight average chain length

δ av :

Average particle distance

ɛ :

Porosity = (1 −c)

η :

Viscosity

η r :

Relative viscosity

η sp :

Specific viscosityη r − 1

η c :

Reduced viscosity =Z =η r = 1/c

lnη r/c:

Inherent viscosity

η ∞ :

Limiting viscosity at “infinite” rate of shear

[η]:

Intrinsic viscosity,\(\mathop {\lim }\limits_{c = 0} \cdot \frac{{\eta _r - 1}}{c}and\mathop {\lim }\limits_{c \to 0} \cdot \frac{{\ln \eta _r }}{c}\)

μ :

Micron, particle size

ϱ :

Specific gravity

τ :

Shear stress

ϕ :

Fluidity = 1/ηr

index 0:

medium or solvent

index 1:

disperse phase

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  1. Ir. R. Rutgers

    Present address: , Rippingstraat 39, Alkmaar, Holland

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  1. Laboratory Royal Mills of Laan Bros, Wormerveer, Netherlands

    Ir. R. Rutgers

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Cordial thanks are due to Mr.H. A. Bok, Director of the Royal Mills of Laan Bros, for giving the opportunity to do the present work, and to Mr.P. van Diepen and Mr.G. Blonk for preparing the typescript and the graphs.

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Rutgers, I.R. Relative viscosity and concentration. Rheol Acta 2, 305–348 (1962). https://doi.org/10.1007/BF01976051

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