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The definition and measurement of some characteristics of mixtures

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Summary

The systematic study of mixing processes requires a quantitative method of expressing “goodness of mixing”, based on conveniently-made measurements. In this paper, mixtures of mutually soluble liquids, fine powders, or gases are considered. It is shown that the important features of such mixtures can be expressed by two statistically-defined quantities, the scale and the intensity of segregation, and methods of measuring these are suggested. The discussion also throws light on some of the factors which affect the efficiency of mixing processes.

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Abbreviations

a :

Concentration (volume-fraction) of componentA

ā :

Mean concentration ofA in mixture

b :

Concentration (volume-fraction) of componentB

b :

Mean concentration ofB in mixture

c :

a−ā

d :

Diameter (of circle, strip, sphere or pipe)

D :

Diffusivity

I :

Intensity of segregation (defined by eqn. (14))

J :

Content ofA in line sample (eqn. (5))

k :

Reaction-velocity constant

K :

Content ofA in volume sample

l :

Length of section of pipe.

m :

Concentration of reactantM in solutionA (moles per unit volume).

n :

Concentration of reactantN in solutionB

r :

Distance apart of two points in mixture.

R(r) :

Correlation coefficient between points in mixture distancer apart.

S :

Linear scale of segregation (defined by eqn. (3))

t :

Time

T :

See eqn. (12)

u :

Velocity of flow

v :

Volume of sample

V :

Volume scale of segregation (defined by eqn. (4))

x :

Distance from one end of line-sample, or general spacecoordinate

X :

Length of line-sample

ξ :

Value ofr for whichR(r) falls to 0

ρ :

Mean reaction rate per unit volume of mixture

σ 2 :

Variance of quantity denoted by subscript

References

  1. Buslik, D., A.S.T.M. Bull.165 (1950) 66.

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  2. Danckwerts, P. V., and E. S. Sellers, Industrial Chemist27 (1951) 395.

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  3. Fluid Motion Panel, Aeronautical Research Committee, “rn Developments in Fluid Dynamics”, Vol. I, p. 269, Oxford University Press (1938).

  4. Moelwyn-Hughes, E. A., “Kinetics of Reaction in Solution”, Oxford University Press (1947).

  5. Taylor, G. I., Proc. Roy. Soc.A 151 (1935) 421.

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Authors and Affiliations

  1. Chemical Engineering Department of the University of Cambridge, Cambridge, UK

    P. V. Danckwerts

Authors
  1. P. V. Danckwerts
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Danckwerts, P.V. The definition and measurement of some characteristics of mixtures. Appl. sci. Res. 3, 279–296 (1952). https://doi.org/10.1007/BF03184936

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  • DOI: https://doi.org/10.1007/BF03184936

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