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Rate Theories

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The Scientific Basis of Flocculation

Part of the book series: NATO Advanced Study Institutes Series ((NSSE,volume 27))

Abstract

The flocculation of particles in a liquid depends on collisions between particles, caused by their relative motion. This relative motion may be caused by Brownian movement, by fluid movement giving rise to velocity gradients, or by particle motion due to an external force (e.g. gravity).

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Abbreviations

d:

centre to centre distance between particles

m

Di :

diffusion coefficięnt for i-particle

m s2-1

g:

gravitational acceleration 9.81

m s-2

G:

velocity gradient

s-1

i:

label for particle of the ith kind

−

j:

label for particle of the jth kind

−

k:

label for particle formed by aggregation of i- and j-particles

−

KB :

Boltzmann’s constant 1.38 x 10-23

J K-1

L:

arc distance of a small sector of liquid undergoing rotational shear

m

Ni :

number of i-particles per unit volume

m-3

Nj :

number of j-particles per unit volume

m-3

NK :

number of k-particles per unit volume

m-3

NO :

initial (t=o) number of particles per unit volume

m-3

Nt :

total number of particles per unit volume at time t

m-3

p:

label for particles of a size limited by shear

−

P:

power dissipated in fluid motion

W

Q:

liquid flow due to velocity gradient

m s3-1

r:

radial distance from the centre of a collector

m

ri :

radius of an i-particle

m

rj :

radius of an j-particle

m

R:

radius of a small sector of liquid in rotational shear

m

Rij :

radius of interaction of i- and j-particles

m

s:

distance term in potential energy function

−

t:

time of flocculation

s

T:

absolute temperature

K

u:

local liquid velocity

m s-1

vi :

Stokes’ velocity of an i-particle

m s-1

vj :

Stokes’ velocity of an j-particle

m s-1

V:

liquid volume

m3

Vi :

volume of an i-particle

m3

Vs :

potential energy at distance s

J

x:

co-ordinate distance along streamline through centre of j-particle

m

y:

co-ordinate distance

m

z:

co-ordinate distance across velocity gradient

m

α:

collision efficiency

θ:

angle of rotation of a small sector of liquid

rad

μ:

dynamic viscosity of liquid

kg m-1 s-1

P:

density of liquid

kg m-3

Pi :

density of i-particles

kg m-3

Ps :

density of floc particles

kg m-3

Ï„:

shear stress in liquid

N m-2

φ:

floc volume per unit liquid volume

References

  1. Smoluchowski, M. von, Versuch einer Mathematischen Theorie der Koagulationskinetik Kolloide Losungen, Zeitschr. Phys. Chem., 92, 129, 1917.

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  2. Camp, T.R. and Stein, P.C., Velocity gradients and internal work in fluid motion, J. Boston Soc. Civ. Engrs., 30, 219, 1943.

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  3. Arp, P.A. and Mason, S.G., Orthokinetic collisions of hard spheres in simple shear flow, Can. J. Chem., 54, 3769, 1976.

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  4. Harris, H.S., Kaufmann, W.J. and Krone, R.B., Orthokinetic flocculation in water purification, J. San. Eng. Div., Proc. Am. Soc. Civ. Engrs., 92,(SA6), 95, 1966.

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  5. Ives, K.J. and Bhole, A.G., Theory of flocculation for continuous flow system, J. Env. Eng. Div., Proc. Am. Soc. Civ. Engrs., 99,(EE1), 17, 1973.

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  6. Fuchs, N., Uber die Stabilitat und Aufladung der Aerosole, Z. Physik, 89, 736, 1934.

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  7. Gregory, J., Flocculation Kineties. Chapter 7 in Monograph in Colloid Science Series, Academic Press, to be published 1977/78.

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  8. Van De Ven, T.G.M. and Mason, S.G., The microrheology of colloidal dispersions, IV. Pairs of interacting spheres in shear flow, J. Coll. Interface. Sci., 57, 505, 1976.

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  9. Ives, K.J., Theory of operation of sludge blanket clarifiers, Proc. Inst. Civ. Engrs., 39, 243, 1968.

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Author information

Authors and Affiliations

  1. University College London, UK

    K. J. Ives (Professor of Public Health Engineering)

Authors
  1. K. J. Ives
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Editor information

Editors and Affiliations

  1. Department of Civil and Municipal Engineering, University College London, UK

    Kenneth J. Ives (Professor of civil engineering) (Professor of civil engineering)

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© 1978 Sijthoff & Noordhoff International Publishers B.V.

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Ives, K.J. (1978). Rate Theories. In: Ives, K.J. (eds) The Scientific Basis of Flocculation. NATO Advanced Study Institutes Series, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9938-1_3

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  • DOI: https://doi.org/10.1007/978-94-009-9938-1_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9940-4

  • Online ISBN: 978-94-009-9938-1

  • eBook Packages: Springer Book Archive

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