523 The Kynch theory of sedimentation
The behaviour of concentrated suspensions during sedimentation has been analysed by Kynch1-46-1, largely using considerations of continuity. The basic assumptions which are made are as follows:
(a) Particle concentration is uniform across any horizontal layer,
(b) Wall effects can be ignored,
(c) There is no differential settling of particles as a result of differences in shape, size, or composition,
(d) The velocity of fall of particles depends only on the local concentration of particles,
(e) The initial concentration is either uniform or increases towards the bottom of the suspension, and
(f) The sedimentation velocity tends to zero as the concentration approaches a limiting value corresponding to that of the sediment layer deposited at the bottom of the vessel.
If at some horizontal level where the volumetric concentration of particles is C and the sedimentation velocity is uc, the volumetric rate of sedimentation per unit area, or flux, is given by:
Then a material balance taken between a height H above the bottom, at which the concentration is C and the mass flux is f, and a height H + dH, where the concentration is
C + (dC/dH)dH and the mass flux is f + (df/dH)dH, gives:
That is: Hence: Thus:
df Jh dC
Ht df df dC df dC
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