Sedimentation Profile. The value ofQgenerally is not constant
during sedimentation. If all particles have exactly the same size, and
sedimentation is not disturbed in any way, a concentration profile of
particles will develop as depicted in Figure 13.11a for creaming. A sharp
boundary between particle concentration¼0 and its original value develops,
moving upward at a constant rate. Hence the flux of particles to the cream
layer—which also has a sharp boundary—is constant until every particle has
arrived. However, nearly all dispersions are polydisperse, and then the
largest particles move fastest. At a given moment all of the larger particles
can be in the cream layer, whereas most of the smaller ones are still in
the subnatant. In other words, the magnitude ofd 53 in the subnatant (i.e.,
the liquid below the cream layer) will continuously decrease and thereby the
particle flux. Figure 13.11b gives an example of how the concentration
profile can evolve. The greater the width of the size distribution, the longer it
will take before sedimentation is complete (for the samed 53 value). This is
further illustrated in Figure 13.11d.
FIGURE13.11 Examples of the concentration profile developing during creaming
of O–W emulsions. Particle concentration is given as volume fractionj.His the
maximum creaming distance. The numbers near the curves denote time after starting
(say, in hours). (a) Calculated for a strictly monodisperse emulsion, assuming Eq.
(13.24) to hold. (b) Polydisperse emulsion, no aggregation. (c) Polydisperse emulsion
with aggregating droplets. (d) Percentage of the droplets creamed as a function of
relative time for the three cases a–c. Highly schematic and only meant to illustrate
trends.