neck containing a crystal. Often the junction becomes larger and firmer
upon aging.
Consequences. Partial coalescence differs from true coalescence in
two important respects.
(a) The process tends to be very muchfasterthan true coalescence,
especially if the emulsion is agitated. For emulsions with and without
crystals, but otherwise similar, coalescence rates often differ by a factor of
106 or even more. Moreover, the process proceeds like orthokinetic
aggregationrather than coalescence. At rest, partial coalescence generally
does not occur, although it may happen if the globules are closely packed.
An example is mayonnaise, wherej&0.8; when it is kept in a refrigerator,
some crystallization may occur in the oil droplets (depending on oil
composition), leading to partial coalescence.
(b) Sinceirregular aggregates or clumps are formed, the effective
volume fraction of the disperse phase increases. This causes an increase in
viscosity. In some cases, a space filling network of globules may even be
formed, although large aggregates are often broken up again during
agitation. Increasing the temperature of the aggregated system leads to
melting of the crystals and coalescence of the clumps into large droplets.
Partial coalescence is quite common for milk fat globules. It leads to
the formation of butter granules during churning of cream. Also in the
whipping of cream, and in the beating-annex-freezing of ice cream mix,
partial coalescence is essential, as it leads to the formation of a space filling
network. In these cases, the process is more complex because air bubbles are
generally present.
Aggregation Rate. We will consider primarily the orthokinetic
rate, since for the globule sizes involved (generally not below 1mm) it will be
much faster than perikinetic aggregation; see Section 13.2.2. The rate is the
product of the encounter frequency and the capture efficiencya. The latter
parameter can in principle be determined as the ratio of the observed
aggregation rate over the calculated one; the latter would roughly be given
by Eq. (13.8) (although a more sophisticated treatment is to be preferred).
Values ofabetween 10^6 and about 1 have been observed. The rate of
partial coalescence depends on a great number of variables. This is
illustrated by Figure 13.21; the presumed underlying mechanisms are
discussed below.
- Volume fraction of globules. Other things being equal, one expects
the encounter rate, and thereby the aggregation rate, to be proportional to
j^2. This is indeed observed (frame a). Forj>0.2 the aggregation rate tends
to increase more strongly withj.