Mutual Interference. One kind of change can affect the rate or
even the occurrence of the other. All changes leading to an increase in
particle size, i.e., (a–e), cause an enhanced sedimentation rate. The effect is
especially strong for aggregation, since sedimentation in turn tends to
enhance the aggregation rate. This means that all of the instabilities would
ultimately lead to demixing, unless aggregation results in the formation of a
space-filling network. Coalescence can only occur if the emulsion droplets or
the gas bubbles are close to each other, and in nearly all cases they have to
be close for a fairly long time, say at least a second. This then means that
coalescence generally has to be preceded either by aggregation or by
sedimentation. Coalescence eventually leads to phase separation,e.g.,
between oil and water.
As mentioned, particle size can increase by various mechanisms
(processes), and it depends on several internal and external variables which
process is predominant. To find a remedy for an undesirable change, it is
necessary to establish which process is occurring. Interference between the
various processes may make it difficult to establish the prime cause.
Free Energy Change. It may be enlightening to consider the
magnitude of the decrease in free energy (DG) involved in some of the
changes that can occur. Consider an O–W emulsion, oil volume fraction
j¼0.1, droplet diameter d¼ 1 mm, O–W interfacial tension
g¼10 mN?m^1.
Aggregation.DGwould amount to 0.5 times the coordination number
of the aggregated particles (say, 6), times the droplet number
concentration (¼ 6 j/pd^3 ), times the decrease in G due to the
formation of one particle–particle ‘‘bond’’ (for example, 500kBT).
This amounts to about 1 J?m^3.
Creaming over a height H (say, 20 cm) would lead to
DG¼ 0 : 5 ?j?Dr?g?H, whereris mass density. This amounts to
about 10 J?m^3.
Coalescence would lead to the release of the interfacial free energy,
which will roughly equal 6?g?j=d. The result is about
6? 103 J?m^3.
Oxidation of the oil is given for comparison. It would occur
spontaneously if the emulsion is in contact with air.DGwould be
given byjtimes the oil density (about 920 kg?m^3 ) times the heat
of combustion (about 37 MJ per kg of triglyceride oil). This result is
about 3: 4? 109 J?m^3.
It may also be illustrative to compare these quantities with the amount
of energy needed to heat the emulsion by 1 K, which equals about