The rate of recoalescence presumably depends on the time lapse
between mutual drop encounters tenc relative to the time needed for
adsorption of surfactanttads. When two drops come very close to each other
before they have acquired sufficient surfactant, they may coalesce, as
illustrated in Figure 11.10c. It can be derived from theory that in all regimes,
tads
tenc&
6 pGj
dcð 11 : 16 ÞFrom this relation it follows qualitatively that more recoalescence will occur
ifcis smaller, ifjis larger, and ifeis larger, since this implies thatd
becomes smaller. This agrees with experimental results on recoalescence and
also with results on average droplet size, as shown, for instance, in Figure
11.9b; an increase injin that case also implies a stronger decrease inc
during emulsification.
Note The picture in Figure 11.10c is to some extent misleading, in
that bare patches are shown on the drop surface. In fact, the
surfactant will generally be distributed more evenly over the
surface, since the spreading rate of surfactant will be quite high.
Equation (10.19) predicts spreading times< 1 ms for small drops
under most conditions.
Most surfactants provide colloidalrepulsionto act between droplets,
thereby preventing their close approach—hence coalescence—upon encoun-
tering each other, and it appears logical to assume that this mechanism also
acts during emulsification (see Figure 11.12a). However, the stress by which
the drops are driven toward each other can be very large. The magnitude is
about the same as that of the stress needed to break up the drops, hence of
the order of the Laplace pressure of the drops. For drops of 1mm, this
means about 2? 104 Pa. In Chapter 12, colloidal interactions between
particles are discussed. It can be derived that the so-called disjoining
pressure, the colloidal interaction force per unit area that drives the drops
apart, will for 1 mm droplets rarely be larger than 2? 102 Pa if due to
electrostatic repulsion. This would thus be far too small to prevent collision
and thereby coalescence.
Nevertheless, small-molecule ionic surfactants like sodium dodecyl
sulfate, which provide repulsion by electrostatic forces only, can be very
efficient in making emulsions with very small droplets, even at low
concentrations. If, then, moreover, the ionic strength is high, which will
greatly reduce the disjoining pressure, the droplet size distribution obtained
is the same as at low ionic strength, although the finished emulsion shows
rapid coalescence (and not at low ionic strength). Hence prevention of