coalescence in a finished emulsion and during emulsification are due to
different mechanisms, at least for many surfactants.
Figure 11.12b shows two drops coming close to each other during
emulsification; it must be assumed that they are not (yet) fully covered by
surfactant. Now c-gradientswill be formed as depicted, because (a) the
outflow of liquid from the thin film will produce them (see Figure 10.28b);
and (b) any additional adsorption of surfactant during the approach will be
least where the film is thinnest. The viscous stress that can be balanced by
such ag-gradient will be roughly twiceDgover the distance, for which we
may take aboutd/2. Assuming thatDgcan reach a value of 0:01 N?m^1 ,
and thatd¼ 1 mm, the maximum stress would be about 4? 104 Pa, i.e., on the
order of the hydrodynamic pressure acting on the droplet pair. It would
certainly be enough to slow down greatly the approach of the droplets,
because it would fully prevent slip of the liquid flowing out of the film at the
droplet surfaces. It cannot, in itself, prevent collision of the drops, but it
would slow down their approach sufficiently during the time that the drops
are being pressed together. Equation (11.9) gives the approximate lifetime of
an eddy, and it would roughly be a microsecond in the present case. Hence,
before the drops are close enough to coalesce, they would probably move
away from each other.
It may be noticed that this stabilizing mechanism resembles the one
prevailing in foam formation discussed in Section 11.2.3: the essential aspect
is the formation ofg-gradients for a long enough time. In foam formation
the recoalescence of bubbles occurs also, and g-gradients play a part in
counteracting this. However, the gradients tend to be much smaller than in
the case of emulsification. The maximum value ofDgmay be somewhat
larger, because there is more time for the surfactant to adsorb and change
conformation, but the effective distance by which it has to be divided is
much larger: the bubbles are typically two orders of magnitude larger than
emulsion droplets (Table 11.1).
The stabilizing mechanism discussed has been called the Gibbs–
Marangoni effect. The Marangoni effect would lead to an inflow of
continuous phase into the film because of theg-gradient formed. This will
presumably not occur in an early stage, because the hydrodynamic pressure
will cause a stronger outflow. As soon as this pressure relaxes, however, the
Marangoni effect may become significant, driving the drops apart. The
strength of theg-gradient developing will depend on theGibbs elasticityof
the film. Its magnitude will at least equal twice the surface dilatational
modulus and be higher for a film of a thickness far smaller than its diameter.
Figure 11.13 gives some examples of surface pressure against surface excess,
plotted in such a way that the slope of the curve would equal the value of
ESD(for not too highG). It is seen that SDS gives already an appreciable
singke
(singke)
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