drainage of the foam layer then leads to a high volume fraction of gas. A
highly concentrated O–W emulsion is more difficult to make: a high ratio of
oil to water is needed and a high concentration of a suitable surfactant.
Agitation then has to provide the forces needed to obtain permanently
deformed droplets. An alternative is to subject a less concentrated emulsion
to centrifugation. Repulsive colloidal interaction forces between the bubbles
or droplets prevent breaking of the thin films between them.
The particles thus do not necessarily attract each other. If a lump of a
foam or an emulsion is put in water or, preferably, in a solution similar to
the continuous phase, the lump often will slowly disperse. The slowness is
largely due to the channels through which the water has to penetrate being
quite narrow.
On deformation of the system, the bubbles are deformed, which
increases their Laplace pressurepL. Moreover, some films between particles
are stretched and others are compressed, causing surface tension gradients
to form, which also needs energy. Above a certain stress, yielding may
occur, which means that bubbles (or drops) start to slip past each other,
which generally occurs in planes about parallel to the direction of flow.
Calculation of theshear modulusand theyield stressfrom first principles is
virtually impossible because of the intricacy of the problem for a three-
dimensional and polydisperse system, but trends can be predicted. One
relation is that these parameters are proportional to theaverage apparent
Laplace pressure
pL;a¼4 g
d 32ð 17 : 20 Þwhere the values ofganddrefer to undeformed particles. Figure 17.27 gives
experimentally established relations.
For a typical food foam withd 32 ¼ 20 mm andgAW¼50 mN?m^1 we
havepL,a¼ 104 Pa. The same result is obtained for a typical O–W emulsion
made with protein and having d 32 ¼ 4 mm and gAW ¼10 mN?m^1.
Assumingj¼0.9, we then obtain from Figure 17.27G¼1600 Pa andsy¼
160 Pa. Putting a heap of this foam of heighthon a table, the gravitational
stress at the bottom will beghDr, and if this value is greater than the yield
stress, the lump will start to subside under its own weight. AssumingDr¼
100 kg?m^3 , the critical height for yielding to occur is 16 cm. For the
emulsion, whereDris about nine times as high, the critical height will be less
than 2 cm.
In practice, most systems are more complicated.Whipped toppings, for
instance, come in various types. Fairly simple are toppings with a gas
volume fraction>jcr. Since they also contain fat globules, the effectivej