11.2 FOAM FORMATION AND PROPERTIES
When a foam is made in a vessel containing a low-viscosity liquid, either by
injection of air bubbles or by beating, phenomena as illustrated in Figure
11.1 will generally occur. As mentioned, foam bubbles are fairly large, and
they cream rapidly, at a rate of 1 mm?s^1 or faster. They thereby form a
layer on top of the liquid. As soon as the layer is a few bubble diameters in
thickness, buoyancy forces cause the bubbles to deform each other against
their Laplace pressure, further increasing the volume fraction of air in the
layer. Often, the bubble size distribution becomes fairly monodisperse,
because small bubbles disappear by Ostwald ripening [see Section 10.5.3,
especially Eq. (10.9)]: small bubbles have a high Laplace pressure, so the air
inside has an increased solubility in water, and the air diffuses to larger
bubbles nearby. Since the diffusional distance is small, this process can be
quite rapid.
11.2.1 Geometry
The phenomena just mentioned lead to formation of apolyhedral foam: the
shape of the air cells approximates polyhedra. For cells of equal volume, the
shape would be about that of a regular dodecahedron (a body bounded by
12 regular pentagons), and the edgeqthen equals about 0.8r, whereris the
radius of a sphere of equal volume. Actually, the structure is less regular,
because of polydispersity. Moreover, close packing of true dodecahedrons is
not possible. In a ‘‘two-dimensional’’ foam, say, one layer of bubbles
FIGURE11.1 Subsequent stages, from (a) via (b) to (c), in the formation of a foam
after bubbles have been made. The thickness of the films between bubbles is too
small to be seen on this scale.