Physical Chemistry of Foods

gravitational pressure. The relation is

pL¼

g

R

¼rwgH ð 11 : 1 Þ

whererwis the density of the aqueous phase (assuming that of air to be
negligible) andHis the height above the bottom of the foam. This means
thatRis smaller at a greater height in the foam (compare Figures 11.3a and
b), i.e., the Plateau borders are thinner and the foam contains less water.
The bubbles in the bottom layer are practically spherical. Assuming all of
the water to be located in the Plateau borders, it can be derived from Eq.
(11.1) and the geometry of the system that the volume fraction of air in the
foam at a given heightHwill be given by

j& 1 
 0 : 5

g

rwgHq

 2

ð 11 : 2 Þ

where the length of the Plateau bordersqequals about 0.4 times the bubble
diameterd. The equation is only valid for values ofHabove which the
foam is truly polyhedral. To give an example: for d¼0.3 mm and
g¼50 mN?m
^1 , and at a height above the liquid of 0.1 m, we obtain
j& 0 :91; ford¼1 mm,jwould then be as large as 0.99. This would mean
that a foam can become very ‘‘dry.’’

FIGURE11.3 Cross sections through Plateau borders and films. (a) Illustration of
the difference of the Laplace pressure between border and film. (b) Plateau border at
a greater height in the foam.