Physical Chemistry of Foods

predictions. Equation (13.33) further implies that the shrinkage of a bubble
goes ever faster, so that it more or less implodes at the end; see Figure 13.23,
curve 2.

Surface Dilational Properties. The calculations just given
suggest that all foam will rapidly disappear, but several foams can be
fairly persistent, and some can hardly be destroyed. Stabilization to Ostwald
ripening (or to disproportionation as foam researchers usually call it) is thus
possible.
Consider a shrinking bubble with a surfactant layer. The decrease in
radius means a decrease in surface area, hence an increase in surface load,
hence adecrease in surface tension(cf. Section 10.2.3). This implies a
mechanism that counteracts the increase in Laplace pressure. The decrease
ingis expressed in the surface dilational modulus ESD:dg=dlnA[Eq.
(10.20)]. According to Gibbs, the following condition now determines
whether the bubble will be prevented from shrinking:

dpL

da

¼

dð 2 g=aÞ

da

¼

2 aðdg=daÞ
 2 g

a^2

¼

4 ESD
 2 g

a^2

50 ð 13 : 34 Þ

where use has been made of the relationdlnA¼(2/a)da. This simply comes
down to

ESD 5

g

2

ð 13 :34aÞ

FIGURE13.22 Concentrationcof the particle material in the continuous phase as
a function of the distance between two particles of different radii. The broken line
gives the concentration corresponding tos?. Concentration profile according to de
Vries (a) and according to SLW theory (b).