Physical Chemistry of Foods

unstable, if the condition

d^2 VðhÞ

dh^2

<

2 p^2 g

R^2 f

ð 13 : 30 Þ

is fulfilled. HereV(h) is the total colloidal interaction free energy per unit
area as a function of distanceh(which equalsdin the present case), and
Rfis the radius of the film. It should be mentioned that for an interaction
profile as depicted in Figure 12.1 (solid curve), the instability criterion may
be met at a relatively large value ofh(near the secondary minimum), but
that upon closer approach the balance shifts again; if so, the film would be
stable.
The theory as discussed thus far already leads to some important
conclusions. The probability of film rupture will be smaller if

gis larger. This may look paradoxical: a surfactant is needed to make

and stabilize emulsions and foams, and it lowersg. Moreover, the

driving force for coalescence is that it causes the interfacial free

energy of the system to decrease, which decrease is greater for a

higher value ofg. This is true enough, but the probability of rupture

is not determined by the concomitant decrease in interfacial free

energy, but by an activation free energy, and the latter is smaller for

a lower interfacial tension.

Colloidal repulsion is stronger(ordremains larger). This is as expected.

The film is smaller, implying that the maximum possiblelvalue is

smaller. This means that smaller droplets or bubbles will be more

stable.

Notice that qualitatively the same effect of the values ofganddis also
predicted by Eq. (13.29).

Gibbs Elasticity. If no surfactant is present, a film is extremely
unstable. This may be due to colloidal repulsion then being very small, but
such films are observed to break at far largerdvalues than predicted. One
shortcoming of the original Vrij theory is that it assumes the interfaces to be
immobile in the tangential direction. However, if no surfactant is present,
this assumption is not true (see Section 10.7). Immobility requires a certain
Gibbs elasticity, or surface dilational modulusESD. It turns out that for a
thin film, the condition isESD>A/8pd^2 , whereAis the Hamaker constant.
The critical magnitude is virtually never larger than 1 mN?m
^1 , a value
that is nearly always reached unless the surfactant concentration is very
small.