Physical Chemistry of Foods

downstream. This implies that ag-gradientis formed. Such a gradient means
that there is atangential stress in the interfaceof magnitude dg/dx (in
N?m
^1 /m¼Pa). If this stress is large enough, the surface will be arrested,
and thereby any motion of the oil. The equality of stresses is given in the
relation

ZW

dvx

dy



y¼ 0

¼

dg

dx

ð 10 : 17 Þ

For a constant gradient, we can useDgrather than dg; its value can at most
equal the value ofP. Assuming this to be 0.03 N?m
^1 , andC¼ 103 s
^1 (i.e.,
quite a large value), we haveZW?C¼1 Pa, and Eq. (10.17) can be fulfilled
forDxup to 3 cm. This implies that a fluid interface that contains surfactant
and that is of mesoscopic size, say 0.01–100mm, would act as a solid wall for
nearly all tangential stresses that may occur in practice.
Ag-gradient is thus very effective in withstanding a tangential stress
and arresting tangential motion of an interface. Actually, the situation is
more complicated. Generally, the surfactant is soluble in at least one of the
phases, and exchange between interface and bulk will thus occur. Moreover,
Eq. (10.17) is not always fully correct. See further Section 10.8.3.
In Figure 10.28c another situation is depicted. Now surfactant is
applied at a certain spot on the interface. The surfactant will immediately
spread over the interface in all directions, because that will cause a decrease
of interfacial free energy. Hence ag-gradient is formed, and this will exert a
tangential stress on both liquids, causing them to flow. This is called the
Marangoni effect. For an air–liquid interface, Eq. (10.17) will hold. It should
be understood that ag-gradient generally is a fleeting phenomenon, since it
tends to be evened out by surface motion and exchange of surfactant with
the bulk.
The Marangoni effect can be induced most easily by adding an
insoluble surfactant onto a liquid surface, but the effect is quite general: any
g-gradient causes flow of the adjacent liquid(s) in the direction of increasing
g. A temperature gradient in an interface does also produce ag-gradient (see,
e.g., Table 10.1), even in the absence of surfactant.
The formation of g-gradients can only be achieved (at constant
temperature) by substances that alter interfacial tension. This capacity may
be the most important property of surfactants. To illustrate this we give here
a few examples.

Foaming and emulsification. The formation ofg-gradients is all that

allows the formation of foams and of most emulsions. Consider

making a foam. Very soon vertical films (lamellae) of liquid