Physical Chemistry of Foods

gives for the ‘‘spreading’’ time

tspr&z^4 =^3 Z^1 =^3 r^1 =^3 jDgj
^2 =^3 ð 10 : 19 Þ

Some sample calculations: for an O–W interface, assuming Dg ¼
0.02 mN?m
^1 andZOrO¼70 kg^2 ?m
^4 ?s
^1 we obtain for

z¼ 1 mm 0.1 mm 1 cm

tspr¼ 0.6ms 0.3 ms 0.1 s

which shows that the motion can be very fast. For an A–W surface, it would
be faster by a factor 701/3&4. The values predicted by Eqs. (10.18) and
(10.19) agree well with experimental results on A–W interfaces at
macroscopic distances.
Figure 10.31 illustrates what would happen if a surface is ‘‘instanta-
neously’’ enlarged. The surfactant spreads according to Eq. (10.19) over the
clean surface created. The surface excess will thus be decreased (by about a
factor of 2), and the interfacial tension will be enlarged (see Section 10.2.3).
This means that adsorption equilibrium does not exist anymore [Eq. (10.2)],
and surfactant will be adsorbed until the original interfacial tension is
reached again (assuming the total amount of surfactant present to be in
excess). The rate of adsorption will be given by Eq. (10.6).
Two cautioning remarks may be useful. First, Eqs. (10.18) and (10.19)
are only valid as long asDgis constant. Its value will often decrease during the
process. It is difficult to deduce how large the effect will be, in part because it
will depend on the surface equation of state, and the author is unaware of a
quantitative treatment of this problem. It may be that spreading times can be
as much as a factor of 10 longer than given by Eq. (10.19).
Second, Eq. (10.18) only holds for evening out of the interfacial
tension. If more than one surfactant is present, the composition of the
adsorbed surfactant layer may differ from place to place, althoughgis
everywhere the same. Especially for poorly soluble surfactants, evening out
of the surface layer composition then has to occur by surface diffusion,
which may be quite slow.