insoluble monolayer at the interface: on dilatation the interface reacts in a
fully elastic manner. In most cases, however, the surfactant is soluble, and
the value of the g-gradient will depend on the value of the surface
dilatational modulus, roughly given by Eq. (10.22). In other words,ESDis
time scale dependent. The higherESD, the more the motion of the interface
will be slowed down. The various situations are depicted in Figure 10.37. In
the presence of a surfactant, the common situation is the one depicted in
frame b, implying that there will nearly always be some, albeit slight,
interfacial motion. This then means, for instance, that the downward flow of
liquid in a foam lamella will be faster than suggested by Figure 10.29b.
Nevertheless, in some situations—nearly always involving macromo-
lecular adsorbates—truly stagnant surfaces are observed. This would mean
that Eq. (10.17) does not hold. Its left-hand side gives the shear stress at the
interface, and this cannot be wrong, but the right-hand side (dg/dx) need not
be the only tangential stress exerted by the interface. If a liquid flows along a
solid surface,nog-gradient is developed, but the elastic reaction force of the
FIGURE10.37 Effect of surface dilatational modulus (ESD) on the motion of an
A–W surface; the aqueous phase flows over a solid support.v¼linear velocity;t¼
time scale; subscript S means at the surface. Highly schematic. It is assumed that the
distance over which the surface can move is small enough to allow Eq. (10.17) to be
valid.