determination of other surface properties is generally needed for a
reasonable interpretation of the results.
10.8.2 Surface Dilatation
Figure 10.33b illustrates how to measure surface dilatational parameters.
An essential aspect is that the interfacial tension is directly measured. If the
surface areaAis increased,gis increased, and vice versa. In principle, one
can also measure a two-dimensional stress, but it is far easier to measureg,
which also has the advantage of excluding any effect of the coupling of bulk
flow with that of the interface. Preferably, the shape of the surface element
remains unchanged upon expansion–compression, to avoid any shearing in
the plane of the surface. The change ingupon a change inAproceeds as a
longitudinal wave, the velocity of which is given by Eq. (10.18).
Asurface dilatational modulusis defined as
ESD:
dg
dlnA
ð 10 : 20 ÞIf it concerns a monolayer of an amphiphile that is insoluble in the
bordering phases, the modulus is purely elastic (although at strong
compression, i.e., largeDA/A, the surface layer may collapse), andESD
is constant in time and independent of the dilatation rate. If the surfactant is
soluble, exchange of surfactant between interface and bulk occurs, andESD
will be time dependent. This means that also an apparentsurface dilatational
viscositycan be measured:
ZSDa :Dg
dlnA=dtð 10 : 21 Þwhich tends to be strongly strain rate thinning.
Note A more sophisticated treatment is possible by introducing a
complex modulus, as discussed in Section 5.1.3; see Figure 5.9.
Prediction ofESDfrom measurable parameters is often possible. We
will mention two fairly simple cases. In the first one, an interface is bounded
by a semi-infinite surfactant solution (the surfactant is not soluble in the
other phase), and the transport of surfactant to and from the interface is
governed by diffusion. The result is
ESD&
dP=dlnG
1 þðDtÞ^0 :^5 dc=dGð 10 : 22 Þ