whereD¼diffusion coefficient,t¼time scale of the deformation, andcis
bulk surfactant concentration (mol?m^3 );Gshould be in mol?m^2 .Ift?
0, i.e., very fast deformation, the denominator?1, andESDis purely elastic
and depends on the surface equation of state only. For finitet, exchange of
surfactant with the bulk occurs, which is governed by surfactant
concentrationcand the adsorption isotherm (which determine dc/dG, see
Section 10.2.2) and, of course, byD.
Some results are shown in Figure 10.34. As predicted,ESDdecreases
with increasing time scale, because of increasing exchange of surfactant with
the bulk. At small t, the modulus is larger for a higher surfactant
concentration; the explanation is simply that the value ofPis higher, soDP
can be larger. At long time scales, the highest modulus is observed for the
FIGURE10.34 Values of the surface dilatational modulusESDof solutions of
decanoic acid at two concentrations (indicated) as a function of time scalet.
(Adapted from E. H. Lucassen-Reynders. Anionic Surfactants. Surfactant Series
Vol. 11. Marcel Dekker, New York, 1981, p. 201.)