Effect of Surfactant Transport on Wave Motion

We see from these equations that for high frequencies p, fi is small, the elasticity is r j(-dy/drj), and the behavior is that foimd in Chapter 5 for an insolnble monolayer. In this case, oscillation is so fast that bulk diffusion is not able to appreciably diminish the interfadal concentration gradients prodnced by the oscillation. On the other hand, at low frequencies fi 1 and we find 

Clearly the real part of the elasticity is substantially reduced by diffusion effects from its value for an insolnble monolayer, an effect that was already noted for the lower molecular weight compounds of Fignre 5.2. 

The ratio of the imaginary part of to P is often called snrface viscosity, although in this case the complex natnre of E arises naturally from the diffusion problem and is umelated to any relationship between interfacial stress and the rate of strain. The reason for this terminology is that the analysis of wave motion in Chapter 5 is carried out without any explicit consideration of snrfactants, but 

In any case, we see that measurement of the damping rate for capillary waves at high frequencies yields information on ro f-dy/dTj). This value can be used with similar damping measurements at low frequencies to calculate the diffusivity D if the adsorption isotherm is known. Or if ) is known from separate experiments, the damping rate can be used to obtain information about dT /dc as a fimction of surfactant concentration, and hmee to determine the adsorption isotherm. 

FIGURE 6.13 Schematic of an apparatus for studying longitudinal waves, after Lucassen and Barnes (1972). 

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