Techniques based on harmonic interfacial disturbances

One of the more recently developed methods to investigate the surface relaxation of soluble adsorption layers due to harmonic disturbances is the oscillating bubble method. The technique 

If area changes are performed in an anisotropic way, for example in trough experiments, the theoretical model has to take into account the lateral transport of adsorbed molecules (Lucassen Giles 1975, Dimitrov et al. 1978, Kretzschmar K6nig 1981). Assuming isotropic area deformations, the diffusional flux at the interface is given by 

If we assume a Langmuir type equation of state (2.37) to describe the equilibrium adsorption behaviour of the system then the following exchange of matter fimction is obtained, 

To model the exchange of matter at the interface of a mixed surfactant solution the same principle can be used as for the system containing only one surfactant. However, one term for each of the r surface active compounds in the system is needed. Garrett Joos (1976) derived the complex elasticity modulus which is given by 

The solution to Eq. (6.15) is found in the same way as described for a single surfactant system and was given in its general form also by Garrett Joos (1976), 

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