Diffusion capillary waves, damping

The equation derived for the transport of surfactant ions through the DL describes the adsorption kinetics as a reversible process. The qualitatively new result in the theory of ionic adsorption kinetics is the incorporation of electrostatic retardation for both the adsorption and desorption process, which is of essential importance for processes close to equilibrium. Such a situation exists at harmonically disturbed surfaces, used in investigations of adsorption dynamics like the damping of capillary waves or oscillating bubbles. At sufficiently high frequencies the diffusion layer becomes very thin and the adsorption-desorption exchange is controlled only by the ion transport through the DL, i.e. by the electrostatic retardation. At... 

Fig. 5.17. Dependence of the damping coefficient ot capillary waves on DACh concentration at the frequency of 200 Hz [168] curves are calculated according to Eq. (5.256) for the diffusion - controlled adsorption mechanism (solid line), for the mixed adsorption mechanism (dotted line), and for the barrier -controlled adsorption mechanism (dashed line).

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. 

The measurements of the propagation characteristics of the capillary wave, e.g., the propagation velocity and the damping coefficient, are effective for the study of the dynamic properties of materials existing on the gas-liquid interface. The theoretical studies for the insoluble monolayers have been performed by Dorrestein, Mayer and Eliassen", and Mann and Du, while those for the soluble monolayer have been performed by van den Tempel and van de Riet, Hansen and Mann, and Lucassen and Hansen. The former has developed their theories taking account of the surface rheologies, and the latter with the assumption that the rate-determining step of surfactant transfer between the surface and the bulk phase is the diffusion process. 

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