Capillary waves diffusion, effect

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. 

Finally, we consider the effect of interfacial turbulences, which are due to mass transfer across the phase boundaries, on the stability of emulsion films. Experimentally, the diffusion transfer of alcohols, acetic acid, and acetone has been studied [549,550]. The observed destabilization of the films can be attributed to the appearance of Marangoni instability [494]. The latter manifests itself through the growth of capillary waves at the interfaces, which eventually can lead to film rupture. Lin and Brenner [521] examined the role of the heat and maSs transfer in an attempt to check the hypothesis of Holly [551] that the Marangoni instability can cause the rupture of tear films. Their analysis was extended by Castillo and Velarde [552], who accounted for the tight coupling of the heat and mass transfers and showed that it drastically reduces the threshold for Marangoni convection. 

A detailed study of water translational dynamics at the water/hydrocarbon interface was carried out by Chowdhary and Ladanyi. The dynamics were probed in the usual laboratory frame as well as the intrinsic frame to provide insight about the effect of capillary waves on the dynamics. The distribution of residence times was fitted by stretched exponentials. The diffusion constant parallel to the interface was determined as above. In agreement with other studies, they found diffusion to be faster at the interface than in the bulk and also faster when viewed in the intrinsic frame. 

The meaning of estimates of the diffusion layer thickness at higher wind speeds is less clear. Under more dynamic conditions, capillary and larger waves extend the interface, bubbles enhance gas transfer and turbulence renews the interface. Thus, any estimate of diffusion layer thickness based on measurements of gas transfer rates must be considered only a nominal or effective thickness. In this regard, Broecker and Peng [3] estimate a global average thickness of the diffusion layer of about 40 pm based on rates of invasion of natural radiocarbon C02. 

---