Abstract

Soluble surfactants adsorb to rising clouds of micro-bubbles and are subsequently deposited on the surface of the bulk liquid. The adsorbed surfactant leads to strongly increased damping of capillary waves, when compared to the damping rate of capillary waves on a clean surface. A theory is developed for the nonlinear dynamics of a bubble cloud, surfactant scavenging, and capillary wave damping. The main ingredients are: (i) an understanding of the connections between spatial structure in the bubble cloud and its mixing properties, deduced from numerical simulation and scaling analysis, (ii) horizontally averaged equations for the surfactant dynamics, and (iii) a (complex) dispersion relation that connects surface properties modified by the presence of surfactants to capillary wave damping.

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