Damping of bubble oscillations induced by transport of surfactants between the adsorbed film and the bulk solution

Abstract

At frequencies well below the resonance, the forced oscillations of a microbubble suspended in a surfactant solution are affected by the dilational elasticity of an adsorbed film and by the adsorbate exchange occurring due to bubble’s surface area oscillations. The model introduced for computation of the exchange rate uses the relaxation time of the adsorption–desorption process, on which the experimental data are available in the literature, as the governing parameter. An important manifestation of the surfactant exchange, as found by solving a linearized problem of the bubble motion coupled with the adsorbate flux, is that it induces a considerable dissipation of acoustic energy. Computations are presented for the driving frequencies (ω) ranging from 102 to 105 s−1 and bubble diameters 10–200 μm. The total damping of a clean bubble is also computed, for comparison. The predicted damping constant for a 20-μm bubble covered with a condensed film of a fatty substance can exceed that for a clean bubble by several orders of magnitude at ω<104 s−1.