Increased mobility of a surfactant-retarded bubble at high bulk concentrations

Abstract

We study theoretically the adsorption of surfactant onto the interface of gas bubbles in creeping flow rising steadily in an infinite liquid phase containing surface-active agents. When a bubble rises in the fluid, surfactant adsorbs onto the surface at the leading edge, is convected by the surface flow to the trailing edge and accumulates and desorbs off the back end. This transport creates a surfactant concentration gradient on the surface that causes the surface tension at the back end to be lower than that at the front end, thus retarding the bubble velocity by the creation of a Marangoni force. In this paper, we demonstrate numerically that the mobility of the surfactant-retarded bubble interface can be increased by raising the bulk concentration of surfactant. At high bulk concentrations, the interface saturates with surfactant, and this saturation acts against the convective partitioning to decrease the surface surfactant gradient. We show that as the Péclet number (which scales the convective effect) increases, larger concentrations are necessary to remobilize the surface completely. These results lead to a technologically useful paradigm where the drag and interfacial mobility of a bubble can be controlled by the level of the bulk concentration of surfactant.