Terminal velocity and mobile surface species in rising microbubbles.

The terminal velocity of rising microbubbles is a sensitive function of the bubble size and the surface concentration of mobile insoluble surfactants at the gas/liquid interface due to the Marangoni effect. With a model that allows for surface convection and diffusion, we delineate the regimes when the terminal velocity varies between the fully mobile (Hadamard-Rybczynski) and the fully immobile (Stokes) behavior at low Reynolds numbers. Results are presented in a universal form to facilitate conversion from bubble rise terminal velocity to trace amounts of surface contaminants.