The effect of surfactant on the terminal and interfacial velocities of a bubble or drop

Stream functions are dervied for a spherical droplet in creeping flow with an arbitary surface tension gradient at its interface. The stream functions are used to show theoretically that the terminal velocity is reduced and that the interfacial velocity is retarded, especially near the rear of the droplet, when a trace of surfactant is present in the exterior phase and when surface aging is controlled by diffusion.