ON SPHERICAL BUBBLES RISING STEADILY IN DILUTE SURFACTANT SOLUTIONS
John F. Harper · The Quarterly Journal of Mechanics and Applied Mathematics · 1974
The effects of small quantities of a soluble surface-active agent on flow around a spherical bubble rising in a liquid are investigated theoretically, with the assumptions of large Peclet number, small effect on the surfactant on the motion, and either large or small Reynolds number. Previously available theories fail near the rear stagnation point; their singularities are resolved here, by methods which should prove useful in other problems involving heat or mass transfer near a rear stagnation point. Surface diffusion is taken into account; it affects the distribution of surfactant considerably if the surface activity is high, but only near the rear stagnation point, and it has little effect on the drag.