Bubble rise in a liquid with a surfactant gas, in particular carbon dioxide

When a gas bubble rises in a surfactant solution, the velocity field and the distribution of surfactant affect each other. This paper gives the theory for small Reynolds and internal Péclet numbers if the surfactant is gaseous or volatile, if its mass flux across the bubble and around its surface dominates its mass flux through the bulk liquid, and if slowness of both adsorption and convective diffusion must be allowed for.The theory is tested on the experiments of Kelsall et al. (J. Chem. Soc. Faraday Trans., vol. 92, 1996, p. 3879). Their bubbles rose as expected in a pure liquid until the apparatus was opened to the atmosphere. That significantly slowed the bubbles down. The effect is so sensitive to small concentrations of slowly adsorbing or reacting surfactants that atmospheric carbon dioxide could have caused it, even though it alters the equilibrium surface tension by less than four parts per million in pure air.There are still unexplained discrepancies between experiment and theory. Additional experiments are suggested that would help to explain them.