I am not sure how much Fick's law has any influence. Most "mixing" inside and outside the bubble will be done by convection rather than by diffusion. Diffusion

I am not sure how much Fick's law has any influence. Most "mixing" inside and outside the bubble will be done by convection rather than by diffusion. Diffusion should have little to no influence on the whole problem. Assuming that you want to take into account mass transport through the phases (Air<->Water), you would have to apply Henry's Law.