Question 307984
The relationship of surface area to diameter is constant for a spherical bubble. 
{{{SA=4*pi*(D/2)^2=pi*D}}}
However the bubble size distribution will depend on how the air in injected into the basin: pressure, temperature, depth, salinity, etc.. You may need to do some experimental work to find bubble diameter as a function of some of these parameters. Here's a link to a paper written to discuss bubble size distributions for different configurations of flow. It may be a good starting point.

http://www.springerlink.com/content/kebeyn0j76fynjml/


Also, check this link that discusses the use of venturis and injectors to produce microbubbles, exactly what I think you're looking for. 

http://www.ozoneapplications.com/info/venturi_injection_vs_bubble_diffusers.htm
Good luck!