Increase in rising air bubble's terminal velocity

[PhyVibDsics]

Hi! As we know air bubble in the water rises due to buoyancy and quickly reaches its terminal velocity. What is more, as bubble rises the pressure decreases, consequently the volume of the bubble increases resulting in buoyancy becoming larger. So the terminal velocity doesn't remain constant, but should increase proportionaly (like a linear function). And the difficult part here is that velocity (speed of rising) depends on buoyancy, but buoyancy depends on the velocity as well.. Sooo..

Does anybody know any useful equations, ways to calculate this? As far as I know, it is only solvable with a computer simulation. Does anybody know where to find any articles adressing this problem? I want to/am planning to do an experiment for a research (so called extended essay in my educational program) and I would like to have some more theory on this..

Thanks for your help, I hope I wasn't too long, but in my opinion it is really interesting haha.. Even though I'm looking for this because of school, I think I wouldn't classify this thread as HW, exercises.. (am a new forum user so don't want to break no rules haha).

 

[Bystander]

Air saturated water? Air-free water? Super-saturated?

 

[PhyVibDsics]

Air saturated water? Air-free water? Super-saturated?

Imagine producing a bubble with pippete or something similar into a normal tap water at the bottom of a 2m high cylinder. Or maybe even oil; that would result in in bubbles being rounder even at little bit bigger radiuses because of surface tension if I'm correct (easier to conduct an experiment)

 

[JRMichler]

Look up coefficient of drag for spheres. An air bubble is not really a sphere, but the the drag coefficient will be close enough for your purposes. You will see that the drag coefficient is a function of velocity and bubble size, so that pretty much forces you to use a numerical (computer simulation) solution.

It should be a fun experiment. Easy to do, easy to measure velocity, easy to change bubble size, and a good chance to compare theoretical speed to measured speed.