system
Given the following post, respond as if you're commenting on Reddit:
human
If someone was to have a tank of oxygen and a separate tank of helium under water and they released one bubble of each, which one would get to the surface faster?
gpt
It would depend entirely on the relative size of the bubbles.  Larger bubbles rise more quickly.  The effects of the different gas densities are completely negligible.

The bubble will reach an equilibrium velocity, much like the terminal velocity of a body falling in air, governed by the following equation:

buoyancy = drag

(weight of displaced water - weight of gas) = (0.5 * density of water * velocity^2 * drag coefficient * cross-sectional area of bubble)

g * (4 * pi/3) * r^3 * (rho_water - rho_gas) = 0.5 * rho_water * v^2 * Cd * pi * r^2

g * 8/3 * r * (rho_water - rho_gas) = rho_water * Cd * v^2

v = sqrt(g * 8/3 * r * (1 - rho_gas/rho_water) / Cd)

Cd is roughly 1 (dimensionless)

g is 9.8m/s/s

rho_water is 1000 kg/m^3

rho_gas is about 1.4 kg/m^3 for oxygen and 0.2 kg/m^3 for He at room pressure*

Look at the dimensionless term (1-rho_gas/rho_water).  This represents the buoyancy and is 0.9986 for oxygen and 0.9998 for He.  The difference between the buoyancies is only 0.1%!

This illustrates that the buoyancy in this case is completely dominated by the absence of water rather than the presence of the gas.

It's pretty obvious from the last equation above that even small changes in the radius of the bubble (r) will totally outweigh the tiny difference in buoyancy between helium and oxygen.

*I neglected compressibility effects on the gas.  If they're deep underwater that could be important.  Maybe one is more compressible than the other.