Bubbles in water, need a method/equations

[NCStarGazer]

I have a need to know how fast gas bubbles will travel from a variable depth in a liquid to the surface. I realize there are a lot of variables here, liquid density, gas density, temp. etc... What I need is a general guideline for calculating the time with different gases through a homogenesis liquid. Any direction to a good article / study or equations is appreciated. Bottom line is probably stated as needing to know the rate of acceleration of a gas in a liquid to the surface, it will be important to be able to calculate the max velocity of the gas too. Example, if I had oxygen at 100 m under water and Helium 100 m under water at what rate will oxygen accelerate to the surface compared to Helium.

Thanks!

 

[dacruick]

I'm not an expert in fluid dynamics, but it makes sense to me that your bubbles' speeds should only be a function of density. And if the density of fluids changes minimally with respect to temperature, you would need a function of density with the variable temperature.

I'm also not sure about this, but how quickly a bubble rises might be equivalent to how quickly water would fall in air but reversed. so if water falls in air at say 9.6 m/s^2, maybe air rises in water at that same acceleration

 

[Andy Resnick]

You may be able to use Stokes flow, if the bubble is small enough to be nearly spherical. Then, the idea is simply F = ma, with the total force being a sum of buoyancy and drag forces.

http://en.wikipedia.org/wiki/Stokes'_law

 

[hane]

Given the bubbles are placed in the water at depth, i think you mentioned 100 M, they will start with a volume based on the pressure at this depth. I think one foot of depth is around .433 pounds for water, so 100 feet would be 43.3 psi and 300 feet (100 meter) 129.3 psi. The original pressure being 14.7 psi. the new pressure being 129.3 psi the volume at the top of water column will be 129.3/14.7 x (original volume of bubble). So its going to float faster as it expands up. That was a temperature constant observation, if the gas is allowed to expand rapidly the internal temperature of gas will drop retarding the volume expansion; less volume means less speed floating. Check out adiabatic gas laws and ideal gas laws.