Then we could treat this a concentration gradient problem...
You could make some assumptions to mathematically simplify the problem. If the results told you that it would take forever under mathematically simplified conditions... well you get the picture. The original question posed was how long would it take? I think an order of magnitude is all that is required an not an exact number.
Assume the mixing occurs instantly inside the two tanks. Essentially there is no concentration gradient inside the tank, only in the piping between the two tanks. This takes the problem and makes it one dimensional, concentration is only a function of time and position inside the piping connecting the two tanks. At one end of the pipe, you have the concentration in the Nitrox tank, at the other end of the pipe, you have the concentration in the air tank. This is probably acceptable as the internal dimensions inside the two tanks are much much larger than the dimensions of the inside of the pipe connecting the two tanks. This problem is governed by the rate of diffusion inside the pipe connecting the two tanks.
Probably easiest to model the problem as two tanks with .4 cuft of internal volume (77.4 cuft/200 bar) connected by a 1/8" diameter tube about 1 1/2 feet long. That diameter might be generous considering the internal dimensions of the valves that are in between the two tanks. Anyone know what the orifice size of the tank valves are?
Remember Fick's laws of diffusion.
Fick's law of diffusion - Wikipedia, the free encyclopedia
The first law states that the rate that rate of diffusion (flux) is a function of the concentration gradient and the diffusivity of the molecules. Would also have to determine the diffusivity... mean free path and temperature (KE) will effect your diffusivity.
Mass diffusivity - Wikipedia, the free encyclopedia
The flux of oxygen in one direction is the same as the flux of Nitrogen in the other... has to be, otherwise one tank would increase in pressure.
Have to set up the appropriate boundary conditions, and perform some ugly integral...
The long story is that to reach equilibrium, assuming that you started with AL 80's at 3000 psi, air in one tank, and 32% (or whatever %) in the other, a net volume of 4.2 cuft (for the 32% case) of oxygen would have to diffuse from the Nitrox tank to the air tank at the same time that 4.2 cuft of nitrogen diffused from the air tank to the nitrox tank, with only the concentration gradient to drive the process, through the tiny little tube connecting the two tanks.
As the concentrations of the two tanks come closer together, the concentration gradient decreases, as does the net flux of oxygen and nitrogen.
More to come next week...