Why is it difficult to mix helium and nitrogen gases? I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for hours or even days after the two gases are injected to get the two gases to mix. 
And once they are mixed they do not separate again.
I was told that the reason this  occurs is the large difference in density. And then I suppose the pressure from diffusion is much smaller than the pressure exerted by gravity and density difference. But hours to days of mechanically agitating sounds excessive, and makes me wonder if there is something more going on than just the tension between the forces of gravity and diffusion.
I have two questions regarding this behavior:
(1) Are density differences the only reason it's difficult to mix the two gases?
(2) Is there simple way to calculate an estimate of how long it would take for nitrogen and helium to mix in a closed container (without mechanical agitation) just under the forces of diffusion? - Assuming He on top.
With (2) perhaps the same calculation can be done for two gases with similar densities like oxygen and nitrogen for comparison.
 A: It's true.  Special equipment and a long time is required to mix helium and nitrogen.  According to one study, a mixture of 2.7% He, 93.3% N$_2$ at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://doi.org/10.1021/je60005a002.  The helium repeatedly slid from one end of the cylinder to the other.  The authors overcame this difficulty by devising a mixing mechanism internal to the cylinders.
The molecular weight of helium is 4.02, and density is .1786 kg/m^3 at standard temperature and pressure.  For nitrogen, molecular weight is 28.02, and density is 1.2506 kg/m^3.  Here's a table of molecular weight and density for various gases: http://www.engineeringtoolbox.com/gas-density-d_158.html.
Helium doesn't mix easily with nitrogen because of the great difference in their densities.  But once mixed, the gas molecules are close together and they move around quite a bit with kinetic energy so they stay mixed and don't separate out into layers.
A: Diffusion is a slow process over the length of a gas cylinder. The diffusivity of helium in air is about $0.7$ cm$^2$/s (source). At 100 atmospheres it would be about a hundred times slower, about $0.006\  {\rm m}^2$/day.
A: Not really a direct answer to the original questions. I offer two observations that everybody experienced. 
1) He can escape a rubber balloon in one day (i.e. He go through tiny holes in rubber)
2) gases are less solid than rubber.
Therefore He can penetrate any gas given sufficient time.
