Can molecules travel "into" a high pressure region?

[f95toli]

I haven't been able to figure out how to approach this. It is actually a real-world problem.but I have simplified it a bit to make it easier to explain.

• A container with helium gas of pressure Pc in it is located in some environment where the surrounding air is at a pressure is Pe and temperature Te (lets say 1 Bar and 300K).
• The container has a small hole in it where gas can exit/enter to/from the environment
• A gas cylinder of helium is attached to the container and a valve can be used to let new helium into the container
• The walls of the container are held at a very low temperature (4K) and any air that enters it will instantly freeze.
• A controller connected to the valve is used to stabilize the pressure in the container so that we always have Pc>Pe, i.e. there is a slight over-pressure (say 40 mBar).

Now, the question: How large should the difference Pc-Pe be to prevent ANY air from entering he container (which is the goal)?

The "obvious" answer is that not air will enter the container as long as Pc>Pe., the gas in the container will be leaking out through the hole (and the gas is then replenished from the cylinder) but no air will go the "wrong way"
However, I wonder if that is really true?
My thinking is the air molecule velocity follows some distribution, and that if the pressure difference too small there might be a chance that a "fast" molecule of air (.e.g. nitrogen) could enter. If that happens and it then hits a wall it will freeze and never leave again. Hence, I guess the question boils down to what happens at the hole?

Does anyone have a (qualitative) answer?

 

[f95toli]

After posting this I realized that a molecular (kinectic) model is obviously not applicable at 1 Bar(duh!). Hence, I guess the question is about fluid dynamics and the flow near the hole

 

[boneh3ad]

I think it is mostly a question of flow rates through the hole. If the flow rate is so low that it nearly becomes a buoyancy problem, I could see some air seeping into the hole by moving in through the bottom portion of the hole while helium escapes over the top of it through the top portion of the hole. It is essentially a competition between pressure forces and buoyant forces. For a small hole with reasonably small over-pressure inside the tank, though, I would imagine this effect would be pretty much negligible. Exactly what pressure you need versus hole size to overcome any buoyancy effects would be a little tougher to calculate, though. I'd have to think about that a bit unless someone else has the answer in their mind already.

 

[256bits]

After posting this I realized that a molecular (kinectic) model is obviously not applicable at 1 Bar(duh!). Hence, I guess the question is about fluid dynamics and the flow near the hole

Why not?

Since your hole is small, your problem could be described by the process of diffusion of one gas with another.

If the container and the outside air were at the same pressure and temperature, and NO flow, then the answer would be straight from the textbook, such as explained here for Equimolecular Counterdiffusion
http://en.wikipedia.org/wiki/Molecular_diffusion

Since you have some difference in temperature of the gases and a pressure differential ( which you want to find out ), some more elaborate calculations would be necessary.

I m not so aquainted on how to proceed, but this could be an area for you to investigate further, ( at least to the point that it doesn't lead you down a garden path to a dead end ).

You said

My thinking is the air molecule velocity follows some distribution, and that if the pressure difference too small there might be a chance that a "fast" molecule of air (.e.g. nitrogen) could enter. If that happens and it then hits a wall it will freeze and never leave again

The molecule of nitrogen may attach to the wall, and then some undetermined time later, may un-attach.

 

[f95toli]

The molecule of nitrogen may attach to the wall, and then some undetermined time later, may un-attach.

Possibly, but unlikely. If a nitrogen molecule is adsorbed on an a 4K surface it is very likely to stay there, this is why cryopumping is such an efficient process.

I suspect there is no "easy" answer to this question. Perhaps I should see if I can set up a COMSOL model to test it.

 

[Chestermiller]

As 256bits said, this is a combined flow and diffusion problem. You can assume that the air concentration is very low, so you don't need to take into account counter diffusion. Even though not much air will diffuse backwards into the tank against the helium flow, it is hard to imagine that not one molecule of nitrogen will get in.

 

[256bits]

Possibly, but unlikely. If a nitrogen molecule is adsorbed on an a 4K surface it is very likely to stay there, this is why cryopumping is such an efficient process.

I suspect there is no "easy" answer to this question. Perhaps I should see if I can set up a COMSOL model to test it.

Right you are.
I was thinking of Boltzmann and kinetic energy of the particles. At low temperature, the probability of the nitrogen molecule to acquire enough energy to dislodge would be very low indeed.

 

[DrDu]

I could imagine a simplified problem: The hole is circular and its diameter is much smaller than the thickness of the wall. Then you could assume that you have pure helium in the inner and pure air on the outer. The diameter of the leak being small and the pressure difference being small, too, you get a Hagen Poisseulle flow. Diffusion of air will be most important near the walls of the pore, as velocity is low there.