Thought experiment: Diffusion between tanks

[Storker]

at the high pressures in a scuba tank the mixing rate is so slow because of the short mean-free-path (they don't travel very far before bouncing off another molecule) and viscosity effects

I'd think that the decreased diffusivity (much shorter mean-free-path for the molecules) was the determining factor. The viscosity of air increases by only 30% as you go from 1 bar (~atmospheric pressure) to 200 bar (2900 psi). At 300 bar it's still only 50% higher than at atmospheric pressure.

Online - Calculation - Air

 

[bl6394]

I'm really enjoying this thread!

My undergrad was Applied Physics - and I was wondering what mechanisms affected the diffusion of gasses when mixing them. Really appreciate the folks contributing. When I have more time - I'll look at some of the links and get a better understanding of the science and math...

 

[lowviz]

Yes, but the thing that is utterly counterintuitive to me, is that filling doesn't create sufficient turbulence to create homogeneity, but shaking the tanks about a bit does.

(Sorry, a bit out of order of the current conversation. -catching up on this thread.)

Filling mostly compresses the gas in the tank to the opposite end. I'm sure that there is some initial mixing, but it gets swamped out by the second fill.

Rolling tanks:
Imagine gas flowing through a pipe due to a pressure difference. The gas velocity will be highest in the middle of the pipe and nearly zero at the wall. (http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html)

Looking at the same thing another way, cut off the pressure forcing the flow and spin the pipe. Now the molecules at the wall are moving at nearly the same speed as the pipe is rotating and the bulk of the gas fill nearest the center stays where it is due to inertia. This means that there is a shear force in the gas and that is what does the mixing.

 

[tridacna]

Yikes, just checked in.

Predict as in "physical-mathematical explanation" or model as in just get an answer that is supported by testing? Yeah, one could do a proper job if one understood this first: Buckingham π theorem - Wikipedia, the free encyclopedia

I have a fuzzy grasp of it (above) and that is usually enough for me to come up with something that can be twiddled with. Just add gradient factors and it will be OK.

This is quite funny. My field was/is topology and vector algebra. And to think I knew the answer all along.

 

[redacted]

Is there any way to predict or model the mixing behaviour of two gases?

OK, I'll play.

In the absense of any pressure differential, I suspect the original problem could easily and adequately be modeled as a Poisson Process with a rate parameter determined for each configuration.

Oops, got to go. My date is here.

 

[tridacna]

I hope that you enjoyed your date. Is Maxwell–Boltzmann distribution not of relevance here? Can't that be used to create a predictor model?

 

[redacted]

I hope that you enjoyed your date. Is Maxwell–Boltzmann distribution not of relevance here? Can't that be used to create a predictor model?

I suppose that could work. Might even be much better; if you are being paid by the hour rather than by the job.

A bit more (lonely) thought and I suspect you still want the poisson process model but might be able to use a Maxwell–Boltzmann distribution based model to estimate rate parameters. But I suspect that can be done better and faster empirically.

 

[scagrotto]

The different gas mixtures almost act like fluids of different densities

I'm not a fluid dynamacist, but wouldn't two gases at equal temperature and pressure but composed of molecules with different weights actually be fluids of different densities? Or was that just some subtle humor?

No gas has a measurable surface tension as there's no "surface."

If gases can become stratified can I safely presume that there's a boundary? If so what makes that different than a surface? I've got no problem accepting the idea that surface tension has to be a function of the friction and attraction between molecules and would therefore decrease as the friction and attraction are reduced, and since the molecules in a gas will be further apart than those in a liquid the friction and attraction are necessarily lower. So is it really about the absence of a boundary, or is it about the relationships between the molecules at the boundary?