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Date: Thu, 21 Dec 1995 23:01:08 -0800 (PST)
From: Eric Maiken <ebmaiken@ea*.oa*.uc*.ed*>
To: PFG@IC*.IF*.UF*.ED*
cc: techdiver@terra.net
Subject: Re: BAD GAS
Hi Pete:

A number of people wrote me about their experiences with unmixed gas.

Being susceptible to reason and evidence, i'll outline a simple "theory" 
of estimated mix time (good to within a factor of 10, lets say). This is 
just a scratch calculation (really just dimensional analysis) to make a 
reasonable guess on how long it takes one gas species to diffuse into 
another. 

Reality is complicated for binary and 3-nary mixtures--the diffusion 
coefficients of each species depend on local composition and may be 
independent of other species. (if you want to flog yourself look into: 
"Diffusion of Carbon Dioxide into a Helium Nitrogen Mixture," J. Chem. 
Phys. 32,1314 (1960).)

for these purposes, consider nitrox. O2 and N2 are about the same size 
and mass, so it's reasonable to assume one diffusion coefficient.
now, a diffusion coefficient (D) measures two things: how fast a molecule 
travels (v) and how far it travels before colliding with another molecule 
(d). A large diffusion coefficient leads to rapid mixing.

D = v*d [cm^2/sec]

a characteristic time can be obtained by L^2/D [sec], where L is a 
dimension characteristic of the system (say a tank, L ~ 10 cm).


at 1 ata:   v~ 5*10E+04 cm/sec; d ~ 2*10E-05 cm, so D ~ 1 cm^2/sec for an 
empty tank. The characteristic mix time would be about: 
((10cm)^2)/(1cm^2/sec) = 100 sec ~about a minute. 

at 200 ata:    v~ 5*10E+04 cm/sec; d ~ 10E-07 cm, and D ~ 5*10E-03 for a 
full tank. The characteristic mix time would be about 20,000 sec or 5.5 
hours.

These values are just rough guesses. In some senses they 
represent an overestimate of time to mix because they don't account 
for the convection and turbulence that occurs due to gas flow during filling.
These processes should reduce the characteristic length L over which 
diffusion occurs.


regards, em



_____________________________________________________________.sig
Eric Maiken                    email: eapg243@ea*.oa*.uc*.ed*              
Dept. of Physics                   o: 714 824-6621   
U of California                  fax: 714 824  2175
Irvine, CA 92715-4575


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