miketsp
Contributor
lamont:bizzare...
my first rough shot at surfing around the net trying to figure this out gives an RMS velocity of around 500 m/s for N2 and O2 and 1348 m/s for He, but a mean-free path at 300 bar of around 50 A for He. that gives a diffusion coefficient of around 2.5 x 10**-6 m^2/s which means an average delta-T of like 400000 seconds (111 hours) to travel a meter.
There seems to be a consistency here.
According to Bird & Welty (see below) the diffusion coefficient is function of pressure & temperature.
There is a formula which I can't reproduce here which starting at a reference condition lets you generate a modelled condition.
If we assume that the temperature is constant, most of the complicated terms disappear leaving a linear pressure relationship.
So starting with an O2 N2 binary pair at 20C the reference diffusion coefficient is approximately 0.22cm2/s.
At 200bar it will be 200 times less, ie. 0.0011cm2/s.
If x is the rms diffusion radius.
So taking x^2=2 x D x t.
In 60seconds, x^2 = 0.13 or x = 0.36cm
In 400000 seconds x=30cm
Within an order of magnitude of your result.
Diffusion is much slower than I would have imagined intuitively. :11:
The obvious answer of course is that most diffusion takes place while pressures are lower at the beginning of the fill and normally the lower pressure gas enters first to occupy the whole volume available.
Transport Phenomena. Bird, R.B., W.E. Stewart, and E.N. Lightfoot. 1960. John Wiley & Sons. NY. 780 pp
Fundamentals of Momentum, Heat, and Mass Transfer, 3rd Ed. Welty, J.R., C.E. Wicks, and R.E. Wilson. 1984. John Wiley & Sons,NY. 803 pp