Fundamentals of Physics – Diffusion

The transport phenomena of the admixture of two different gases does not
proceed as the theory predicts. This observation is confirmed in practice by
the mixing of gases for commercial use and an example is the mixture of
nitrogen and helium, which is used to test high pressure piping and
equipment for leaks, as it escapes through the smallest of apertures and
simple equipment is available to detect the gas.
However Helium, as a rare gas, is in short supply and is very expensive,
and a mixture of 5% helium and 95% nitrogen serves the purpose, and
companies producing medical and industrial gases are able to supply this
But simply introducing both gases into a storage cylinder, in any order,
does not achieve a homogeneous mixture suitable for practical use (i.e.
with the helium atoms evenly distributed within the more numerous
nitrogen atoms) unless it is left undisturbed for weeks, which is,
commercially speaking, impractical.
If the principles of the kinetic atomic theory of gases are applied to the
example of static mixing, we see that, according to the theory, the average
velocity of nitrogen molecules in air is around 500 metres per second and
that of helium atoms is 1300 metres per second. The relative mass of
nitrogen is around 14, 3.5 times the mass of helium at 4 amu, and a typical
industrial gas cylinder is around 1.5 metres high and 200 mm in diameter.
If introduced after the nitrogen into the top of the cylinder, the lighter
helium content would occupy 75mm of the internal height, while the
nitrogen the remaining 1425mm.

The diagram above depicts the nitrogen molecules and the helium atoms at
the separation point in terms of the Kinetic Atomic Theory of Gases and
the numbers conform to Avogadro’s Law.
If uninhibited by collisions, at these velocities it would be possible for the
slower nitrogen molecules that are in the vicinity of the helium atoms at
the top of the cylinder to travel to the top of the cylinder and back 3,300
times in one second, 200,000 times in one minute. Extending the time to
one hour would enable each nitrogen molecule to travel this distance 12
million times, a total distance of 600 kilometres.
With respect to each of the helium atoms, in one second they could each
travel in the other direction to the bottom of the cylinder and back around
400 times, 24,000 times in a minute. In one hour 1,500,000 times and
traveling a total distance of over 2,800 kilometres.
But of course collisions of any single atom with others are frequent and
such an atom would not move linearly, but in a completely random
This is an unusually frank comment from a Russian textbook:- (1)
“Since this transport is ensured by motion of the molecules, and the
velocities of the molecules are high, diffusion should seem to occur rapidly
with the concentrations leveling out almost instantaneously . Experiments
show, however, that at atmospheric pressure diffusion is a very slowprocess, and mixing in the absence of motion of the gas as a whole may
last several days.” (My emphases)
Ref: Molecular Physics, Kirkoin and Kirkoin, Mir Publishers, Moscow
In an attempt to explain this problem the proponents of Kinetic Theory
suggest that while the molecules in the above example move chaotically at
high velocity, somehow collisions with the molecules of the other gas
mean they always end up in the area from which they started in the first
place, somehow, in this particular instance, showing both chaotic and
ordered characteristic’s at the same time. In other words suggesting that
any collisions that they endure with molecules of the other gas must result
in their returning to the area in which they originated.
But this is a direct contradiction of the principle that the collisions are
completely random or chaotic, and instead is saying that these interactions
are, by some inexplicable means, regulated or controlled.
Given the postulated random, kinetic movement, together with the large
volumes of empty space separating molecules and atoms and their high
velocities, the fact that mixing, in commercial and experimental practice,
is very slow, is direct and incontrovertible proof that this theory is invalid.
To produce a usable gas for commercial usage, after injecting the helium
into the nitrogen in the cylinder, a quicker method of mixing is achieved
by placing it horizontally on rollers and rotating (or ‘rumbling’) it for
This process creates a frictional effect between the internal walls of the
rotating cylinder and the gases in contact with it, as indicated in the
diagram below, where the more massive nitrogen atoms are experiencing a
greater frictional effect from the cylinder walls than the lighter helium
Clearly mixing can only occur if there is a consistent interaction between
the internal gases and the internal surfaces of the cylinder.

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