Are you guys having fun with this? I hope so. However, you have
to realize that much research has been done with this topic and
you are essentially trying to reinvent the wheel without the
aid of enough experience in chemistry and without a laboratory.
The solubility of nitrogen in water is not the same at 1 atm of
pressure above the water as it is at higher pressure, nor is the
solubility the same at low and high temperatures. Since CO2
forms carbonic acid in solution, its solubility is affected by
pH, and beer is not neutral. The bubbles that
come out of solution are not the same thing as the foam that forms
above the head, the physical behaviour of the foam is not the same
as the physical behaviour of a bubble. The nitrogen that is in the
foam doesn't have to come solely from the small amount of nitrogen
that was in the liquid, it can diffuse into the foam as it forms
from the bubbles. There are many processes going on including the
initial bubble formation, creaming, disproportionation and drainage,
each of which has its own complex equation. The most important
factors for bubble/foam stability are the solubility of the gas,
which is why nitrogen impacts greatly the stability of the head in
stout, and the initial size of the bubbles that come out of solution
(that is where the widget comes in). There are many many factors
involved which were initially successfully realized in beer purely
by fortuitous experiment but which would probably be impossible
to understand analytically without the input of many minds.
There are many free articles available at the Journal of the Institute
of Brewing, Bamforth's paper "The relative significance of physics
and chemistry for beer foam excellence", 2004
(use
http://onlinelibrary.wiley.com/advanced/search and
type in institute of brewing and select publication title and then
select for article title and type in stout on the next line) has
an excellent summary and also a nice table where you can see clearly
the huge difference pure nitrogen versus pure co2 makes in the lifetime
of a bubble. He also references a Ph.D thesis by Ronteltap titled
"Beer Foam Physics" that is also freely availabe (search the author
and title at scholar.google.com).
Ray