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>Posted on 7 Jul 1996 at 23:14:52 by Scott Cherf

I believe it was me who wrote in a weak moment:
>>As for the elementary processes behind the formation of
>>bubbles being chaotic - I hope not :-).
>
>Isn't it true that a system is considered 'chaotic' if it's
>progress in state space is sensitive to initial conditions?


I would have added "overly" ahead of sensitive to indicate
that the "path" in phase space due to an infinitesimal
change in one or a set of initial parameters can lead a
totally different final state.  (Final here just means
the phase space at some later point in time).


I know I'm on thin ice on this issue.  Ideally I should
have read everything Hill, Yount, Weinke, Maiken and others
have written up on bubble dynamics to spare this list
my musings.  This is how *I* see things:


Gas bubbles cause DCI.  Gas bubbles cannot spontaneously
form (at least not at a rate we need to worry about)
in a liquid kept well below the point of boiling.

Gas bubbles can develop well below the point of boiling
if there are "seeds" present in the liquid.  These "seeds"
are born through the process of tribonucleation.

That's about it.


I see the process of tribonucleation as "chaotic" in the
sense that miniscule gas phase nuclei might form anywhere
at any time in the presence of a dynamic disturbance.

(I'll duck the issue of size and frequency of these nuclei
for now.  That'll have to be for another day).


I'm very hesitant to agree to that the *growth* of an
insignificant seed into a full fledged mortal soldier
is chaotic as it takes trillions of molecules to make a
bubble (a cubic foot of gas at roomtemp and 1 atm
contains of the order 10"{24} gas molecules).


I see the growth of a micronuclei into a bubble
as a simple application of molecular transport
physics at the surface of the bubble but for
just a few complications: the presence of dynamic
disturbances and bubble-bubble dynamics.
The latter I'm pretty uncertain about.


I am not suggesting that I can predict what a fully
grown bubble will do if allowed to come into existance.
That's pretty random.


A purely stochastic
>model might predict the maximum likelyhood of the state of a system over
>time assuming that the system was not sensitive to initial conditions.  An
>example might be the progress in state space of two isolated systems that
>are brought together, say a box full of O2 and another box full of N2.
>Statistical mechanics can reliably predict the maximum likely configuration
>of this sort of system at time t, t+1...t+n.

I have arguments for why the growth of a bubble is a system
in or very near equilibrium.  Before I go on I'd like to
know how you'd solve the *non-equilibrium* problem you pose.
Say I want to know what the distribution of N2 is 10 seconds
after the dividing wall is removed.  Just how would you
solve it using statistical mechanics ?


>A chaotic system can't be modeled this way, because it's sensitive to
>initial conditions.  Is there some reason to believe that bubble
>formation is not chaotic?

You tell me :-).


John
cc015012@br*.br*.ed*

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