From: tenney@med.unc.edu (Charles R. Tenney)
Subject: Re: Air bubbles in a universe of water
Organization: UNC-CH School of Medicine
Date: Wed, 22 Jul 1992 04:28:01 GMT

In article <142ggrINN6u@agate.berkeley.edu> aephraim@physics.Berkeley.EDU (Aephraim M. Steinberg) writes:
>In article <1992Jul15.202609.23833@galois.mit.edu> jbaez@taylor.mit.edu (John C. Baez) writes:
>>In article <91075@bu.edu> tvaughan@buphyk.bu.edu (Timothy Vaughan) writes:
>>>The question about boiling liquids in zero gravity reminded of the
>>>following question, which never seems to fail to cause a debate:
>>
>>>Suppose we are inside an elevator that is free-falling, and that the
>>>elevator is filled with air.  If we place two drops of water in the
>>>elevator, they will gravitationally attract each other, thus moving
>>>toward each other until they form one drop.  (Let's ignore EM effects
>>>like polarizability, and the strong and weak and fifth force, etc.!) 
>>
>>>Now, suppose we filled the same elevator with water, and then put two
>>>air bubbles inside.  Do they attract or repel each other?
>>
>>I'd say they go to the walls of the elevator, or if you like, the water
>>wishes to fall to the center of the elevator.  If this seems odd to anyone,
>>consider a gigantic elevator the size and shape of the earth, full of
>>water, falling towards (or, if you prefer, around) the sun.  In other
>>words, imagine a planet made of water.  Now put two bubbles near the
>>center of the planet.  They will rise to the surface.  (Of course, there
>>is no tendency for a bubble to rise if it is EXACTLY at the center.)
>
>Sure, but a SINGLE bubble would also "rise" to the outside of the elevator.
>Relative to this case, the force between the two bubbles is attractive.
>If the elevator were really big and the bubbles were both off in approximately
>the same direction from the center, as they rose they would attract and
>coalesce.  If the elevator were infinitely large, the attractive force
>would be all there was.
>
>A simple justification that no one likes is that the bubbles act like
>negative mass particles, but gravitation attraction goes as m^2, so
>works fine for two "mass holes."
>
>A less hand-wavy way to see it is to first consider the force exerted
>by one hole on nearby particles of water; it is clear by the superposition
>principle that this effective force is repulsive.  By repelling nearby
>water, a bubble will attract nearby bubbles.
>
>aephraim
>
>-- 
>Aephraim M. Steinberg                    | "WHY must I treat the measuring
>UCB Physics                              | device classically??  What will
>aephraim@physics.berkeley.edu            | happen to me if I don't??"
>                                         |       -- Eugene Wigner

I'm not sure one way or the other.  Certainly, the system would seek its
lowest energy configuration.  In the "water planet" above, which has lower
gravitational energy:  one bubble sitting on the surface, say at the north
pole, or two bubbles, one at the north pole and one at the south pole?  I
suspect the latter, as it is closer to the situation in which both bubbles
spread across the entire surface, resulting in a slightly smaller sphere.
Which is what would happen in the absence of surface tension and wall
effects (working together).

It might well be sensitive to the geometry and initial conditions.  For
example, in a cubical elevator, the lowest energy configuration would be
with bubbles in diagonally opposite corners.  But it would seem that each bubble
would tend to head to the nearest corner, as the water in the corner tried
to fall to the center, shoving the bubble aside.  So, they might end up in
corners diagonally opposite on the same face, or on adjacent corners, or in the
same corner (thus coalescing).


-- 
--
Charles R. Tenney	tenney@med.unc.edu   | What would the UNC school of
					     | Medicine want with my opinions?
	"My karma ran over my dogma."	     | What would I want with theirs?
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