🚀 go-pugleaf

In article <1992Aug3.163925.1625@gacvx2.gac.edu> kiran@gacvx2.gac.edu writes:
>I was fascinated by the following problem in a multiple choice question book on
>physics:
>
>When two soap bubbles of unequal size are connected by a tube, what happens to
>the bubble sizes?
>
>The unexplained answer of the book was that the larger bubble becomes larger, 
>while the smaller bubble becomes smaller.
>
>At first I couldn't believe the answer!
>
>A friend of mine suggested that the air pressure inside the larger bubble is
>less than that in the smaller bubble because the radial component of the
>"outward" surface tension force around a small region of the bubble's surface
>is less in the larger bubble because of the lesser curvature. 

The book's answer sounds fine to me.  Rather than worrying about forces,
which should give the right answer if one doesn't get hopelessly
confused, it might be easier to note that bubbles try to minimize their
surface area.  Roughly speaking, one can pretend that the bubble is
trying to hold a certain volume of air with the least amount of surface
area.  (This neglects the compressiblity of the air.  With a tube
around one also should worry about the soapwater/tube forces, but I will
neglect these too.)   You can hold more air with a given amount of
sruface area if you use one big bubble than if you use 2 medium sized
bubbles.  I.e. the situation in which both bubbles are the same size is
an energy *maximum*, or unstable equilibrium, not an energy minimum the
way you seem to have thought.

If formulas make one feel happy, say one has a unit volume one is trying to
enclose in 2 spheres.  Say one sphere holds a volume V and the other
1-V.  The surface area of a sphere grows like the volume to the 2/3
power times some constant which I will ignore.  So the total surface
area is like

V^{2/3} + (1-V)^{2/3}

and this has a local MAXIMUM at V = 1/2.