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Re: [Phys-l] bubbles



On 11/27/2011 06:45 PM, Michael Barr asked about:

"Hey i noticed that they do one of four things
when they collide. they bump and move away, they bump and pop, they
fuse together into one super bubble or they half-fuse into this weird
siamese bubble. what is it that allows them to behave this way?"

Well, some pretty basic physics allows them to do that.

To a first approximation, a bubble involves an equilibrium between
pressure and surface tension.
a) The air inside the bubble has a pressure.
b) The liquid film has a surface tension.

That's the raw physics. Now we do the scaling argument.
a) As always, pressure is proportional(*) to energy per unit volume.
That means the energy scales like length cubed.
b) As always, surface tension is proportional(*) to energy per unit area.
That means the energy scales like length squared.
c) Therefore the bubble /as a whole/ is not scalable. We expect
that a large bubble will *not* be just a scaled-up copy of a small
bubble.

You can do the calculus of variations to convince yourself that
a sphere is the most-favored shape. Start with a cylinder, and
calculate the energy as a function of a single parameter, namely
the aspect ratio, for a constant amount of film and a constant
amount of enclosed gas. This will rule out pancake-shaped and
needle-shaped cylinders. Then show that the cylinder is disfavored
relative to the corresponding sphere.

Additional physics: When bubbles collide, if there is actual
water-to-water contact, they will stick or merge. Conversely, they
will bounce if/when they collide without actually touching ... which
is possible because of the air between them. A very thin layer of
air suffices to prevent water-to-water contact. The air simply
doesn't have time to get out of the way during the encounter. You
can verify this by calculation, using the known viscosity of air.

Also: A twin bubble has a different /topology/ from a single merged
bubble. There are lots of topological conservation laws in physics.
In this case, this means there is a /potential barrier/ that makes
the twin bubble /metastable/ against conversion to a single larger
bubble.

Bottom line: All this is pretty much typical of real-world physics:
There are a whole bunch of things going on, none if which is particularly
complicated by itself. The first step is to analyze the situation piece
by piece, and then put everything back together again.

scaling
calculus of variations
pressure
surface tension
viscous flow
topology
metastability
et cetera

==============

*) Tangential footnote: Note that I said "proportional to" not "equal
to". Pressure is not equal to energy per unit volume. For ordinary
air, the pressure is numerically equal to about 40% of the actual
energy per unit volume. For the purposes of scaling arguments,
proportionality is all we need, but I mention it because for other
purposes you'll get into trouble if you treat things as equal when
they are merely proportional.

==========================================

On 11/28/2011 06:44 AM, Dr. Keith S. Taber wrote:
I hope you will offer some advice first on research ethics for
studies with human subjects.

Indeed.