bubbles

[Nick Thompson]

Ok, so the grandkids are messing about with bubbles.  When two bubbles of equal size conjoin, the “membrane” between them appears to be a flat circle.  How general is this, we asked?  So what if the conjoined bubbles are of unequal size.   Our experiments seemed to suggest that the answer was, “No!”, and that the smaller bubble bulged into the larger one.  Why would that be?  Am I correct that a bubble will expand (if it can do so without breaking) until the pressure inside equals the pressure outside?  So, the pressure in the two bubbles should be the same?  So why would they bulge in either direction? 

 

How did the sale go, Roger?  I couldn’t get there to block the door.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

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[Roger Critchlow-2]

you scared everybody away anyway, two customers, 14 books sold out of 49 boxes.  still got chemistry and Lysenko for you, ...

-- rec --

On Sun, Dec 6, 2015 at 3:45 PM, Nick Thompson <[hidden email]> wrote:

Ok, so the grandkids are messing about with bubbles.  When two bubbles of equal size conjoin, the “membrane” between them appears to be a flat circle.  How general is this, we asked?  So what if the conjoined bubbles are of unequal size.   Our experiments seemed to suggest that the answer was, “No!”, and that the smaller bubble bulged into the larger one.  Why would that be?  Am I correct that a bubble will expand (if it can do so without breaking) until the pressure inside equals the pressure outside?  So, the pressure in the two bubbles should be the same?  So why would they bulge in either direction? 

 

How did the sale go, Roger?  I couldn’t get there to block the door.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

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[Nick Thompson]

Lee,

Thanks.  This is absolutely stunning.  I am forwarding this to FRIAM as we
speak and will reply in greater detail later.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: [hidden email] [mailto:[hidden email]]
Sent: Sunday, December 06, 2015 7:34 PM
To: Nick Thompson <[hidden email]>
Subject: Re: [FRIAM] bubbles

> Ok, so the grandkids are messing about with bubbles.  When two bubbles
> of equal size conjoin, the "membrane" between them appears to be a flat
circle.
> How general is this, we asked?  So what if the conjoined bubbles are of
> unequal size.   Our experiments seemed to suggest that the answer was,
> "No!", and that the smaller bubble bulged into the larger one.  Why
> would that be?  Am I correct that a bubble will expand (if it can do
> so without
> breaking) until the pressure inside equals the pressure outside?

No, I think you're not correct there (though the statement is very
attractive).

There are THREE forces acting on any small region of a bubble (be it simple
or compound):
the force exerted on the region by the pressure of the gas inside the
bubble, the force exerted on the region by the pressure of the gas outside
the bubble, AND the force exerted on the region by the elastic properties of
the material forming the bubble itself.  This latter is proportional to (a
particular numerical measure of) the curvature of the bubble; the measure in
question is (I think) what's called the "Gaussian curvature", and has an
interesting property (classically phrased in terms of "curvatura integra"):
as the bubble changes its shape (say, as a balloon is inflated, or a soap
bubble detached from the bubble- blowing frame adjusts itself to the fact
that the soap is accumulating at the bottom of the bubble because of
gravity), without (of course) adding or removing any material, THE TOTAL
CURVATURE REMAINS CONSTANT.  If, therefore, the AREA OVER WHICH THIS
CONSTANT CURVATURE IS DISTRIBUTED IS CHANGING (because the pressure either
inside or outside the balloon is being increased by inflation/deflation or
temperature change), then THE CURVATURE PER UNIT AREA changes inversely to
that change.  Now, when the balloon/bubble is in equilibrium, the three
forces must sum (vectorially) to 0.  Therefore the pressure inside is NEVER
equal to the pressure outside, unless the contribution from the curvature is
0: there always has to be MORE PRESSURE INSIDE to keep the bubble inflated!

Further analysis (with more idealization) shows that a surface of constant
curvature has very constrained geometry.  Essentially (for closed bubbles;
NOT for fancy soap films on frames) it has to be spherical; the curvature of
a sphere of radius R is proportional (by a universal
constant) to 1/R.  That means that a "sphere of curvature 0" has radius 1/0;
with some magical thinking you can convince yourself that such a sphere is
actually A FLAT PLANE (and without any magic you can calculate that the
curvature of a plane is, indeed, 0).  

Now consider a compound bubble.  It should made out of spherical pieces,
right?  (Wave your hands at this point).  In case the bubble is compounded
of two equal spheres, it will have three pieces, two congruent parts of the
original spheres, with a planar face between them (which is a disk); the
case you first observed.  The pressure inside each part will be the same,
and larger than the pressure outside; across the planar disk, the pressure
differential is 0.  

If the bubble is compounded of UNequal spheres, then the three pressure
differentials (between the part interior to the remains of Original Sphere 1
and the outside, between the part interior to the remains of Original Sphere
2 and the outside, and between the two remains) will all be different, so
the interior wall between the two remains will be a piece of a THIRD
(non-original) sphere.  BEST OF ALL, the dihedral angles anywhere along the
triple boundary circles are all 120 degrees (I think).

I can never figure out how to send this to FRIAM without it bouncing, so
it's just going to you.  Forward ad lib.

Look up "Plateau's problem" in Wikipedia, too.  (The "double bubble
theorem", done rigorously, is actually very hard, and was only quite
recently proved, by a professor at Williams College and some of his
genuinely talented undergraduates. But the account I've given is pretty much
what everybody has believed for a long time, and it's truthy enough for you
and your grandkids, I think.)


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[Stephen Guerin]

Nick,

Nice way to get the grandkids observing!

A quick lookup yields pressure in a soap bubble scales inversely with radius - thus smaller bubbles will push into the bigger ones.

from:

http://soapbubble.dk/english/science/air-pressure-in-bubbles/

_______________________________________________________________________
[hidden email]

CEO, Simtable  http://www.simtable.com

1600 Lena St #D1, Santa Fe, NM 87505

office: <a href="tel:%28505%29995-0206" value="[phone]" target="_blank">[phone] mobile: <a href="tel:%28505%29577-5828" value="[phone]" target="_blank">[phone]

twitter: @simtable

On Sun, Dec 6, 2015 at 3:45 PM, Nick Thompson <[hidden email]> wrote:

Ok, so the grandkids are messing about with bubbles.  When two bubbles of equal size conjoin, the “membrane” between them appears to be a flat circle.  How general is this, we asked?  So what if the conjoined bubbles are of unequal size.   Our experiments seemed to suggest that the answer was, “No!”, and that the smaller bubble bulged into the larger one.  Why would that be?  Am I correct that a bubble will expand (if it can do so without breaking) until the pressure inside equals the pressure outside?  So, the pressure in the two bubbles should be the same?  So why would they bulge in either direction? 

 

How did the sale go, Roger?  I couldn’t get there to block the door.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

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Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com

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[Nick Thompson]

Thanks, Steve,

 

I admire your ability to find this stuff.  I did look. 

 

All best,

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

From: Friam [mailto:[hidden email]] On Behalf Of Stephen Guerin
Sent: Sunday, December 06, 2015 11:54 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] bubbles

 

Nick,

 

Nice way to get the grandkids observing!

 

A quick lookup yields pressure in a soap bubble scales inversely with radius - thus smaller bubbles will push into the bigger ones.

 

from:

http://soapbubble.dk/english/science/air-pressure-in-bubbles/

 

_______________________________________________________________________
[hidden email]

CEO, Simtable  http://www.simtable.com

1600 Lena St #D1, Santa Fe, NM 87505

office: <a href="tel:%28505%29995-0206" target="_blank">[phone] mobile: <a href="tel:%28505%29577-5828" target="_blank">[phone]

twitter: @simtable

 

 

On Sun, Dec 6, 2015 at 3:45 PM, Nick Thompson <[hidden email]> wrote:

Ok, so the grandkids are messing about with bubbles.  When two bubbles of equal size conjoin, the “membrane” between them appears to be a flat circle.  How general is this, we asked?  So what if the conjoined bubbles are of unequal size.   Our experiments seemed to suggest that the answer was, “No!”, and that the smaller bubble bulged into the larger one.  Why would that be?  Am I correct that a bubble will expand (if it can do so without breaking) until the pressure inside equals the pressure outside?  So, the pressure in the two bubbles should be the same?  So why would they bulge in either direction? 

 

How did the sale go, Roger?  I couldn’t get there to block the door.

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

 

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Meets Fridays 9a-11:30 at cafe at St. John's College
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