For the holiday season, and inspired by Aaron
Burden's wonderful photo of a frozen soap bubble, I have pulled out my physics
education to estimate the weight of a soap bubble.

First, what is the
volume of a bubble's spherical shell?

For a very thin shell, as we
have here, we can approximate the volume as the surface area times the
thickness of the film, so it is 4*pi*R^2*t. Thus a 1 cm diameter bubble shell
with a 0.5 micron thick film would have a volume of 1.6 x10-4 cubic
centimeters. Since there are no interference colors in the photo above, the
bubble must be less than about 1/3 micron thick.

Bubble Film
thickness

Of course the thickness of the bubble film varies from the
top to the bottom as the liquid runs down. But when you see interference colors
the film is typically less than half a micron thick. As the bubble dries you
can easily be 0.25 microns thick.

Bubble Density Water weighs
about 1 gram per cubic centimeter. The other components in soap weigh about the
same, so our the shell of our 1 cm diameter bubble will weigh about 1.6x10-4
grams (160 micrograms).

Weight of the air inside At the beach
the inside of the bubble will contain air at about 1 atmosphere pressure,
1.2x10-3 grams/cubic cm (at 20°C), up here in the mountains about 10% less.
The volume of our 1 cm diameter bubble is 4/3*pi*R^3 = 0.52 cm^3. So
the weight of air in our 1 cm bubble is 0.52 * 0.0012 = 6.2x10-4 grams (620
micrograms).

Total So the total weight of the bubble is
6.2 +1.6 = 7.8 x 10-4 grams (780 micrograms), about one quarter soap film and
three-quarters air. So it is no wonder that the bubble will float on the
breeze.

Helium If we fill our bubble with helium the weight
of the helium in the bubble will be a tiny 8.6*10-6 grams, so most of the
weight of the bubble will be soap film, and the bubble should soar, the bubble
will weigh about a quarter of the air it displaces.

Methane If
we fill our bubble with methane at 20°C, the gas will weigh 3.4x10-4 grams
(370 micrograms), and the soap film will weigh 1.6 x10-4 grams (160
micrograms), so the total would be about 5.3 x10-4 grams (530 micrograms),
still about 2/3 of the weight of the air it is displacing, and it will float
with an upward buoyancy of 90 micrograms.

Buoyancy Which
points out a principle that is sometimes misunderstood. Hydrogen has half the
weight per cubic meter of helium, but it doesn't have twice the buoyancy, which
is the weight of the air displaced minus the weight of the
gas.

Scaling

As the diameter of the bubble increases, the
weight of the shell will increase proportional to the square of the diameter,
and the weight of the gas inside will increase as the cube of the diameter.
This means that a bubble will be more buoyant the larger it is.

Diameter

Weight of Air

Weight of shell

Weight of CH_{4}

Total

Buoyancy

1 cm

620 µg

160 µg

370µg

530µg

90 µg

2 cm

5026 µg

628 µg

3000 µg

3628

1400 µg

4 cm

40,200 µg

2513 µg

24,000 µg

26,500

13,700 µg

Disclaimer: Information presented here is the opinion of the
author. No warranties regarding the correctness or value of this information
are implied or should be assumed.