We review the elementary theory that gives the internal pressure of a soap bubble in terms of its radius and surface tension. The theory is generalized to relate the pressure difference across any element of a soap film to its local curvature. This result is used to introduce the concept of the mean curvature of a surface element and is applied to a double soap bubble to obtain the relation between the three radii that characterize its geometry. We also describe a simple setup, suitable for the undergraduate laboratory, to produce mini bubbles and to obtain the surface tension of the soap solution by measuring the radius and internal pressure of the bubbles.

1.
C. V.
Boys
,
Soap Bubbles and the Forces Which Mould Them
(
Society for the Promotion of Christian Knowledge
,
London
,
1890
).
2.
An excellent introduction to the scientific aspects of soap bubbles can be found in Cyril Isenberg
,
The Science of Soap Films and Soap Bubbles
(
Dover
,
New York
,
1992
).
3.
D.
Lovett
,
Demonstrating Science with Soap Films
(
Institute of Physics Publishing
,
Bristol
,
1994
).
4.
P. G.
de Gennes
,
F.
Brochard-Wyart
, and
D.
Quéré
,
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
(
Springer
,
New York
,
2004
).
5.
F.
Behroozi
,
P.
Mohazzabi
, and
J. P.
McCrickard
, “
Remarkable shapes of a catenary under the effect of gravity and surface tension
,”
Am. J. Phys.
62
,
1121
1128
(
1994
).
6.
F.
Behroozi
and
D.
Olson
, “
Colorful demos with a long-lasting soap bubble
,”
Am. J. Phys.
62
,
856
857
(
1994
).
7.
F.
Behroozi
,
P.
Mohazzabi
, and
J. P.
McCrickard
, “
Unusual new shapes for a catenary under the effect of surface tension and gravity: A variational treatment
,”
Phys. Rev. E
51
,
1594
1597
(
1995
).
8.
M. A.
Rutgers
,
X. L.
Wu
, and
W. B.
Daniel
, “
Conducting fluid dynamics experiments with vertically falling soap films
,”
Rev. Sci. Instrum.
72
,
3025
3037
(
2001
).
9.
F. L.
Román
,
J.
Faro
, and
S.
Velasco
, “
A simple experiment for measuring the surface tension of soap solutions
,”
Am. J. Phys.
69
,
920
921
(
2001
).
10.
L. M.
Gratton
and
S.
Oss
, “
Soaps, colors, holes and much more
,”
Phys. Teach.
43
,
338
339
(
2005
).
11.
F.
Behroozi
, “
Soap bubbles in paintings: Art and science
,”
Am. J. Phys.
76
,
1087
1091
(
2008
).
12.
F.
Behroozi
, “
Surface tension in soap films: Revisiting a classic demonstration
,”
Eur. J. Phys.
31
,
L31
L35
(
2010
).
13.
D. P.
Jackson
and
S.
Slayman
, “
Analysis of a deflating soap bubble
,”
Am. J. Phys.
78
,
990
994
(
2010
).
14.
F.
Behroozi
and
P. S.
Behroozi
, “
The effect of soap film on a catenary: measurement of surface tension from the triangular configuration
,”
Eur. J. Phys.
32
,
1237
1244
(
2011
).
15.
H. S. M.
Coxeter
,
Introduction to Geometry
, 2nd ed. (
John Wiley & Sons
,
New York
,
1969
), pp.
352
353
.
16.
See for example, Cyril Isenberg
,
The Science of Soap Films and Soap Bubbles
(
Dover
,
New York
,
1992
), pp.
163
167
.
17.
J.
Hass
,
M.
Hutchings
, and
R.
Schlafly
, “
The double bubble conjecture
,”
Electron. Res. Announc. Amer. Math. Soc.
1
,
98
102
(
1995
).
18.
M.
Hutchings
,
F.
Morgan
,
M.
Ritoré
, and
A.
Ros
, “
Proof of the double bubble conjecture
,”
Ann. Math.
155
,
459
489
(
2002
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.