Determination of surface tension from the measurement of internal pressure of mini soap bubbles

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.