The surface energy of finite clusters of soap bubbles

A simple derivation is presented of a general integral equation relating th e surface energy of a free cluster of bubbles to the pressure excesses in t he bubbles and a new differential equation for the change in energy in reve rsible transformations of a cluster is derived. It is shown that the integr al equation has a simple geometrical interpretation. A general form of the equation is written which can be applied to wet clusters with finite Platea u borders. Other consequences of the energy equation are drawn. (C) 2001 Am erican Institute of Physics.