On the stability of double bubbles and double drops.

The stability problems for equilibrium standard "double bubble" and "double drop" configurations are considered. Recent work has shown that a double bubble is stable to volume-preserving perturbations. In this paper, the stability to perturbations that do not conserve the volumes of the individual bubbles is examined. It is shown that a double bubble shape is also stable to these perturbations and, thus, is stable to arbitrary perturbations. The analysis is based on the principle of minimum total energy. A variational principle is used to formulate the stability problem for an equilibrium double drop configuration formed under zero gravity by two drops of immiscible incompressible liquids.