An analytical solution for the profile and volume of a small drop or bubble symmetrical about a vertical axis

Abstract

A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.