The Shape and Energy of a Revolving Liquid Mass Held Together by Surface Tension

Abstract

The shape of a drop of incompressible fluid held together by the action of surface tension and made to rotate about an axis is determined, the effect of gravity being neglected. Two distinct problems are investigated. In the first an isolated drop of liquid in the form of a surface of revolution is considered. At zero angular speed the drop is spherical and with increasing angular momentum the oblateness increases until a maximum angular speed is reached (where the total mechanical potential is a minimum) beyond which a new linear series of equilibrium forms emerges. A solution in the form of a toroid is also found.