Three-Lobed Shape Bifurcation of Rotating Liquid Drops

Abstract

The evolution of axisymmetric equilibrium shapes of a rigidly rotating liquid drop can be extended beyond the 2-lobed shape bifurcation point if the rotating drop is driven in the n = 2 axisymmetric shape oscillation (perturbation), where n is the mode of oscillation. A reason for the extended stability of the perturbed rotating drop is that the inertia of the driven axisymmetric shape oscillation suppresses growth of a natural nonaxisymmetric shape fluctuation which leads to the 2-lobed shape bifurcation. The axisymmetric shape of the drop eventually bifurcates into either a 2- or a 3-lobed shape at a higher bifurcation point which is asserted to be the 3-lobed shape bifurcation point.