Nonlinear oscillations of inviscid drops and bubbles

Abstract

Moderate-amplitude axisymmetric oscillations of incompressible inviscid drops and bubbles are studied using a Poincaré–Lindstedt expansion technique. The corrections to the drop shape and velocity potential caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions. The frequency of oscillation is found to decrease with the square of the amplitude; this result compares well with experiments and numerical calculations for drops undergoing two-lobed oscillations.