A model for nonlinear axisymmetric droplet vibrations

Abstract

Nonlinear inviscid droplet vibrations can be described by Luke's variational principle. The model equations for axisymmetric motion are derived from this principle with the Rayleigh-Ritz method using four surface and four bulk modes. The equations fulfill the energy, mass and axial momentum conservation exactly. Poincaré sections are shown for various energies. Several bifurcations are obtained. A singularity of the type of a weak collapse, which is associated to the splitting of the drop, is also found. For higher energies, irregular motion associated to the collapse singularity occurs.