Three-dimensional large-amplitude drop oscillations: experiments and theoretical analysis

Three-dimensional large-amplitude oscillations of a mercury drop were obtai ned by electrical excitation in low gravity using a drop tower. Multi-lobed (from three to six lobes) and polyhedral (including tetrahedral, hexahedra l, octahedral and dodecahedral) oscillations were obtained as well as axisy mmetric oscillation patterns. The relationship between the oscillation patt erns and their frequencies was obtained, and it was found that polyhedral o scillations are due to the nonlinear interaction of waves. A mathematical model of three-dimensional forced oscillations of a liquid d rop is proposed and compared with experimental results. The equations of dr op motion are derived by applying the variation principle to the Lagrangian of the drop motion, assuming moderate deformation. The model takes the for m of a nonlinear Mathieu equation, which expresses the relationships betwee n deformation amplitude and the driving force's magnitude and frequency.