Star-Shaped Oscillation of Water Drops under Vertical Periodic Excitation.

This paper investigates the star-shaped oscillation of liquid drops under vertical excitation theoretically and experimentally. When simply put on a solid surface, a liquid drop approximately adopts the shape of a spherical cap. However, when the drop is subjected to a vertical periodic excitation the drop’s initial axial symmetry is broken and star-shaped oscillation occurs. In the first part, two numbers determining the azimuthal and radial wave modes are found and dispersion relation is derived. A parametric resonance model is proposed to derive the correlation between the excitation frequency and corresponding standing wave patterns. In the second part, we show that the air cushion under the drop due to Leidenfrost effect exert a periodical force on the drop and thus the phenomenon of "Leidenfrost star" can be explained. Experiments are in good agreement with theory.