Vibrational Modes of a Spherical Drop and Spherical Harmonic Functions

Yoji Arai¹, Makito Kashiwabara² and Ryuji Takaki²

¹Kyoritsu Women Junior College, Chiyoda, Tokyo 101-8433, Japan
²Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan

(Received April 9, 1993; Revised January 31, 1998; Accepted March 27, 1998)

Keywords: Spherical Drop, Regular Polyhedra, Vibrational Mode, Spherical Harmonic Function, Minimum Dissipation Principle

Abstract. A review is given on experimental and theoretical works of the present authors for vibrational modes of a spherical drop in an immiscible liquid with neutrally buoyant condition. Observed instantaneous drop shapes had an axisymmetry or symmetries similar to regular polyhedra. A mathematical method to express drop shapes are given, so that they are expressed by a single spherical harmonic functions or a superposition of those functions. Calculated drop shapes are shown to agree nearly with observed ones. A discussion is given on a selection mechanism of modes in terms of viscous dissipation and packing problem on a sphere.