Oscillations of a liquid spherical drop encapsulated by a non-concentric spherical layer of dissimilar liquid

The oscillation spectrum of a compound drop, consisting of two immiscible liquids, one constituting a liquid central core, surrounded by a liquid layer of the second liquid, resembles that of two coupled harmonic oscillators. From frequency analysis it is possible to determine the surface tension of the outer liquid, and the interfacial tension between the two liquids. In previous treatments of the problem it has been always assumed that the inner core and the outer shell are concentric. This is not necessarily true; this paper removes this restriction and discusses the influence of non-concentricity on the frequency spectrum. It is shown that, except for particular cases, the correction is of second order in eccentricity. Also, the degeneracy of the concentric system with respect to the azimuthal number is lifted.