Surface- and interface oscillations of freely floating spheres of immiscible viscous liquids

Spherical configurations of immiscible liquids with surface and interfacial tension and varying density and viscosity are investigated analytically for zero-gravity conditions. The configurations studied include spherical globules, liquids around rigid spheres, and liquids in rigid spherical containers. The exact damped-axisymmetric-frequency equation is derived and solved, and the results of numerical calculations are presented graphically. For each mode, a single natural damped frequency omega and an infinite number of rapidly decaying nonoscillatory solutions are found. The value of omega increases with decreasing viscosity and increasing surface tension, while the decay factor increases by significant and slight amounts, respectively. The results for liquids in spherical containers are of importance for analyzing the stability of spacecraft with partially filled spherical propellant tanks.