Abstract
The natural damped axisymmetric frequencies are determined for an arrangement of immiscible liquids of different density, viscosity and exhibiting surface- and interfacial tension. The system is in a zero-gravity environment. Many special cases of interest are obtained, such as the oscillation of a freely floating single sphere, that of a liquid around a rigid sphere and the sloshing of a liquid in a spherical container in zero-gravity. The numerical results of the solution of the transcendent characteristic equation show one damped oscillatory root and an infinite number of rapidly decaying non-oscillatory roots for each mode. The roots exhibit with increasing viscosity increasing decay with a decreased frequency of oscillation. Surface tension increase increases the oscillation frequency with a slight increase of decay.
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