Surface- and interface oscillations in an immiscible spherical visco-elastic system

Abstract

The transcendental frequency equation is presented for various visco-elastic immiscible spherical liquid arrangements exhibiting free surface- and interfacial tension. The system is in a zero-gravity environment. The natural damped frequencies depend on the viscosity, surface tension, density and the Maxwell relaxation time. For a freely floating sphere the numerical results of the frequency equation are presented and exhibit with larger surface tension higher natural frequencies, for small relaxation times stronger and for larger relaxation times weaker decay of the oscillations. The increase of viscosity renders stronger decay of the oscillations. For smaller surface tension the oscillation ceases to exist and yields for small relaxation parameter τν/a2 an aperiodic motion of the drop, while for higher surface tension the oscillation of the visco-elastic sphere exhibit higher frequencies and larger decay. Increase of visco-elasticity (relaxation time) renders the begin of aperiodic motion of a liquid sphere a larger diameter. For further increased relaxation time, however, the sphere always oscillates.