Free surface and interface oscillations of an infinitely long visco-elastic liquid column

Abstract

For an infinite liquid column consisting of various immiscible visco-elastic liquids exhibiting free surface and interface tension the transcendental frequency equation is presented. The natural damped frequencies depend on the viscosities, densities, surface and interface tensions and upon the Maxwell relaxation times. For a single liquid column the damped frequencies are numerically evaluated for the circumferential axisymmetric case m = 0, as well as for the asymmetric modes m = 1 and 2. The frequencies are increasing with larger tension parameter and show slightly increases decay magnitude for the smaller relaxation time parameters and less damped oscillations for stronger Maxwellian liquids. For smaller surface tension parameter the more viscously acting liquid (small relaxation time) ceases to oscillate and is only able to perform aperiodic motions, while for the larger relaxation times this feature gets lost and the liquid always oscillates exhibiting more pronounced elasticity.