Surface- and interface oscillations of a rotating viscous liquid column of immiscible liquids

Abstract

The natural damped coupled frequencies of a rotating viscous infinite liquid column with no axial dependency (∂/∂z=0) have been determined. The frequency equation is presented for a single liquid column, an annular liquid column around a rotating rigid center core, two immiscible liquids with a free- and interfacial surface and also for two immiscible liquids in a rigid container. Only the rotating single liquid column was evaluated numerically and exhibited a rather surprising result. It was found that a viscous column is less stable than that consisting of frictionless liquid. In addition it was found that the conjugate complex roots for each mode in the non-rotating case become two complex roots which are no longer conjugate complex and that the purely decaying roots in the non-rotating case turn into complex roots for rotating liquid, exhibiting damped oscillations.