Instability of a rotating thread in a second immiscible liquid

Abstract

We consider the surface-tension-driven instability of a cylindrical liquid column surrounded by a second liquid when the entire system is rotating. Our calculations are in the limit that the flows in both the liquid thread and the outer fluid are viscously dominated, and include the centripetal and Coriolis forces; the effect of the Coriolis force has not previously been studied in the case that the flows in both liquids are viscous. We present numerical results of a linear temporal stability analysis, and an analytical result valid in the large-Taylor-number limit. We also use the boundary-integral method to consider the evolution and instability of a finite cylindrical thread, which then relaxes when the rotation rate is reduced. These results are discussed in connection with recent experimental observations.