Stability of a two-fluid rod annular flow

Two concentric fluid annuli are enclosed in the gap between an axial rod and an outer cylinder. Motion is driven both by a pressure gradient and by axial translation of the rod. The linear stability of the flow to axisymmetric and nonaxisymmetric disturbances is studied. New stability regions in parameter space are found for both a stationary and a moving rod. If the fluid viscosities differ, the flow can control the capillary instability at the fluid interface, but may itself be unstable, both at moderate Reynolds number and in the inviscid limit. These flow instabilities may be concentrated either at the interface or the solid boundaries. The interplay between these instabilities depends critically on the problem parameters, and nonaxisymmetric modes can be the most unstable. When the outer fluid is more viscous than the inner, complete stabilization can occur for a sufficiently thick stationary rod, whereas in the absence of the rod, the system is always unstable. Moving the rod can have a stabilizing influence either with or without the driving pressure gradient.