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Instability of thread-annular flow with small characteristic length to three-dimensional disturbances

We present a linear stability analysis of viscous, pressure-driven flow in an annular pipe with a moving core. The core moves with constant speed along its axis and rotates with constant angular frequency. At both boundaries the fluid obeys slip boundary conditions. Our numerical results highlight the important role of asymmetric perturbations in the instability of the system. Boundary slip is seen to be stabilizing, as has been observed for other types of parallel flows. We show that motion of the solid core with respect to the outer cylinder causes the neutral curve to split into two distinct curves. In particular, we show that rotation has a surprising destabilizing effect.