No abstract

We investigate the centrifugal instability of a pair of radially stratified immiscible liquids in the annular gap between concentric, corotating cylinders: two-fluid Taylor–Couette flow. Experiments show that a two-layer flow with a well-defined interface and Taylor vortices in each phase can be obtained. The experimental results are in good agreement with predictions of inviscid arguments based on a two-phase extension of Rayleigh’s criterion, as well as with detailed linear stability calculations. For a given geometry, the most stable configuration occurs for fluids of roughly (exactly in the inviscid limit) equal dynamic viscosities. For fluids with sufficiently low viscosity, we also experimentally observe another instability that is evidently the two-fluid analog of the instability of a thin film of liquid coating the inside of a rotating drum.

Flow instabilities occum'ng in rotatingflows can

We computationally investigate the stability of a pair of radially stratified immiscible liquids undergoing countercurrent axial flow in the annular gap between rapidly corotating coaxial cylinders: two-fluid Taylor-Couette flow with counterflow. A simple analysis determines conditions under which a nearly cylindrical interface is maintained in the presence of counterflow ͑i.e., axial pressure gradients͒. Stability analysis reveals that for small axial Reynolds numbers, the flow is slightly stabilized against Taylor-Couette instability, consistent with results for a single phase. At axial Reynolds numbers greater than about ten, however, the flow is susceptible to a ͑generally nonaxisymmetric͒ Kelvin-Helmholtz instability, which precedes the Taylor-Couette mode. Furthermore, new results are presented for the case without axial flow. A bifurcation to vortices that corotate with their counterparts in the other phase is found. Finally, limitations of the generalized Rayleigh criterion developed in our earlier work are elucidated. In particular, we show how it fails if one of the fluid layers is very thin.

No abstract