The centrifugal instability of two-layer Couette flow between corotating concentric cylinders has received little attention, despite the potential for interesting interactions between centrifugal and interfacial instabilities. Furthermore, the geometry may find application in a liquid-liquid extraction device for bioseparations designed by Professor E. N. Lightfoot, which uses solvent pairs that have very low interfacial tension and small density differences. In this device, the Taylor vortices provide efficient mass transfer and rapid surface renewal without generating a large amount of surface area or dispersing one fluid into another.
We are experimentally and computationally studying this ``two-fluid Taylor-Couette" flow. Along with the two-fluid analogue of the single-fluid Taylor-Couette instability, our experiments show a fascinating variety of time-dependent patterns, including standing wave and helical traveling wave motions. Visualization of the interface is achieved with laser induced fluorescence. For viscous pairs of liquids, a linear theory ignoring gravity produces quantitatively correct results for the onset of vortices. For fluid pairs with small viscosity, gravity is important even at fairly high rotation rates, and a long-wavelength Rayleigh-Taylor type instability is observed. We are currently constructing an asymptotic theory for this instability, as well as studying the effects of instability on transport in this novel, fascinating flow.
One example of two-fluid Couette flow is the flow of two centrifugally stratified immiscible fluids in the annulus between horizontal coaxial cylinders. If the inner cylinder is then rotated at a critical rate above the outer cylinder rate, a centrifugally induced hydrodynamic instability, known as two-fluid Taylor-Couette flow, is produced.
Two-Fluid Taylor-Couette flow in laboratory experiments
Frontal view
Two-Fluid Taylor-Couette flow of a glycerine-water phase and mineral oil-kerosene phase. Flow visualization of the vortices in the water phase is with dye and Kalliroscope.
Interface view:
The water phase contains a small amount of dye that flouresces red when exposed to laser light; the kerosene phase is undyed and therefore remains black. As a result, the two phases may be distinguished and the interface characterized. The vortex structure is visible with the addition of flow visualization particles to reflect the laser light.
At the onset of the Two-fluid Taylor-Couette flow, the interface is flat and the vortices are approximately square. As the inner cylinder rate is further increased, the interface deforms with the vortex wavelength.
The Barber Pole pattern
When one of the fluids has a low viscosity (approximately that of water), a new flow pattern, known as the barber pole pattern, is observed. The barber pole pattern is non-axisymmetric with an axial wavelength much longer than that for Two-fluid Taylor-Coutte flow. The barber pole is observed only at rotation rates just above the minimum rate required to centrifugally stratify the two fluids. With these same fluids at higher rotation rates, Two-fluid Taylor-Couette flow is observed. For this reason, it is hypothesized that the barber pole pattern is a lingering gravitational effect.
The Barber pole pattern in laboratory experiments
Frontal view:
The Barber pole pattern produced with water and kerosene. The water phase contains blue dye to distinguish the two phases. The phases remain stratified without interface break-through to either cylinder (as seen in the interface view). At extreme differences between the inner and outer cylinder rotation rates, the two fluids begin to emulsify.
Interface view
The addition of a laser induced flourescent dye in the water phase allows the water phase (red) and the kerosene phase (black) to be distinguished and the interface visualized. The interface of the barber pole pattern deforms with a much longer wavelength than for Two-Fluid Taylor-Coutte flow.
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