Hysteresis in a two-liquid whirlpool

Abstract

This experimental study reveals a curious phenomenon—hysteresis in a lab-scale two-liquid flow. The rotating bottom disk drives a toroidal circulation of water–glycerin solution (lower fluid) and sunflower oil (upper fluid) in a vertical cylindrical container. As the rotation speeds up, the solution–oil interface and the oil–air (free) surface deform rising near the sidewall and depressing near the axis as typical of whirlpools. We choose that the oil–solution volume ratio be small (having in mined oil-pollution applications) but not too small (for convenient observation). As the rotation speeds up, the oil separates from the sidewall and collects in the solution funnel. Next, the interface touches the bottom, and this is the point of no return. The centrifugal force pushes the near-bottom oil to the periphery and the buoyancy pushes oil upward. The Rayleigh–Taylor instability breaks the interface, and oil droplets disperse in the solution. If before this breakdown, the rotation starts to decrease, the oil separates from the bottom at the angular velocity ω being remarkably smaller than that for which the oil touches the bottom. Therefore, the hysteresis is a capillary-induced phenomenon.