This experimental and numerical study of a two-fluid swirling flow reveals a discontinuity of the radial velocity at the interface. The motion is driven by the rotating lid in a sealed vertical cylindrical container. The upper fluid radially diverges near the lid, goes downward near the sidewall, converges to the axis near the interface, and rises near the axis. This centrifugal circulation drives a bulk counter-circulation of the lower fluid at a slow rotation. As the rotation intensifies, a new circulation cell emerges in the lower fluid. The numerical simulations, performed under the continuity condition for all velocity and stress components, predict that the new cell emerges near the bottom and expands upward. In contrast, the new cell emerges near the interface and expands downward in the experiment. A slip condition is proposed for the radial velocity at the interface. The slip occurs due to the centrifugal force and difference in the fluid densities. The numerical simulations, performed with the slip condition, agree with the experiment.

This experimental study reveals a spectacular and important phenomenon—double vortex breakdown—in a swirling flow of two immiscible fluids where vortex breakdown bubbles evolve simultaneously in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, topological metamorphoses occur, resulting in a multicellular flow. Two new circulation cells (vortex breakdown bubbles) simultaneously develop near the centers of both fluids while the flow remains steady and axisymmetric. Such a pattern can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors.

This experimental study reveals a counterflow slip at the interface of two immiscible fluids filling a sealed vertical cylindrical container whose bottom disk rotates while other walls are stationary. An advanced particle image velocimetry helps us analyze and quantify streamline patterns and velocity profiles of the steady axisymmetric flows of both fluids. As the angular velocity of a disk increases, starting from zero, three changes occur in topology of the upper-fluid flow while topology of the lower-fluid flow remains invariant. These changes result in the counterflow slip at the entire interface, whose nature is speculatively discussed and requires further research.

This paper reveals the flow topology hidden in the experimental study by Fujimoto and Takeda [“Topology changes of the interface between two immiscible liquid layers by a rotating lid,” Phys. Rev. E 80, 015304(R) (2009)]. Water and silicone oil fill a sealed vertical cylindrical container. The rotating top disk induces the meridional circulation and swirl of both fluids. As the rotation strength Re_o increases, the interface takes shapes named, by the authors, hump, cusp, Mt. Fuji, and bell. Our numerical study reproduces the interface geometry and discloses complicated flow patterns. For example at Re_o = 752, where the interface has the “Mt. Fuji” shape, the water motion has three bulk cells and the oil motion has two bulk cells. This topology helps explain the interface geometry. In addition, our study finds that the steady axisymmetric flow suffers from the shear-layer instability for Re_o > 324, i.e., before the interface becomes remarkably deformed. The disturbance energy is concentrated in the water depth. This explains why the instability does not significantly affect the interface shape in the experiment.

This paper explains a mechanism of eddy formation in a slow air–water motion, driven by the rotating top disk, in a vertical sealed cylinder. The numerical simulations reveal nine changes in the flow topology as water volume fraction $H_{w}$ varies from 0 to 1. At $H_{w}$ around 0.8, there are two large regions of the clockwise meridional circulation, one in air and one in water. These regions are separated by two small cells of the anticlockwise circulation adjacent to the interface near the sidewall in water and near the axis in air. The air cell is a thin layer and topologically is a bubble–ring for $0.745 < H_{w} < 0.785$ . Alterations of this flow pattern are explored as (i) pressure increases, (ii) the bottom disk co-rotates and (iii) the top-disk rotation speeds up. This paper provides the physical reasoning behind the flow transformations; the results are of fundamental interest and can be utilized in bioreactors.

This paper describes the first experimental evidence of the vortex breakdown development in the lower fluid in a sealed vertical cylindrical container in which two immiscible fluids circulate, driven by a rotating lid. The lower fluid is water, and the upper fluid is sunflower oil. In both fluids, the rotation generates centrifugal meridional circulations separated by a thin anticentrifugal circulation layer attached to the interface from below. An advanced technique of particle image velocimetry and proper laser illumination allows for the measurement of velocity and recognition of the patterns of flow in oil and water. As the rotation speeds up, a tornadolike swirling ascending jet forms near the axis-bottom intersection. A circulation cell (vortex-breakdown bubble, VBB) then emerges near the center of the water domain, approaches the bottom, and disappears. This scenario of the appearance and disappearance of the VBB is similar to that occurring in a single-fluid flow and in the upper fluid of a two-fluid flow.