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In the course of the search for a flow pattern optimal for culture growth in vortex bioreactors, our experiments discovered striking flow patterns that existing theoretical models cannot explain. Three immiscible liquids fill a vertical open cylindrical container whose sidewall is still, while the bottom disk rotates driving a fluid motion. The centrifugal force pushes the lower liquid (L, aqueous glycerol) from the axis to the periphery near the bottom, creating its toroid circulation that in turn drives middle liquid (M, sunflower oil) and upper liquid (U, alcoholic glycerin) circulations. With increasing rotation, counterflows develop near both interfaces LM and MU in upper fluids: the liquids move toward (away from) the axis below (above) the interface that seems paradoxical. Then, unusual topological transformations occur again in the middle liquid flow caused by competition between effects of radial friction and centrifugal forces. Near cylinder boundary at interface MU, new reverse circulation zone developed where the radial velocity became zero and then change sign. These counterintuitive results wait for their theoretical explanation and formulation of new contact conditions at the LM and MU interfaces. [ABSTRACT FROM AUTHOR]

This experimental study reveals a striking nonlinear-physics phenomenon of fundamental and practical interest—changing conditions at the interface of two swirling immiscible fluids filling a vertical cylindrical container. To this end, we use a new measurement technique significantly advanced compared with prior studies. The rotating bottom disk drives a steady axisymmetric flow of both fluids. The lower fluid makes the centrifugal circulation (CC): It spirals on toroid surfaces going to the periphery near the bottom and going back to the axis near the interface. At a slow rotation (Re = 100), the upper fluid makes the anti-centrifugal circulation. As the rotation intensifies (Re = 175), the upper-fluid flow reverses into CC near the interface-axis intersection. For strong swirl (Re = 500), the CC occurs at the entire interface. In prior studies, the spatial resolution (1 mm) was insufficient to resolve the near-interface velocity field. Here, we use the advanced (light field) measurement technique, which has significantly better resolution (0.14 mm) and clearly shows that the radial velocity at the interface is negative for small Re and becomes zero for large Re. During these metamorphoses, the topology of the lower-fluid flow remains invariant, the interface has no visible deformation, and the flow is steady and axisymmetric. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This experimental and numerical study discusses the formation of double vortex breakdown in a swirling flow of two immiscible fluids where new circulation cells evolve 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, multiple topological changes occur in the flow. This study explains how two new circulation cells (vortex breakdown bubbles) almost simultaneously develop near the centers of both upper and lower fluids while the flow remains steady and axisymmetric. Such multi-cell flows can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Reo 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 Reo = 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 Reo > 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. [ABSTRACT FROM AUTHOR]

It is shown that the viscous fluid motion in the depth of a narrow cavity is a counterflow moving and periodically varying along the cavity length. The obtained exact solutions of the Stokes equations describe unsteady three-dimensional flows, developing as the distance from the cavity surface increases. The found asymptotic motion is common for a variety of boundary conditions and cavity shapes. Creeping flows between parallel and inclined planes, coaxial cylinders, and concentric cones are particularly addressed. For these flows, the analytical asymptotes and numerical results merge as the gap width decreases. [ABSTRACT FROM AUTHOR]

A liquid issuing from a capillary needle adopts a cone-jet structure if the liquid is further driven by a coflowing gas jet. In the present work, flow patterns appearing in this cone-jet structure are studied by the volume-of-fluid numerical method. Axisymmetric motions of the liquid and gas, both treated as viscous incompressible fluids, are simulated. As the gas/liquid mass ratio increases, the meridional circulation develops in the meniscus region of the liquid flow. As the ratio exceeds a threshold, the flow becomes time periodic and droplet generating. Swirl, added in the gas jet, affects the liquid flow in two ways. First, the threshold value increases with swirl. Second, the circulation region transforms from the bubble-like into ring-like pattern and then becomes two-cellular. As swirl further increases, the cells separate, one cell disappears, and a new cell emerges being attached to the needle wall. The predicted metamorphoses of the flow topology might be important for atomization of a liquid fuel. [ABSTRACT FROM AUTHOR]

This paper focuses on the physical mechanism of elongated counterflows occurring in vortex tubes and hydrocyclones. To this end, a new solution to the Navier–Stokes equations is obtained which describes a flow pattern consisting of two through-flows and the global meridional circulation. One of the through-flows has U-shape geometry. It is shown that swirl decay due to fluid-wall friction induces both the U-shape through-flow and the circulation. The circulation does not deteriorate particle separation. The solution illustrates how the swirl-induced pressure distribution drives the counterflow and results in the paradoxical centrifugal stratification where the high-density fluid located at the periphery is hot while the low-density fluid located near the axis is cold. [ABSTRACT FROM AUTHOR]

The global meridional circulation of a viscous fluid, caused by swirl decay in a cylindrical container, is studied. To this end, a new solution to the Navier–Stokes equations is obtained, and simple experiments are performed to verify the predictions of the theory. The swirl decay mechanism explains elongated counterflows in hydrocyclones and vortex tubes sometimes extending over a hundred diameters. [ABSTRACT FROM AUTHOR]

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided. [ABSTRACT FROM AUTHOR]

This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)-(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears. [ABSTRACT FROM AUTHOR]