Opposing ultrasonic speakers can be used to trap and levitate droplets against gravity using acoustic pressure. Changes to field strength can do things like bring separate objects together or flatten droplets. The squished shape of the droplet is the result of a balance between acoustic pressure trying to flatten the drop and surface tension, which tries to pull the drop into a sphere. If the acoustic field strength changes with a frequency that is a harmonic of the drop’s resonant frequency, the drop will oscillate in a star-like shape dependent on the harmonic. The video above demonstrates this for many harmonic frequencies. It also shows how alterations to the drop’s surface tension (by adding water at 2:19) can trigger the instability. Finally, if the field strength is increased even further, the drop’s behavior becomes chaotic as the acoustic pressure overwhelms surface tension’s ability to hold the drop together. Like all of this week’s videos, this video is a submission to the 2103 Gallery of Fluid Motion. (Video credit: W. Ran and S. Fredericks)
Tag: chaos
The Fluid Dynamical Sewing Machine
Originally posted: 3 Jan 2012 Nonlinearity and chaos are important topics for many aspects of fluid dynamics but can be difficult to wrap one’s head around. But this video provides an awesome, direct example of one of the key concepts of nonlinear systems–namely, bifurcation. What you see is a thread of very viscous fluid, like honey, falling on a moving belt. Initially, the belt is moving quickly and the thread falls in a straight line. When the belt slows down, the thread begins to meander sinusoidally. With additional changes in the belt’s speed, the thread begins to coil. A multitude of other patterns are possible, too, just by varying the height of the thread and the speed of the belt. Each of these shifts in behavior is a bifurcation. Understanding how and why systems display these behaviors helps unravel the mysteries of chaos. (Video credit: S. Morris et al.)
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Liquid Mushrooms
The Rayleigh-Taylor instability can form at the interface between two liquids of different density under the influence of gravity, but a similar instability can occur in the absence of gravity. The image sequence above shows the Richtmyer-Meshkov instability, which occurs between two liquids of differing densities (regardless of their orientation) when impulsively accelerated. In this case, the experiment was conducted in a drop tower to simulate microgravity with the apparatus dropped on a spring to provide the impulse. As the instability grows, asymmetries appear. Nonlinear dynamics will amplify these distortions, eventually leading to turbulent breakdown. (Photo credit: C. Niederhaus/NASA Glenn, J. Jacobs/University of Arizona)
The Fluid Dynamical Sewing Machine
Anyone who has poured a viscous fluid like honey or syrup will have noticed its tendency to coil like rope. A similar effect is observed when a viscous fluid stream falls onto a moving belt. The photos above show some of the patterns seen in these “fluid-mechanical sewing machines” depending on the height of the thread and the speed of the moving belt. Notice how some of the patterns are doubles of another (i.e. two coils per side instead of one). This period doubling behavior is often seen in systems on their way to chaos. (Photo credits: S. Chiu-Webster and J. Lister)
The Chaos of a Bouncing Droplet
This video explores chaos in a bouncing droplet. A drop of silicon oil bounces on a vibrating bath of oil; the thin layer of air injected with each bounce between the droplet and bath keeps them from coalescing. Initially, the droplet behaves like a bouncing ball, jumping once per oscillation. As the vibration amplitude increases, the droplet begins making a small jump, then a large jump, then a small jump, and so on. This is called period doubling since the droplet now jumps in a pattern with twice the period of the original and is a hallmark of nonlinear dynamical systems. Further increase in the vibration amplitude leads to chaotic bouncing and occasional ejecta. (Video credit: D. Terwagne et al.)
The Vibrating Network
We’ve seen the Faraday instability on vibrating fluids (and granular materials) before. Here researchers explore the effect on a a network of fluid-filled cells. Each square is filled with liquid and small holes near the bottom of each cell ensure the liquid levels are the same throughout the array. Then the entire container is vibrated. Above the threshold frequency, standing waves form but do not interact. When the wave amplitudes grow high enough for fluid to get exchanged from cell to cell, patterns begin to form. The waves in adjacent cells synchronize, eventually resulting in a regular pattern across the entire grid. Order out of chaos.(Video credit: G. Delon et al.)
Labyrinth
A labyrinthine pattern forms in this timelapse video of a multiphase flow in a Hele-Shaw cell. Initially glass beads are suspended in a glycerol-water solution between parallel glass plates with a central hole. Then the fluid is slowly drained over the course of 3 days at a rate so slow that viscous forces in the fluid are negligible. As the fluid drains, fingers of air invade the disk, pushing the beads together. The system is governed by competition between two main forces: surface tension and friction. Narrow fingers gather fewer grains and therefore encounter less friction, but the higher curvature at their tips produces larger capillary forces. The opposite is true of broader fingers. Also interesting to note is the similarity of the final pattern to those seen in confined ferrofluids. (Video credit and submission: B. Sandnes et al. For more, see B. Sandes et al.)
Fractal Fluids
These images from a numerical simulation of a mixing layer between fluids of different density show the development and breakdown to Kelvin-Helmholtz waves. The black fluid is 3 times denser than the white fluid, and, as the two layers shear past one another, billow-like waves form (Fig 1(a)). Inside those billows, secondary and even tertiary billows form (Fig 1(a) and (b)). Fig 1 (c)-(e) show successive closeups on these waves, showing their beautiful fractal-like structure. (Photo credit: J. Fontane et al, 2008 Gallery of Fluid Motion) #
Viscous Fluid Falling on a Moving Belt
In this video a very viscous (but still Newtonian) fluid is falling in a stream onto a moving belt. Initially, the belt is moving quickly enough that the viscous stream creates a straight thread. As the belt is slowed, the stream begins to meander sinusoidally and ultimately begins to coil. Aside from some transient behavior when the speed of the belt is changed very quickly, the behavior of the thread is very consistent within a particular speed regime. This is indicative of a nonlinear dynamical system; each shift in behavior due to the changing speed of the belt is called a bifurcation and can be identified mathematically from the governing equation(s) of the system. (Video credit: S. Morris et al)
Structures in Turbulence
Despite its appearance, there is order in the chaos of turbulence. These snapshots from a turbulent channel flow simulation outline these coherent structures in black. The top photo shows a top view looking down on the channel and the bottom image shows a side view of the channel. It is thought that studying these coherent structures may help shed light on turbulence and its formation, which remains one of the great open questions of classical physics. (Photo credit: M. Green)
