When a stream of liquid falls, a surface tension effect called the Plateau-Rayleigh instability causes small variations in the jet’s radius to grow until the liquid breaks into droplets. For a kitchen faucet, this instability acts quickly, breaking the stream into drops within a few centimeters. But for more viscous fluids, like honey, jets can reach as many as ten meters in length before breaking up. New research shows that, while viscosity does not play a role in stretching and shaping the jet as it falls–that’s primarily gravity’s doing–it plays a key role in the way perturbations to the jet grow. Viscosity can delay or inhibit those small variations in the jet’s diameter, preventing their growth due to the Plateau-Rayleigh instability. In this respect, viscosity is a stabilizing influence on the flow. (Photo credit: Harsha K R; via Flow Visualization)
Tag: instability
Egg-Spinning Fun
If you have any leftover hard-boiled eggs, you can recreate this bit of fluid dynamical fun. Spin the egg through a puddle of milk, and you’ll find that the egg draws liquid up from the puddle and flights it out in a series of jets. As the egg spins, it drags the milk it touches with it. Points closer to the egg’s equator have a higher velocity because they travel a larger distance with each rotation. This variation in velocities creates a favorable pressure gradient that draws milk up the sides of the egg as it spins, creating a simple pump. To see the effect in action check out this Science Friday video or the BYU Splash Lab’s Easter-themed video. (Photo credit: BYU Splash Lab)
Colorful Spirals
Artist Fabian Oefner captures these colorful portraits of fluid instability by dripping acrylic paints onto a metal rod, which is connected to a drill. When the drill is switched on, paint is flung away from the rod, creating these snapshots of centripetal force and surface tension. Note how droplets gather at the ends of the spiral arms like in a Plateau-Rayleigh or a rimming instability. For more, check out Oefner’s webpage, which includes a video showing how the images are made, or his previously featured work, “Millefiori”. (Photo credit: F. Oefner; submitted by Stephen D.)
The Boundary Layer Visualized
Any time there is relative motion between a solid and a fluid, a small region near the surface will see a large change in velocity. This region, shown with smoke in the image above, is called the boundary layer. Here air flows from right to left over a spinning spheroid. At first, the boundary layer is laminar, its flow smooth and orderly. But tiny disturbances get into the boundary layer and one of them begins to grow. This disturbance ultimately causes the evenly spaced vortices we see wrapping around the mid-section of the model. These vortices themselves become unstable a short distance later, growing wavy before breaking down into complete turbulence. (Photo credit: Y. Kohama)
Tuning Fork Fluids
This high-speed video shows a liquid crystal fluid vibrating on a tuning fork. As the surface moves, tiny jets shoot upward, sometimes with sufficient energy that the fluid column is stretched beyond surface tension’s ability to keep it intact, resulting in droplet ejection. The jets and surface waves create a mesmerizing pattern of fluid motion. (Video credit: J. Savage)
Flapping Flags
Sometimes structural forces and aerodynamic forces combine to produce instabilities. One of the most common and familiar examples of this, a flag flapping in the breeze, remains extremely complex to analyze and describe. The flexibility of the flag, and its small but finite resistance to bending, combine with the variability of air flow around the flag to create a fascinating dance of effects. This same aeroelastic flutter can create disastrous results for structures and aircraft. For more on the flapping flag, see Argentina and Mahadevan (2004). (Video credit: S. Morris)
The Red Crown
A drop of red dye falls into a thin layer of milk, forming a crown splash. Notice the pale edges of the droplets at the rim of the crown; this is milk that has been entrained by the original drop. The rim and satellite droplets surrounding the splash are formed due to surface tension effects, chiefly the Plateau-Rayleigh instability–the same effect responsible for breaking a falling column of liquid into droplets like in a leaking faucet. The instability will have a most unstable wavelength that determines the number of satellite droplets formed. (Photo credit: W. van Hoeve et al., University of Twente)
Dye Flow
Fluid flow near a surface–inside the boundary layer–can often be unstable. This image shows one possible instability, formed when a cylinder is rotated back and forth about its longitudinal axis. This oscillation and the curvature of the cylinder destabilize flow in the boundary layer, forming vortices that line the cylinder. This particular behavior is called a Görtler instability. To visualize it, threads soaked in fluorescing dye have been embedded into slits in the cylinder. The cylinder is oscillated in a water tank and ultraviolet light is used to fluoresce the dye for the image. (Photo credit: Miguel Canals/University of Hawaii)
Fishbones
When two liquid jets collide, they can form an array of shapes ranging from a chain-like stream or a liquid sheet to a fishbone-type structure of periodic droplets. This series of images show the collision of two viscoelastic jets–in which polymer additives give the fluids elasticity properties unlike those of familiar Newtonian fluids like water. The jet velocities increase with each image, changing the behavior from a fluid chain (a and b); to a fishbone structure (c and d); to a smooth liquid sheet (e); to a fluttering sheet (f and g); to a disintegrating ruffled sheet (h), and finally a violently flapping sheet (i and j). The behavior of such jets is of particular interest in problems of atomization, where it can be desirable to break an incoming stream of liquid up into droplets as quickly as possible. (Photo credit: S. Jung et al.)
Liquid Sculptures
Artist Corrie White uses dyes and droplets to capture fantastical liquid sculptures at high-speed. The mushroom-like upper half of this photo is formed when the rebounding jet from one droplet’s impact on the water is hit by a well-timed second droplet, creating the splash’s umbrella. In the lower half of the picture, we see the remains of previous droplets, mixing and diffusing into the water via the Rayleigh-Taylor instability caused by their slight difference in density relative to the water. There’s also a hint of a vortex ring, likely from the droplet that caused the rebounding jet. (Photo credit: Corrie White)
