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)
With the Oscars just over, it seems like a good time for some movie-trailer-style fluid dynamics. This video shows a rotating water tank from the perspective of a camera rotating with the tank at 10 rpm. Initially, the tank and its contents are at rest. When the tank begins spinning, the fluid inside responds. Pink potassium permanganate crystals at the bottom of the tank show fluid motion as they dissolve, and food coloring is spread on the water’s surface to show motion there. Fluid near the edge of the tank reaches the tank’s rotational velocity fastest, due to friction with the wall, while fluid near the center of the tank takes longer to spin up to speed. This creates the spiral-galaxy-like shape in the dye. Eventually viscosity will transmit the effects of the wall’s motion even into the center of the tank. (Video credit: UCLA Spinlab)
Remember that 83-year-old pitch drop experiment designed to measure the viscosity of pitch? Well, rumor has it that the ninth drop is due to fall at any time. Will you catch it on the webcam?
The Kaye effect is an instability particular to a falling stream of non-Newtonian fluids with shear-thinning properties. When these fluids are deformed, their viscosity decreases; this, for example, is why ketchup flows out of a bottle more easily once it’s moving. Like most fluids, the falling shampoo creates a heap on the surface. The Kaye effect is kicked off when the incoming jet creates enough shear on part of the heap that the local viscosity decreases, causing the streamer—or outgoing jet—to slip off the side of the heap. As the incoming jet continues, a dimple forms in the heap where the streamer originates. As the dimple deepens, the streamer will rise until it strikes the incoming jet. This perturbation to the system collapses the streamer and ends the Kaye effect. This video also has a good explanation of the physics, along with demonstrations of a stable form of the Kaye effect in which the streamer cascades down an incline. (Video credit: Minute Laboratory; inspired by infplusplus)
In this video, mixtures of inks (likely printer toners) and fluids move and swirl. Magnetic fields contort the ferrofluidic ink and make it dance, while less viscous fluids spread into their surroundings via finger-like protuberances. (Video credit and submission: Antoine Delach)
Reader kylewpppd asks:
Have you seen the post of a man in Siberia throwing boiling water off of his balcony? Can you provide a better explanation of what’s going on?
As you can see in the video (and in many similar examples on YouTube), tossing near boiling water into extremely cold air results in an instant snowstorm. Several effects are going on here. The first thing to understand is how heat is transferred between objects or fluids of differing temperatures. The rate at which heat is transferred depends on the temperature difference between the air and the water; the larger that temperature difference is the faster heat is transferred. However, as that temperature difference decreases, so does the rate of heat transfer. So even though hot water will initially lose heat very quickly to its surroundings, water that is initially cold will still reach equilibrium with the cold air faster. Therefore, all things being equal, hot water does not freeze faster than cold water, as one might suspect from the video.
The key to the hot water’s fast-freeze here is not just the large temperature difference, though. It’s the fact that the water is being tossed. When the water leaves the pot, it tends to break up into droplets, which quickly increases the surface area exposed to the cold air, and the rate of heat transfer depends on surface area as well! A smaller droplet will also freeze much more quickly than a larger droplet.
What would happen if room temperature water were used instead of boiling water? In all likelihood, a big cold bunch of water would hit the ground. Why? It turns out that both the viscosity and the surface tension of water decrease with increasing temperature. This means that a pot of hot water will tend to break into smaller droplets when tossed than the cold water would. Smaller droplets means less mass to freeze per droplet and a larger surface area (adding up all the surface area of all the droplets) exposed. Hence, faster freezing!
High viscosity silicon oil is sandwiched between two circular plates. As the upper plate is lifted at a constant speed, air flows in from the sides. The initially circular interface develops finger-like instabilities, due to the Saffman-Taylor mechanism, as the air penetrates. Eventually the fluid will completely detach from one plate. (Photo credit: D. Derks, M. Shelley, A. Lindner)
A viscous fluid inside a horizontally rotating circular cylinder forms a shark-tooth-like pattern along the fluid’s free surface. This is one of several patterns observed depending on the fluid’s viscosity and surface tension and the rotational rate of the cylinder. (Photo credit: S. Thoroddsen and L. Mahadevan; for more, see Thoroddsen and Mahadevan 1996 and 1997)
Many common fluids—like air and water—are Newtonian fluids, meaning that stress in the fluid is linearly proportional to the rate at which the fluid is deformed. Viscosity is the constant that relates the stress and rate of strain, or deformation. The term non-Newtonian is used to describe any fluid whose properties do not follow this relationship; instead their viscosity is dependent on the rate of strain, viscoelasticity, or even changes with time. A neat common example of a non-Newtonian fluid is oobleck, a mixture of cornstarch and water that is shear-thickening, meaning that it is resistant to fast deformations. Like the cornstarch-based custard in the video above, these fluids react similarly to a solid when struck, resisting changing their shape, but if deformed slowly, they will flow in the manner of any liquid.
Part of the beauty of numerical simulation is its ability to explore the physics of a situation that would difficult or impossible to create experimentally. Here the Rayleigh-Taylor instability—which occurs when a heavier fluid sits atop a lighter fluid—is simulated in two-dimensions. Viscosity and diffusion are set extremely low in the simulation; this is why we see intricate fractal-like structures at many scales rather than the simulation quickly fading into gray. (The low diffusion is also what causes the numerical instabilities in the last couple seconds of video.) The final result is both physics and art. (Video credit: Mark Stock)
