The simple drip of a faucet is more complicated when frozen in time. Any elongated strand of water tends to break up into droplets due to surface tension and the Plateau-Rayleigh instability. Whenever the radius of the water column shrinks, surface tension tends to drive water away from the narrow region and toward a wider point. This exaggerates the profile, making narrow regions skinnier and wider regions fatter. Eventually, the neck connecting the droplets becomes so thin that it pinches off completely, leaving a string of falling droplets. (Image credit: N. Sharp)
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Daily Fluids, Part 1
Just getting cleaned up and ready for the day involves a lot of fluid physics. Here are a few of the phenomena you may see daily without realizing:
Plateau-Rayleigh Instability
This behavior is responsible for the dripping of your faucet. More specifically, it’s the reason that a falling jet breaks up into droplets. It works on rain, too!
Forced Convection
Everyone is familiar with a winter wind making them colder or hot air from a dryer getting the moisture off their hands. These are examples of forced convection – heat transfer by driving a fluid past a solid. Another common example? The fans in your computer!
Liquid Atomization
This is the process of breaking a liquid into lots of tiny droplets. Aside from any aerosol can ever, this phenomenon is also key to your daily shower and internal combustion in your car.
Archimedes Principle
This might be one of my favorite bits of the whole video because it hearkens back to some of my own earliest fluid dynamics exposure. Archimedes Principle says that buoyancy is equal to the weight of the fluid a body displaces. My mom (a science teacher) taught me about this one in the bathtub! It’s key to everything that ever floated, including us!Tune in all week for more examples of fluid dynamics in daily life. (Image credit: S. Reckinger et al., source)
Watching a Sneeze
What does a sneeze look like? You might imagine it as a violent burst of air and a cloud of tiny droplets. But this high-speed video shows, that’s only part of the story. The liquid leaving a sneezer’s mouth and nose is a mixture of saliva and mucus, and in the few hundred milliseconds it takes to expel this air/mucosaliva mixture, there’s not enough time for the liquid to break into droplets. Instead, liquid leaves the mouth as a fluid sheet that breaks into long ligaments.
Because mucosaliva is viscoelastic and non-Newtonian, it does not break down into droplets as quickly as water. Instead, when stretched, the proteins inside the fluid tend to pull back, causing large droplets to form with skinny strands between them – the beads-on-a-string instability. The end result when the ligaments do finally break is more large droplets than one would expect from a fluid like water. Understanding this break-up process and the final distribution of droplet sizes is vital for better understanding the spread of diseases and pathogens. (Video credit: Bourouiba Research Group; research paper: B. Scharfman et al., PDF)
From Dripping to Beading
When water drips, it quickly breaks up into a string of smaller droplets due to a surface-tension-driven instability called the Plateau-Rayleigh instability. But adding just a tiny bit of polymer to the fluid changes the behavior entirely. Instead of breaking into droplets, a narrow filament dotted with tiny satellite droplets forms between the larger drops. This is known as the beads-on-a-string instability. The viscoelasticity the polymers add is one key to seeing this behavior. Polymers consist of large molecule chains that, when stretched, act a little like rubber bands–they pull back against the stretch, providing an elastic effect. Without this elasticity, the tiny filament connecting the drops would break up immediately. (Image credit: M. Berman, source; research credit: P. Bhat et al.)
Breaking Jets Into Drops
A falling stream of water will break into droplets due to the Plateau-Rayleigh instability. Small disturbances can create a wavy perturbation in the falling jet. Under the right conditions, the pressure caused by surface tension will be larger in the narrower regions and smaller in the wider ones. This imbalance will drive flow toward the wider regions and away from the narrower ones, thereby increasing the waviness in the jet. Eventually, the wavy jet breaks into droplets, which enclose the same volume of water with less surface area than the perturbed jet did. The instability is named for Joseph Plateau and Lord Rayleigh, who studied it in the late 19th century and showed that a falling jet of a non-viscous fluid would break into droplets if the wavelength of its disturbance was larger than the jet’s circumference. (Image credit: N. Morberg)
Spinning Paint
Fluid dynamical behaviors are often the result of competing forces. Here paint flung from a spinning rod illustrates the effects of adhesion, surface tension, and centrifugal force. In general, surface tension tries to hold a fluid together, and adhesion allows it to stay attached to a surface. Centrifugal force, on the other hand, tends to push the fluid outward. As the spinning rod accelerates, centrifugal force wins over adhesion and the paint spirals outward. For awhile, surface tension manages to hold the paint together, stretching it into spiraling ligaments of fluid. But when centrifugal force overpowers surface tension as well, the ligaments of paint snap into smaller droplets, still flying outward. Check out the full video for more great slow motion shots, and be sure to look at photographer Fabian Oefner’s “Black Hole“ series, which inspired the video. (Image credit: BBC Earth Unplugged, source video)
The Milk Crown
This frequently imitated photograph of a drop of milk splashing was taken by engineer Harold Edgerton in 1934. Edgerton pioneered the application of stroboscopic photography to everyday objects, allowing him to capture images with an effective shutter speed much faster than could be mechanically achieved. The photo captures the crown or coronet of a splash. The momentum of the incoming drop flings a thin sheet of liquid radially outward. The rim of this sheet breaks down into thin ligaments that eject tiny droplets at their tips when surface tension can no longer hold the milk together. (Image credit: H. Edgerton, via The Art Reserve; submitted by Vince G)
Beading Fluids
Adding just a few polymers to a liquid can substantially change its behavior. The presence of polymers turns otherwise Newtonian fluids like water into viscoelastic fluids. When deformed, viscoelastic fluids have a response that is part viscous–like other fluids–and part elastic–like a rubber band that regains its initial shape. The collage above shows what happens to a thinning column of a viscoelastic fluid. Instead of breaking into a stream of droplets, the liquid forms drop connected with a thin filament, like beads on a string. In a Newtonian fluid, surface tension would tend to break off the drops at their narrowest point, but stretching the polymers in the viscoelastic fluid provides just enough normal stress to keep the filament intact. If the effect looks familiar, it may be because you’ve seen it in the mirror. Human saliva is a viscoelastic liquid! (Image credit: A. Wagner et al.)
Hydrophobicity and Viscous Flow
Hydrophobic surfaces are great for creating some wild behaviors with water droplets, but they make neat effects with other liquids, too. The viscous honey in the first segment of this Chemical Bouillon video is a great example. Because the honey doesn’t adhere to the hydrophobic surface, the viscoelastic fluid does not maintain the form it had when drizzled on the surface. Instead, the honey contracts, with surface tension driving Plateau-Rayleigh-like instabilities that break the contracting ligaments apart to form nearly spherical droplets of honey on the surface. (Video credit: Chemical Bouillon)
The Real Shape of Raindrops
We often think of raindrops as spherical or tear-shaped, but, in reality, a falling droplet’s shape can be much more complicated. Large drops are likely to break up into smaller droplets before reaching the ground. This process is shown in the collage above. The initially spherical drops on the left are exposed to a continuous horizontal jet of air, similar to the situation they would experience if falling at terminal velocity. The drops first flatten into a pancake, then billow into a shape called a bag. The bags consists of a thin liquid sheet with a thicker rim of fluid around the edge. Like a soap bubble, a bag’s surface sheet ruptures quickly, producing a spray of fine droplets as surface tension pulls the damaged sheet apart. The thicker rim survives slightly longer until the Plateau-Rayleigh instability breaks it into droplets as well. (Image credit: V. Kulkarni and P. Sojka)