In this simple demonstration, we see what seems like a special effect. But it's not. Here's how laminar flow makes reality look like an optical illusion.
Top animation adapted from a demonstration video by the UNM Physics Department
It looks totally fake. Corn syrup dyed yellow, blue and red is added to a container full of undyed syrup. The combination is stirred, smearing the colors into a muddled streak of brownish orange. But when the stirring is reversed, the colors we thought were irretrievable whirl into view: the drops of yellow, blue and red are restored! Magic? Fakery? Nope and nope. It's the result of a phenomenon known as laminar flow. But HOW DOES IT WORK?
We first introduced you to this experiment and the wonders of laminar flow a couple years ago, with this video by the University of New Mexico's Physics Department. Since then, we've received a pretty steady stream of requests from people asking us to explain the demonstration in greater detail. We have heard your cries. Let's get right to it, then, shall we?
So waaaay back in 2011, we told you that the reversibility of the mixing demonstrated in the video was due to an extreme form of laminar flow called Stokes flow. Also known as "creeping flow," Stokes flow is what you get when a fluid is so viscous that it resists the sort of irreversible mixing that we're used to seeing when we introduce motion to a liquid mixture.
Ever stirred cream into coffee? Then you've witnessed this kind of disorder firsthand. The instant that cream hits coffee, it starts to diffuse. A couple swirls with a spoon and things really get out of hand; if anything, reversing the direction of your stirring only agitates things even more. In a few seconds, things are looking pretty uniformly mixed. The effects of inertia on the fluid have won out over viscosity, and there's no going back.
In fluid dynamics, this competition between inertia and viscosity is described by a quantity called the "Reynolds number." I'm summarizing here, but the Reynolds number, R, can be described in simplest terms as the ratio of the inertial effects* over viscous ones for a given fluid. More formally, it's described as R=ρνR/η, where ρ is density, ν is the speed of the fluid, R is the size of the flow, and η is viscosity. To understand this conceptually, think back to our previous example: Coffee, which is mostly water, is not very viscous. Corn syrup, on the other hand, has a viscosity thousands of times that of water. Because the Reynold's number is inversely related to viscosity, η, corn syrup stirred in the manner demonstrated here has a very small Reynolds number. When a Reynolds number is much, much smaller than 1, it allows for the extreme form of laminar flow – aka Stokes flow – that we discussed above, and mixing becomes reversible:
Animation adapted from Low-Reynolds-Number Flows via The National Committee for Fluid Mechanics Films
A common analogy states that a fluid with a sufficiently low Reynolds number will flow along distinct paths in parallel layers (like fanning a deck of cards), which prevents disruption of the fluid. "Fan the cards" back and you wind up right back where you started. Another great way of understanding Stokes flow is to consider it in terms of diffusion. One of the best explanations I've seen comes via the always-awesome F*ck Yeah Fluid Dynamics tumblr, which states that in examples of extreme laminar flow like the ones seen here, the motion of the fluid is the result of two forms of diffusion. The first is molecular diffusion, which describes the tendency for the dye molecules to disperse spontaneously and evenly throughout the liquid. The second is what's known as momentum diffusion:
The former is random but slow, and the latter is exactly reversible. Reversing the rotation of the fluid undoes the momentum diffusion and any distortion remaining is due to molecular diffusion of the dye.
Granted, not all laminar flow is inherently reversible, but there's almost always something more orderly about it. Flow lines that are laminar are often described as "coherent." It's a word that conveys consistency, order and unification. It stands in stark contrast against the disorder observed in what are known as "turbulent" flows. Laminar flows over an airplane wing are a good thing. Turbulent flows,
unsurprisingly, give rise to nasty turbulence aren't actually responsible for the turbulence you experience on an airplane, but rather what are called "turbulent boundary layers," which – as nsharp points out below – leads to an increase in both drag and fuel-usage.
One thing the Reynolds number does really well is collect the various conditions that affect the flow of a fluid, and combine them to determine whether they might give rise to laminar or turbulent flow, or how a flow can transition from one state to another. In the demonstration seen here, for example (borrowed from this study by J. P. Kubitschek and P. D. Weidman), increasing the velocity at which a viscous liquid jet is rotating causes its rotational Reynold's number to increase, in turn resulting in a transition from laminar flow:
To turbulent flow:
This effect is also how we get gorgeous images like these. (Fun fact: you may notice there's still some "order" to this high Reynolds number, turbulent-flow. That's because rotating jets of viscous liquid jets tend to demonstrate a preference for what are known as "helical instabilities." The more you know, right?)
Just to clarify, something that the previous demonstration illustrates is that Reynolds number is not constant for any particular fluid. Remember: "R" is a quantity that describes several different factors, all of which are subject to change in and of themselves. A fluid's density, for instance, changes with temperature, and a fluid's speed can change dramatically depending on the forces acting upon it. Scientists and engineers weigh these properties to determine Reynolds number for a variety of applications, whether it's designing a city's sewer infrastructure or – a personal favorite – describing the motion of self-propelled organisms in water:
Table of self-propelled organisms by Vogel via Hitech Projects
Note that the Reynolds number range from very large values to very small, across a variety of water-dwelling organisms. The numbers indicate that for more massive organisms, like a whale, the effects of inertia dominate those of viscosity. This allows whales to coast for long periods of time with every stroke of their fins. Conversely, bacteria must contend with a small Reynolds number, denoting the strong influence of viscosity. A whale in motion will tend to stay in motion. A bacterium? Not so much.