milk rings – Bean Thinking

vortices in coffee — Vortices behind a spoon dragged through coffee.

Dragging a spoon through coffee (or tea) has got to remain one of the easiest ways to see, and play with, vortices. Changing the way that you pull the spoon through the coffee, you can make the vortices travel at different speeds and watch as they bounce off the sides of the cup. This type of vortex can be seen whenever one object (such as the spoon) pulls through a fluid (such as the coffee). Examples could be the whirlwinds behind buses (and trains), the whirlpools around the pillars of bridges in rivers and the high winds around chimneys that has led some chimneys to collapse.

Yet there is another type of vortex that you can make, and play with, in coffee. A type of vortex that has been associated with the legends of sailors, supernovae and atomic theory. If you add milk to your coffee, you may have been making these vortices each time you prepare your brew and yet, perhaps you’ve never noticed them. They are the vortex rings. Unlike the vortices behind a spoon, to see these vortex rings we do not pull one object through another one. Instead we push one fluid (such as milk) through another fluid (the coffee).

It is said that there used to be a sailor’s legend: If it was slightly choppy out at sea, the waves could be calmed by a rain shower. One person who heard this legend and decided to investigate whether there was any substance to it was Osborne Reynolds (1842-1912). Loading a tank with water and then floating a layer of dyed water on top of that, he dripped water into the tank and watched as the coloured fluid curled up in on itself forming doughnut shapes that then sank through the tank. The dripping water was creating vortex rings as it entered the tank. You can replicate his experiment in your cup of coffee, though it is easier to see it in a glass of water, (see the video below for a how-to).

Reynolds reasoned that the vortices took energy out of the waves on the surface of the water and so in that way calmed the choppy waves. As with Benjamin Franklin’s oil on water experiment, it’s another instance where a sailor’s myth led to an experimental discovery.

chimney, coffeecupscience, everydayphysics, coffee cup science, vortex — In high winds, vortices around chimneys can cause them to collapse. The spiral around the chimney helps to reduce these problem vortices.

Another physicist was interested in these vortex rings for an entirely different reason. William Thomson, better known as Lord Kelvin, proposed an early model of atoms that explained certain aspects of the developing field of atomic spectroscopy. Different elements were known to absorb (or emit) light at different frequencies (or equivalently energies). These energies acted as a ‘fingerprint’ that could be used to identify the elements. Indeed, helium, which was until that point unknown on Earth, was discovered by measuring the light emission from the Sun (Helios) and noting an unusual set of emission frequencies. Kelvin proposed that the elements behaved this way as each element was formed of atoms which were actually vortex rings in the ether. Different elements were made by different arrangements of vortex ring, perhaps two tied together or even three interlocking rings. The simplest atom may be merely a ring, a different element may have atoms made of figure of eights or of linked vortex rings. For more about Kelvin’s vortex atom theory click here.

Kelvin’s atomic theory fell by the way side but not before it contributed to ideas on the mathematics (and physics) of knots. And lest it be thought that this is just an interesting bit of physics history, the idea has had a bit of a resurgence recently. It has been proposed that peculiar magnetic structures that can be found in some materials (and which show potential as data storage devices), may work through being knotted in the same sort of vortex rings that Kelvin proposed and that Reynolds saw.

And that you can find in a cup of coffee, if you just add milk.

Causing a stir

coronal hole, Sun — Where it all begins. The dark object is a Coronal hole on the Sun. Image credit and copyright NASA/AIA

What’s the difference between your cup of coffee and the solar wind (the fast stream of charged particles emanating from the Sun)? Perhaps this seems a strange question, we ought first to ask what connects your coffee with the solar wind. But, when we look at what connects them, you may be surprised to find the reason that they are different.

The solar wind is a flow of charged particles that streams past the Earth at roughly 400 km/s. To put this figure into some perspective, 400 km/s is 24, 000 km/min which means that the wind travels from the Earth to the Moon in 16 minutes. In comparison it took Apollo 11 over 3 days between leaving Earth’s orbit and entering the Moon’s (over 4 days between launch and landing). The particles in the solar wind originate in the Sun’s Corona where temperatures get so hot that the gases have enough energy to escape the gravitational pull of the Sun itself. As these particles reach the Earth, they encounter the Earth’s magnetic field and, being rapidly slowed down by the Earth being in the way, a shock wave forms which is known as the Earth’s Bow Shock.

We must all have dragged a spoon through coffee and watched as the vortices form behind the spoon. It is a low-speed example of turbulent behaviour in the coffee. So it is perhaps not surprising that when the very hot and very fast solar wind hits the magnetic field region of the Earth, we find turbulence there too.

Now when we stir our coffee, we will see that there is one big rotation of fluid in the direction of the spoon but we may also notice smaller eddies in the drink. Some of these form from the fact that the coffee is rotating but the mug’s walls are staying motionless, friction forces the fast moving coffee to slow down at the walls. You can actually see this effect if, rather than stirring your coffee, you put it on a record player (or other rotating platform) as has been featured on Bean Thinking previously. Similarly, when you have a large vortex in the form of a smoke ring, it can decay into many smaller vortex “smoke rings” in what is known as a vortex cascade. This too is an effect that you can see in coffee (but rather than smoke rings you can make milk rings with a straw). Very often these milk rings will decay into many smaller rings in the same sort of vortex cascade as you get with the smoke, you can see a video of the effect here or at the bottom of this post. Big vortices decay into smaller vortices until they (to our eyes) disappear entirely.

vortices, turbulence, coffee cup physics, coffee cup science — Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player). This is an image of water in a rotating mug with a drop of ink placed next to the mug’s wall.

The important thing is that this type of vortex cascade has also been observed in the solar wind. Rather than a giant spoon though, the solar wind stirs itself as the fast wind encounters the (relatively) slow Earth. We are used to stirring our coffee as a way of cooling it down, perhaps we blow on it gently to speed up the cooling process. But this is the difference between your coffee and the solar wind. When the solar wind is stirred up, it gets hotter. To examine how this occurs, scientists have been examining data from the Cluster set of satellites. Launched by the European Space Agency to study the magnetosphere of the Earth, Cluster has provided clues as to how the solar wind differs from a cup of coffee. Back in 2009, scientists analysed the data from Cluster looking at precisely how the turbulence produced as the solar wind meets the magnetosphere cascades into different sorts of eddies, different levels of turbulence. Comparing the data to theoretical models, they showed how the turbulence started off on large length scales (of the order 100 000 km), and decayed into smaller and smaller length scales until it reached 3km. At this point, all that energy, all that motion was dissipated as heat. Stirring the solar wind heated it up.

Why does stirring the solar wind heat it up whereas stirring your coffee cool it down? It’s to do with the environment of the coffee and the wind. On the Earth, the coffee will be surrounded by a cooler atmosphere. Stirring the coffee brings the hot liquid into contact with the cooler air and so the heat from the coffee can escape more efficiently into the atmosphere. They say in space, no one can hear you scream, which is another way of saying that there is no atmosphere through which sound waves can travel¹. No atmosphere means that there is no way of the heat generated by all that turbulence getting dissipated into a cooler air around it. So, as heat is energy, all that energy involved in stirring up the solar wind gets dissipated as heat in the wind which then has a higher temperature to that which we would naively expect.

So, next time you are waiting for your coffee to cool and stir it to hasten the process, take a moment to think about what is happening approximately 90 000 km above your head where the solar wind is being effectively stirred, and heated, by our planet’s magnetic field.

Seeing a vortex cascade in coffee:

¹The origin of the phrase however suggests that this was not quite the meaning that was intended, it was a promotional phrase used for the film Alien.