On rings, knots, myths and coffee

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.


Thinking of foraging at Damson & Co

Damson and Co, like its wild counterpart, easy to miss

Damson & Co on Brewer St.

At approximately this time of year, it is possible to start foraging for damsons in the UK countryside. These small plums make lovely cakes and muffins and, very importantly, great damson gin. A bit like sloe gin but, in my opinion, better. All this is a digression. When I found out about a cafe called Damson & Co I had to try it, purely for the name which brings back fond memories of country walks and gin shared with friends. However, even armed with its address and location on a map I missed it! Damson & Co is very inconspicuous in the way that it is situated on the street. Just as with its wild counterpart, it is easy to walk past without noticing that it’s there but once you’ve seen it, it is obvious, a location that you mark down in order to return to it again and again.

Inside, lavender decorated the table tops in the small but extremely friendly cafe. We enjoyed an Americano, an iced latte and a lovely chocolate brownie that had been warmed almost to the point of melting. They were also extremely helpful when I asked the dreaded “does it contain nuts?” question, checking the ingredients, informing me of the (obligatory) “it may have had contact with a nut at some point in its manufacture” line, but ultimately helping me to choose what was a great nut-free cake. Complementary water was automatically put onto the table and so we had, for the brief moment before I ate the cake, a range of ‘phases of matter’ on the table. Water in the forms of liquid in the bottle, solid ice and steam rising up from the coffee and a brilliantly gooey, viscous chocolate cake somewhere between liquid and solid. At that point it was quite clear what the physics bit of this cafe-physics review would have to be: phases of matter and phase changes.

interior of Damson & Co

Lavender in a jar with sugar in the window of Damson & Co

As ice melts into water, or evaporates to form steam, it undergoes many changes in its properties: Ice is of course solid; liquid water conducts heat much readily more than steam (more on this another day). Another property that changes is the heat capacity of the ice/water/steam. The heat capacity is the amount of energy that it takes to heat a substance by one degree in temperature. At the temperature that the substance changes, say between a liquid and a solid, there will frequently be a spike in a plot of “heat capacity” vs. temperature. This tells us that, as the solid changes to a liquid (or vice versa) the response of the material to being heated changes. Physicists often measure the heat capacity of substances to see if any phase changes occur. A phase change does not necessarily mean that the substance goes from liquid to solid or to gas. A substance will be said to undergo a phase change if it becomes ferromagnetic (like iron at room temperature) or if it becomes superconducting (like aluminium at approximately -272C). Back in the 1920s it was the investigation of the heat capacity of liquid helium that helped to suggest that there was a new form of matter lurking at extremely low temperatures.

Heike Kamerlingh Onnes (a great physicist and apparently a very nice man) had managed to liquify helium gas in 1908. Helium gas becomes a liquid below -269C. By the 1920s it was clear that something very strange happened to liquid helium if you cooled it even more, to temperatures below -271C. The behaviour of the heat capacity spiked indicating that the helium was undergoing another phase change, but to all appearances it was still a liquid. There was no indication that the helium was solidifying, what could it be? More experiments revealed that below -271C the helium liquid started to behave very strangely indeed. It climbed up the walls of its container ‘by itself’ and it managed to leak through minuscule cracks in the glass containers that it was kept in (for a video click here). Cracks that could not be detected before the ultra-cold helium started to leak through them. It took until 1937/38 before this new state of matter was named and it is still not clear that we understand it.

There is so much more to the phases of matter than meets the eye while watching ice melt in a glass of water on a hot summer’s day.

Damson & Co can be found at 21 Brewer St. London

Helium in your coffee?

C-C bond, Esters N16

The sign board at Esters. Note the zig zag underline

As a website based on the physics inside a coffee cup, it was only a matter of time before I visited Esters in Stoke Newington. The name has significance to anyone interested in the physics (or chemistry) of coffee and the signboard outside the shop confirmed it. Under the name, there is a zig zag underline that represents part of a molecular structure. The end of each straight line signifies a carbon atom which is bonded to its neighbouring carbon atom by either a single (one line) or a double (two lines) bond. Inside you can enjoy (as I did) single estate coffees that can be prepared (if there are 2 or 3 of you) in a Chemex, appropriately enough. As I left Esters, I wandered through a local park where, near the entrance to the park, were two helium balloons caught in a tree. One had deflated, the other floated, dejectedly, just beneath the branches. Such a timely observation! The story of the discovery of helium connects the signboard at Esters, a cup of coffee and helium itself, how could that be? You’ll just have to keep reading to find out.

neon sign, light emission

The colours of “neon signs” depend on the particular gas (eg. neon) in the tubes

Helium is the second most plentiful element in the universe but on earth it is relatively rare. It was therefore not discovered on earth but, instead, by looking at the Sun. Its ‘discovery’ in the Sun was due to the way in which atoms interact with light. The atoms in each element emit (or absorb) light at specific frequencies. These frequencies correspond to different colours. It is this property of atoms that creates colours such as the distinctive hue of neon lights. In 1868 two astronomers were observing the same solar eclipse. Independently of each other, they noticed a distinct emission of light from the Sun at a wavelength of 587.49 nanometres (yellow-ish). This emission line corresponded to no element that had been found on earth and so one of them, Norman Lockyer suggested naming this new element helium, after ‘Helios’ the Greek god of the Sun. Helium was not found on earth for another 27 years when William Ramsay isolated it from a uranium based compound. The gas that Ramsay extracted, absorbed and emitted light at the same frequency as the two astronomers had observed for the element in the Sun. Helium had been found on earth.

Think of energy levels as rungs on a ladder. Image credit © www.artemisworks.co.uk

Think of energy levels as rungs on a ladder. Image credit © www.artemisworks.co.uk

Atoms absorb (and emit) light because of the way that the electrons in the atoms are arranged around the atomic nucleus. The electrons exist in discrete energy states that we can imagine as rungs on a ladder.  Electrons move between the states by absorbing, or emitting, light at specific energies (corresponding to a step up, or a step down on the ladder). As the energy of light depends on its frequency, the colour of an element depends on the spacing of the rungs of this atomic ladder, which is different for different elements. The energy ladder of helium atoms means that helium emits light at 587.49 nanometres. In organic molecules (ie. all the molecules that make up you and I and coffee), it is often the double carbon bonds that provide the energy ‘step’ in the visible range of light. Depending on the number of carbon atoms that are double bonded and the number in the molecule that are not, the energy step is tweaked slightly so that it will absorb in the red region in some materials and in the blue in others. We have our link between the sign at Esters and the observations of the astronomers.

However the explanation above depends on knowing some properties of electrons in atoms and some details of quantum mechanics. Neither electrons (discovered in 1897) nor quantum mechanics were known to the discoverers of helium. How did the astronomers recognise that their observation of a particular colour of light meant that they had identified a new element? Part of the answer must be based on experience. Experimentalists had already found out that different materials absorbed (and emitted) light at different but specific, frequencies. The other part of the answer brings us to our link with coffee.

A milk ring in water. Once it was thought that atoms might look like this.

A milk ring in water. Once it was thought that atoms might look like this (but a lot smaller).

In the video Coffee Smoke rings, we can make rings of milk travel through coffee or water. These rings are vortices which are closed up on themselves to form a doughnut shape. Mathematically, the vortex ring is a completely stable structure, it never decays. You could argue that the reason that it decays in the video is because we live in a non-ideal world with non-ideal liquids (milk and water). Returning to the mathematical world, each vortex ring will vibrate at specific, (resonance) frequencies dependent on its diameter, just like a bell rings with a note dependent on the size of the bell. So, even without knowing about electrons or quantum mechanics, it becomes conceivable that the atoms that go to make up a substance have specific resonance frequencies. If you imagine that atoms are in fact extremely small vortex rings (of the kind you find in a coffee cup), the model even has a predictive power. In 1867 William Thomson proposed such a “vortex atom” model and suggested that the distinct vibrations of the rings led to energy levels, like the ladders of later quantum mechanics and exactly of the sort that were observed by the astronomers. By considering that a sodium atom was made out of two inter-locked vortex rings, the light emission of sodium could even be accounted for. It was therefore entirely conceivable that elements would have distinct fingerprints as the astronomers had observed for this new element, helium.

We have therefore found the connection between the signboard at Esters, milk rings in a coffee cup and the discovery of helium. You would be forgiven for thinking that part of the connection is purely historical, after all, our current models of the atom do not rely on vortex rings at all. However, there is a relatively new theory called “string theory”. More fundamental than atoms, string theory proposes that there exist ‘strings’ that may be closed on themselves and that have specific vibrations that depend on their size and geometry. Sound familiar? Perhaps the connection with the milk rings lives on.