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Coffee cup science Home experiments Observations

Cracking Magnets

Rare earth magnets are very strong despite their size. These magnets are several times stronger than an ordinary fridge magnet.

Can you hear it? The first, second and then third and fourth cracks as a magnet is brought near a magnetic (but not magnetised) material, such as a piece of cutlery? Unlike the first and second cracks during coffee roasting, which are clearly audible, it is unlikely that you would have actually heard the cracks of a magnet. To hear them you would need to amplify the effect and connect it to a loudspeaker (there’s a link to how you can do this experiment here). Nonetheless, if you were to do so, you would hear the cutlery cracking. And while these sounds are not connected to the first and second cracks in coffee roasting, they are connected, via physics, to coffee. To see why we need to think a bit more about what is causing these magnetic creaking noises.

The effect is known as the Barkhausen effect after Heinrich Barkhausen who discovered it in 1919. It turns out the the effect reveals quite a lot about how magnets work because it reveals what is going on at an atomic level in the kitchen fork. Some metals are attracted to magnets but not others. So a fridge magnet would stick onto materials containing iron but would not stick to a sheet of aluminium; we can pick up pins, paper clips and some cutlery with a strong magnet but we could not pick up a piece of kitchen foil. These iron containing metals are magnetic but not magnetised, they will be attracted to a magnet but they will not ordinarily attract other items to themselves. We may remember from school that we can make them magnetised by continuously stroking a strong magnet along the length of the pin (or fork, or paper clip) until the pin itself is able to attract other pins to it. We may even remember the explanation for this which was that for something to be magnetised, it had to have a clear magnetic orientation of North-South throughout its structure. Within the pin (or fork or paper clip) there are many small regions, called domains, which within themselves have a north-south orientation but they do not all point in the same way throughout the fork. Each little region points in a different direction to the others and so the net effect is that there is no overall North-South magnetism in the fork as a whole. As the strong magnet is used to stroke the fork, so the small regions move to align to the direction of the stroke of the magnet. The regions stop cancelling each other out and align so that the fork itself becomes a magnet with its own North-South.

inverted Aeropress and coffee stain
The link between coffee and the Barkhausen effect in magnets can be seen in this photo: a coffee spillage. It is the way that coffee evaporates and that coffee stains form that forms this physics connection between coffee and magnetism.

To return to our un-magnetised fork, you can imagine that where all these domains meet, there will be an area of confusion where the direction changes from one orientation to that of the neighbouring domain. This is called a ‘domain wall’ and it is these domain walls that are responsible for the Barkhausen effect. You can feel the effects of domains and domain walls in this experiment taken from the Institute of Physics Spark series: take two flat fridge magnets and turn them over so that the magnetic side of each faces the other. Move one of the magnets along the length of the other one. Think about how it feels to move it. Now move the same magnet perpendicular to the direction that you initially moved it in. Try it again. You will find that in one direction the movement feels smooth whereas in the other the magnets judder against each other, the movement is not smooth at all. You are feeling the effects of moving across a series of domains and domain walls, you can read more about the experiment here.

What actually happens as you bring a strong magnet towards an object such as a fork is that those domains in the fork that are aligned in the same direction as the magnet will tend to grow slightly at the expense of the ones that are not aligned with the magnet. The initial growth happens as the aligned domains get a bit bigger, a bit rounder and fatter. The domain walls bend a bit and the domains of the non-aligned regions get a bit thinner, a bit more squished. As the magnet is brought closer still, the aligned domains will actually start to grow at the expense of the non-aligned: the domain walls of the aligned domains will start to move outwards ‘eating’ into the neighbouring regions. It is at this point that you can pick up the Barkhausen effect because as the domain walls move, they can get stuck on defects in the metal rather like an elastic band would get stuck on an obstacle. The defect could be just one or two atoms that are out of place but the effect is that, just like the elastic band, the wall around the obstacle continues growing and the domain wall stretches more like an elastic band until pop – crack – the wall moves releasing a bit of energy that you pick up on the loudspeakers. This is what you hear as the Barkhausen effect. As the walls continue to grow so they will repeatedly get snagged on different defects in the metal and repeatedly ping – crack – into growth. Eventually, as the fork itself becomes magnetic* the last few non-aligned domains also start to align with the approaching strong magnet and the whole fork acts as if it is one magnet.

coffee ring, ink jet printing, organic electronics
A coffee stain. There are many experiments you can do at home with these.

The pinging domain walls have a direct link with an effect you can see in coffee, or more specifically spilled coffee. When you spill a few drops of coffee on a movable surface, you may have noticed that you can angle the surface a surprising amount before the drop starts to run down the side. You could try it now on a coaster if you have one available to you. The drop does not move because the edge is stuck, ‘pinned’, on defects on the surface of the coaster. These defects could be a crack in the material or a bit of dust or even a slight irregularity on the surface. Whatever it is, this defect acts to keep the edges of the drop in place. The first effect you would notice is that you can move the drop to a near vertical without it moving, the drop shape gets distorted but the drop itself does not move. The second effect is more subtle and is what happens if you leave the coffee drop there to dry.

Once spilled, the water in the droplet starts evaporating and eventually the droplet will dry leaving a coffee stain. The consequence of the pinning that you have just noticed is that the edges of the drop are quite stuck: the drop can’t just shrink. Instead, as the water evaporates, the drop will get flatter and because the water evaporates more quickly from the droplet edge (to see why click here), there will be a flow of water inside the drop from the centre to the edges. As the water flows outwards so it takes the coffee sediment with it which means that the dried coffee becomes a ring of sediment at the edge of the dried droplet.

Although it is on a different scale, it is the same sort of pinning that is happening in the coffee ring and in the Barkhausen effect. There are connections between physics and coffee to be found in many surprising places. Where will you find one today?

*This is an instance in which scientific English is not the same as English-English. In scientific-English, the fork is always a magnetic material it is just not fully magnetised. In English-English we tend to use the word ‘magnetic’ only for those materials that attract iron etc. to them. For ease of reading I have kept with the English-English usage here but if you are interested, you can read more in these links about magnetism and magnetic materials.

Categories
Home experiments Observations Science history

21 years of the coffee stain

dried coffee stains, alcohol and coffee
Happy 21st birthday to the coffee stain. But there is still much for us to learn 21 years after the first paper on the coffee stain was published.

On the 23rd October, 1997, a paper was published in the journal Nature titled “Capillary flow as the cause of ring stains from dried liquid drops.” The title is in the dry style that scientific papers can be written. An alternative title could have been “How coffee stains form”*. Perhaps you would think, surely someone had known how coffee stains formed before 1997? And maybe you would go on to think: certainly 21 years later in 2018, we’d know all there was to know about the coffee stain? I hope that readers of Bean Thinking would not think “who cares about coffee stains?”, but I wonder whether it was the combination of disinterest and assuming that someone somewhere surely knew how they formed that meant it took until 1997 for anyone to ask the question: well how do they form?

Coffee is a very popular drink among scientists, though even this does not explain how popular this paper has become. A paper’s popularity can be measured in ‘number of citations’ which tells you how many times other authors have found this piece of work important enough to reference it in their own published paper. As of early November 2018, this paper has been cited nearly 3300 times. Why? Well, there seem to be at least two reasons. Firstly, it turns out that the coffee stain effect is of enormous technological relevance; it may even have been used in the manufacture of the device you are using to read this website. But secondly even now, 21 years later, we still don’t understand what is going on, there is still much to learn and some of it is some very subtle and very beautiful physics.

the droplets ready to dry
What happens when you form coffee stains using drops containing two liquids (alcohol and water) compared to just one (water)?

Very recently for example, a new paper was published in Physical Review Letters. This one was titled “Density-driven flows in evaporating binary liquid droplets“. Another exciting title, another time we’ll retitle it for the purposes of this post: “what happens when you mix alcohol with a coffee type suspension, dry it at different angles and film it drying.” Arguably this time the given title is more succinct. Why does it make a difference if you add alcohol to your coffee rather than just drink it straight (the coffee, not the alcohol)? And what happens to the resulting coffee stain?

Maybe of an evening you’ve been relaxing with a glass of wine, or something stronger, and noticed the “legs” rising up the glass. Their formation and appearance is due to the differing surface tensions between alcohol and water and the fact that alcohol evaporates more easily than water, you can read more about that effect here. The point is that because of the difference in surface tension between alcohol and water, you get a flow of liquid from areas of low surface tension (higher alcohol content) to high surface tension (high water content). And it was this that had been thought to drive coffee stain formation in droplets which were a mix of liquids, water and alcohol for example. But how do you isolate this effect from the other effect in which alcohol evaporates more quickly than water and so there are changes in density and buoyancy of the droplet?

pendulant droplets
Drying droplets upside down. The things we do for coffee science.

To answer this you could add n-butanol to the water (or coffee) rather than alcohol. Just like ethanol based alcohol (the sort you may get in gin), n-butanol has a much lower surface tension and lower density than water but unlike alcohol, it evaporates much less readily than water. So, in a water-butanol mix it will be the water that goes first, while exactly the opposite will happen for an alcohol-water mix. In a drying droplet, the liquid evaporates most quickly from the edge of the drop. Therefore, after an initial, chaotic stage (imaginatively called stage I), you will end up with a droplet that is water rich around its rim in the alcohol-water mix but n-butanol rich around the droplet edge in an n-butanol-water mix (stage II). This suggests a way that you can distinguish the flows in the drop due to surface tension effects from those due to the differences in density between water and alcohol/n-butanol.

How would you test it? One way would be to compare the droplets evaporating as if you had spilled them on the table top with droplets evaporating ‘upside-down’, as if you had tipped the table by 180° after spilling your coffee. You can then watch the flow by taking many photographs with a camera. In this way you would be able to test whether it was surface tension flow (which should be in the same direction within the drop whether the droplet is upright or suspended) with gravity driven flow which should be opposite (the drop is upside down after all).

schematic drops upright and upside down
A cartoon of the flow found in droplets of alcohol and water mix. When upright, the flow is up through the centre of the drop and down the sides. This is expected for both surface tension based flows and flows due to gravity. When upside down, the flow is still upwards through the centre of the drop but this time the drop is upside down. So this is what you’d expect if the dense water at the edge of the drop flowed downwards (gravity based) but not if the flow were dominated by surface tension effects which should be the same, relative to the drop-interface as if the drop were upright.

The authors of the study did this and found that the flow in upright drops of alcohol-water was opposite to that in n-butanol-water drops. This is what is expected both in surface tension dominated flow and in gravity dominated flow. But, when the drops were inverted, the flow within the droplet did not change absolute direction, instead it changed direction relative to the substrate (it may be helpful to see the cartoon), in both droplet types. Expected for a gravity driven flow (dense liquids move downwards), this is exactly the opposite to what would be expected with surface tension driven flow. It is sensible to conclude that the flow in drying droplets containing two liquid types is dominated by gravity, or as the authors phrased it “density-driven flows in evaporating binary liquid droplets”.

dried upside down drops
The resultant coffee stains of drops that had been suspended upside down. They seem fairly similar to the upright ones with the exception of the central dot in many of the stains. The arrow shows some coffee that spilled down the surface as the tray was flipped over.

While the authors did a lovely job of watching the flows within the droplet, what happened to the the actual coffee stain? It could prompt us to do an experiment at home. How does adding alcohol affect the appearance of a coffee stain if the drop is upright compared to if you turned the drops all upside down? What happens if the droplet is not held upside down but instead at an angle to the vertical? There are many ways you could play with this result, see what happens, have a glass of wine and see if that gives you any insight into what you see with your coffee. As ever, have fun and if you do get any interesting results, please do let me know here, on twitter or over on FB.

 

*The dry scientific author in me wants to point out that although catchier, the title “how coffee stains form” does not actually capture the extent of the physics nor what the paper was about (the fact that this happens more often than just in coffee) and the given title was much better. The coffee drinker in me thinks yes, but, surely we could make it all about coffee anyway…

Categories
Coffee cup science General Home experiments Observations Science history

Coffee Rings: Cultivating a healthy respect for bacteria

coffee ring, ink jet printing, organic electronics
Why does it form a ring?

It is twenty years since Sidney Nagel and colleagues at the University of Chicago started to work on the “Coffee Ring” problem. When spilled coffee dries, it forms rings rather than blobs of dried coffee. Why does it do that? Why doesn’t it just form into a homogeneous mass of brown dried coffee? Surely someone knew the answer to these questions?

Well, it turns out that until 1997 no one had asked these questions. Did we all assume that someone somewhere knew? A bit like those ubiquitous white mists that form on hot drinks, surely someone knew what they were? (They didn’t, the paper looking at those only came out two years ago and is here). Unlike the white mists though, coffee rings are of enormous technological importance. Many of our electronic devices are now printed with electrically conducting ink. As anyone who still writes with a fountain pen may be aware, it is not just coffee that forms ‘coffee rings’. Ink too can form rings as it dries. This is true whether the ink is from a pen or a specially made electrically conducting ink. We need to know how coffee rings form so that we can know how to stop them forming when we print our latest gadgets. This probably helps to explain why Nagel’s paper suggesting a mechanism for coffee ring formation has been cited thousands (>2000) of times since it was published.

More information on the formation of coffee rings (and some experiments that you can do with them on your work top) can be found here. Instead, for today’s Daily Grind, I’d like to focus on how to avoid the coffee ring effect and the fact that bacteria beat us to it. By many years.

There is a bacteria called Pseudomonas aeruginosa (P. aeruginosa for short) that has been subverting the coffee ring effect in order to survive. Although P. aeruginosa is fairly harmless for healthy individuals, it can affect people with compromised immune systems (such as some patients in hospitals). Often water borne, if P. aeruginosa had not found a way around the coffee ring effect, as the water hosting it dried, it would, like the coffee, be forced into a ring on the edge of the drop. Instead, drying water droplets that contain P. aeruginosa deposit the bacteria uniformly across the drop’s footprint, maximising the bacteria’s survival and, unfortunately for us, infection potential.

The bacteria can do this because they produce a surfactant that they inject into the water surrounding them. A surfactant is any substance that reduces the surface tension of a liquid. Soap is a surfactant and can be used to illustrate what the bacteria are doing (but with coffee). At the core of the bacteria’s survival mechanism is something called the Marangoni effect. This is the liquid flow that is caused by a gradient in surface tension; there is a flow of water from a region of lower surface tension to a region of higher surface tension. If we float a coffee bean on a dish of water and then drop some soap behind it, the bean accelerates away from the dripped drop (see video). The soap lowers the surface tension in the area around it causing a flow of water (that carries the bean) away from the soap drop.

If now you can imagine thousands of bacteria in a liquid drop ejecting tiny amounts of surfactant into the drop, you can hopefully see in your mind’s eye that the water flow in the drying droplet is going to get quite turbulent. Lots of little eddies will form as the water flows from areas of high surface tension to areas of low surface tension. These eddies will carry the bacteria with them counteracting the more linear flow from the top of the droplet to the edges (caused by the evaporation of the droplet) that drives the normal coffee ring formation. Consequently, rather than get carried to the edge of the drop, the bacteria are constantly moved around it and so when the drop finally dries, they will be more uniformly spread over the circle of the drop’s footprint.

Incidentally, the addition of a surfactant is one way that electronics can now be printed so as to avoid coffee ring staining effects. However, it is amusing and somewhat thought provoking to consider that the experimentalist bacteria had discovered this long before us.

Categories
Coffee cup science General Home experiments Observations slow

Coffee ring bacteria

coffee ring, ink jet printing, organic electronics
Why does it form a ring?

We have all seen them: Dried patches of coffee where you have spilled some of your precious brew. The edge of the dried drop is characteristically darker than the middle. It is as if the coffee in the drop has migrated to the edge and deposited into a ‘ring’. It turns out though that these coffee rings are not just an indication that you really ought to be cleaning up a bit more often. Coffee rings have huge consequences for the world we live in, particularly for consumer electronics. Various medical and diagnostic tests too need to account for coffee ring effects in order to be accurate. Indeed, coffee rings turn up everywhere and not just in coffee. Moreover, the physics behind coffee rings provides a surprising connection between coffee and the mathematics of bacteria growth. To find out why, we need to quickly recap how coffee rings form the way they do.

When you spill some coffee on a table it forms into droplets. Small bits of dust or dirt or even microscopic cracks on the table surface then hold the drop in the position. We’d say that the drop is pinned in position.

artemisdraws, evaporating droplet
As the water molecules leave the droplet, they are more likely to escape if they are at the edge than if they are at the top. Illustration by artemisdraws.com

As the drop dries, the water evaporates from the droplet. The shape of the drop means that the water evaporates faster from the edges of the drop than from the top (for the reasons for this click here). But the drop is stuck (pinned) in position and so cannot shrink but instead has to get flatter as it dries. As the drop gets squashed, water flows from the centre of the drop to the edges. The water flow takes the coffee particles with it and so carries them to the edge of the drop where they deposit and form into a ring; the coffee ring. You can see more of how coffee rings form in the sequence of cartoons below and also here.

However in this quick explanation, we implicitly assumed that the coffee particles are more or less spherical, which turns out to be a good assumption for coffee. The link with the bacteria comes with a slightly different type of ‘coffee’ ring. What would happen if we replaced the spherical drops of coffee particles with elliptical or egg shaped particles? Would this make any difference to the shape of the coffee rings?

Artemisdraws
As water evaporates from A, the drop gets flatter. Consequently, the coffee flows from A to B forming a ring. Illustration by artemisdraws.com

In fact the difference is crucial. If the “coffee” particles were not spherical but were more elliptical, the coffee ring does not form. Instead, the elliptical particles produce a fairly uniform stain (you can see a video of drying drops here, yes someone really did video it). The reason this happens is in part due to a pretty cool trick of surface tension. Have you ever noticed how something floating on your coffee deforms the water surface around it? The elliptical particles do the same thing to the droplet as they flow towards the edge. (Indeed, the effect is related to what is known as the Cheerios effect). This deformation means that, rather than form a ring, the elliptical particles get stuck before reaching the edge and so produce a far more uniform ‘coffee’ stain when the water dries.

E Coli on a petri dish
A growing E. Coli culture. Image courtesy of @laurencebu

By videoing many drying droplets (containing either spherical or elliptical particles), a team in the US found that they could describe drying drops containing elliptical particles with a mathematical equation called the Kardar-Parisi-Zhang equation (or KPZ for short). The KPZ equation is used to describe growth process such as how a cigarette paper burns or a liquid crystal grows. It also describes the growth of bacterial colonies. Varying the shape of the elliptical particles in the drying drop allows scientists to test the KPZ equation in a controllable way. Until the team in the US started to ask questions about how the coffee ring formed, it was very difficult to test the KPZ equation by varying parameters in it controllably. Changing the shape of the particles in a drying drop gives us a guide to understanding the mathematics that helps to describe how bacterial colonies grow. And that is a connection between coffee and bacteria that I do not mind.

As ever, please leave any comments in the comments section below. If you have an idea for a connection between coffee and an area of science that you think should be included on the Daily Grind, or if you have a cafe that you think deserves a cafe-physics review, please let me know here.