kitchen top experiments

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…

Coffee (beans) in the blood?

Brazil nut effect

A green bean ‘floating’ in coffee grounds. When you pour your beans into your grinder, do they behave like a liquid flow or do they have their own type of ‘granular’ flow?

When you first learn about liquids, solids and gases, you may learn about the fact that a solid keeps its shape whereas a liquid flows. A solid is rigid and can be moved as one block whereas a liquid will spread and change shape. Solids can be stacked up like bricks though this is not true of liquids.

A slightly unfair question is then put to you. What about sand? (Or, in the context of this website, what about coffee beans?). A pile of beans will initially stack but as the pile builds, avalanches will occur to prevent the tower being too vertical. When you pour your beans into your grinder hopper, the beans will level out, in much the same way as the eventual coffee will in the cup. Do the collection of coffee beans move more as if they are a liquid or a solid?

Clearly to some extent the question is wrong, the beans represent their own class of structure but perhaps a better way of asking the question would be, how do a collection of coffee beans flow? It is a question with consequences beyond the coffee hopper. From pharmaceuticals to civil engineering projects and beyond, understanding how granular materials flow is an important topic.

Beans on a plate. The aspect ratio of the coffee bean is similar to that of the particles used in a new study to analyse granular flow.

And yet it has apparently been difficult to analyse this problem owing to the difficulty in tracking individual coffee beans (tablets or particles of cement) as they are pushed in one direction or another. A start was made nearly 20 years ago when a team at the University of Chicago used Magnetic Resonance Imaging (MRI, yes, the same MRI as you get in hospitals) to image individual mustard and poppy seeds as they flowed between two cylinders. The imaging allowed researchers to track the position and velocity and packing density of the seeds as they moved around the cylinders. Then, last year a new study used X-ray tomography to watch individual particles in a rectangular box as they were subjected to being pushed at various pressures in different directions. This, more recent study used plastic ellipses with a minor axis of 6.35mm and an aspect ratio of 1.5. Sadly, not real coffee beans but a fairly large plastic equivalent. While the aspect ratio will of course vary from varietal to varietal and even bean to bean, the coffee beans in my hopper at the moment have an aspect ratio of 1.3 (and a minor axis of 4.5mm) which makes them pretty close to the plastic used in the study.

Brew&Bread, latte art Sun, KL latte art

The structures in milk allow the milk to be ‘frothed’ and so enable latte art. They also make milk an example of a complex fluid.

By tracking each bean, the study discovered that such granular collections moved as if they were “complex fluids”. Which is all very well but does makes you wonder, what is a complex fluid? Is coffee a complex fluid?

Does the definition help? The definition on the Physics (APS) website says that: complex fluids “can be considered homogeneous at the macroscopic (or bulk) scale, but are disordered at the “microscopic” scale, and possess structure at an intermediate scale.”. What does that mean? Well, it seems to mean that complex fluids contain things that are larger than the molecules that make up the liquid and so affect how the fluid flows. Milk has long chains of proteins and fats (which give it the foam like qualities when it is frothed in a cappuccino) and so is a complex fluid. Chocolate and blood are other complex fluids as are emulsions and gels. Pure water would not be a complex fluid and my guess is that coffee (which contains water molecules and various molecules associated with the coffee itself) is also not a complex fluid. Were you to have a latte or a cortado though, the milk would transform your coffee into a complex fluid. Although I much prefer to keep my coffee simple, it would seem that there is more to the saying “you have coffee in your blood” than it would at first appear, particularly as regards the coffee beans. It may be time for some experimental tests of coffee bean (and coffee or latte liquid) flow….

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.

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.

 

Theme on a V60

bloom on a v60

V60 bubbles. There is much to be gained by slowing down while brewing your coffee.

Preparing a coffee with a pour-over brewer such as a V60 is a fantastic way to slow down and appreciate the moment. Watching anti-bubbles dance across the surface as the coffee drips through, inhaling the aroma, hearing the water hit the grind and bloom; a perfect brewing method for appreciating both the coffee and the connectedness of our world. The other week, while brewing a delightful Mexican coffee from Roasting House¹, I noticed something somewhat odd in the V60. Having placed it on the kitchen scales and, following brewing advice, measured the amount of coffee, I poured the first water for the bloom and then slowly started dripping the coffee through. Nothing unusual so far and plenty of opportunity to inhale the moment. But then, as I poured the water through the grind, I noticed the scales losing mass. As 100g of water had gone through, so the scales decreased to 99g then 98g and so on. It appeared the scales were recording the water’s evaporation.

science in a V60

Bubbles of liquid dancing on the surface of a brewing coffee.

It is of course expected that, as the water evaporates, so the mass of the liquid water left behind is reduced. This was something that interested Edmond Halley (1656-1742). Halley, who regularly drank coffee at various coffee houses in London including the Grecian (now the Devereux pub), noted that it was probable that considerable weights of water evaporated from warm seas during summer. He started to investigate whether this evaporating vapour could cause not only the rains, but also feed the streams, rivers and springs. As he told a meeting of the Royal Society, these were:

“Ingredients of a real and Philosophical Meteorology; and as such, to deserve the consideration of this Honourable Society, I thought it might not be unacceptable, to attempt, by Experiment, to determine the quantity of the Evaporations of Water, as far as they arise from Heat; which, upon Tryal, succeeded as follows…”²

Was it possible that somehow Halley’s demonstration of some three hundred years ago was being replicated on my kitchen scales? Halley had measured a pan of water heated to the “heat of summer” (which is itself thought provoking because it shows just how recent our development of thermometers has been). The pan was placed on one side of a balance while weights were removed on the other side to compensate the mass lost by the evaporating water. Over the course of 2 hours, the society observed 233 grains of water evaporate, which works out to be 15g (15 ml) of water over 2 hours. How did the V60 compare?

Rather than waste coffee, I repeated this with freshly boiled water poured straight into the V60 that was placed on the scales. In keeping with it being 2017 rather than 1690, the scales I used were, not a balance, but an electronic set of kitchen scales from Salter. The first experiment combined Halley’s demonstration with my observation while brewing the Mexican coffee a couple of weeks back. The V60 was placed directly on the scales and 402g of water just off the boil was poured into it. You can see what happened in the graph below. Within 15 seconds, 2 g had evaporated. It took just a minute for the 15g of water that Halley lost over 2 hours (with water at approximately 30 C) to be lost in the V60. After six minutes the rate that the mass was being lost slowed considerably. The total amount lost over 12 minutes had been 70g (70ml).

evaporation V60 in contact with scales

A V60 filled with 400g of water just off the boil seemed to evaporate quite quickly when placed directly on the scales.

Of course, you may be asking, could it be that the scales were dodgy? 70g does seem quite a large amount and perhaps the weight indicated by the scales drifted over the course of 12 minutes. So the experiment could be repeated with room temperature water. Indeed there did appear to be a drift on the scales, but it seemed that the room temperature water got moderately heavier rather than significantly lighter. A problem with the scales perhaps but not one that explains the quantity of water that seems to have evaporated from the V60.

control

Hot water (red triangles) loses more mass than room temperature water (grey squares).

Could the 70g be real? Well, it was worth doing a couple more experiments before forming any definite conclusions. Could it be that the heat from the V60 was affecting the mass measured by the electronic scales? After all, the V60 had been placed directly on the measuring surface, perhaps the electronics were warming up and giving erroneous readings. The graph below shows the experiment repeated several times. In addition to the two previous experiments (V60 with hot water and V60 with room temperature water placed directly on the scales), the experiment was repeated three more times. Firstly the V60 was placed on a heat proof mat and then onto the scales and filled with 400g of water. Then the same thing but rather than on 1 heat proof mat, three were placed between the kitchen scales and the V60. This latter experiment was then repeated exactly to check reproducibility (experiment 4).

You can see that the apparent loss of water when the V60 was separated from direct contact with the scales was much reduced. But that three heat proof mats were needed to ensure that the scales did not warm up during the 12 minutes of measurement. Over 12 minutes, on three heat proof mats, 14g of water was lost in the first experiment and 17g in the repeat. This would seem a more reasonable value for the expected loss of water through evaporation out of the V60 (though to get an accurate value, we would need to account for, and quantify the reproducibility of, the drift on the scales).

V60 Halley

The full set: How much water was really lost through evaporation?

Halley went on to estimate the flow of water into the Mediterranean Sea (which he did by estimating the flow of the Thames and making a few ‘back of the envelope’ assumptions) and so calculate whether the amount of water that he observed evaporating from his pan of water at “heat of summer” was balanced by the water entering the sea from the rivers. He went on to make valuable contributions to our knowledge of the water cycle. Could you do the same thing while waiting for your coffee to brew?

Let me know your results, guesses and thoughts in the comments section below (or on Twitter or Facebook).

¹As this was written during Plastic Free July 2017, I’d just like to take the opportunity to point out that Roasting House use no plastic in their coffee packaging and are offering a 10% discount on coffees ordered during July as part of a Plastic Free July promotion, more details are here.

²E Halley, “An estimate of the quantity of vapour….” Phil. Trans. 16, p366 (1686-1692) (link opens as pdf)

Making a splash

You spilled your coffee, a terrible accident or an opportunity to start noticing?

Why do some droplets splash  while others stay, well, drop like? It turns out that there is some surprising physics at play here. When a drop of water, or coffee, falls from a height and onto a flat surface (such as glass), we are accustomed to seeing the droplet fracture into a type of crown of smaller droplets that form a mess over the surface. Visually spectacular, these splashing droplets have even been made into an art form (here).

Fast frame-rate photography reveals how each micro-droplet breaks away from the splashing drop:

Video taken from Vimeo – “Drop impact on a solid surface”, a review by Josserand and Thoroddsen.

 

So it perhaps surprising to discover that there are many things about this process that we do not yet understand. Firstly, if you reduce the gas pressure that surrounds the drop as it falls, it does not make a splash. In the extreme, this means that if you were to spill your coffee in a vacuum, you would not see the crown-like splashing behaviour that we have come to expect of falling liquids. Rather than splash, a droplet falling in low pressure spreads out on impact as a flattening droplet. This counterintuitive result was first described in a 2005 study (here) that compared the effect on splashing of droplets with different viscosities (methanol, ethanol, 2-propanol) falling through different gasses.

cortado, Brunswick House, everyday physics, coffee cup science

Don’t spill it!
But would a latte splash more or less than a long black?

The authors of the study ruled out the effect of air entrapment surrounding the droplet as it falls as high speed photography had not indicated any air bubbles in the droplet just before impact. Instead they considered that whether a drop splashes on impact – or not – depended on the balance between the surface tension of the falling liquid and the stress on the drop created by the restraining pressure of the surrounding gas. Calculating these stresses led to a second surprising result. Whether a drop splashes on impact or not depends on its viscosity (as well as the gas pressure and the speed of impact). But the surprising bit is that the more viscous the liquid, the greater the splash.

From a common-sense perspective (that may or may not have any bearing on the reality of the situation), an extremely viscous liquid like honey should not splash as much as a less viscous liquid like coffee. This suggests that there is an upper-limit in viscosity to the relation predicted in the 2005 study. After all, although the authors did change the viscosity of the liquids, the range of viscosity they studied was not as great as the difference between coffee and honey. This sounds like a perfect experiment for some kitchen-top science and so if any reader can share the results of their experiments on the relative splashes formed by coffee and honey, I would love to hear of them.