The effects of surface tension can be seen in the light reflected from a coffee
UK Coffee week is once again upon us meaning that all week we can be justified in thinking about, drinking, appreciating and celebrating coffee. And of course, as soon as we start to do this, we realise we have to drink, appreciate and celebrate water which is, ultimately, what really makes most of the cup of coffee. So UK Coffee Week raises money for Project Waterfall which is a charity that brings clean water to coffee growing communities. Giving something back by enjoying something good.
In keeping with the water theme, this week The Daily Grind is all about water, including an experiment that enables you to make a hole in it. As this is also the week between Palm Sunday and Easter, perhaps we could call the post “Holey water for Holy Week”.
But moving quickly to the experiment. While drinking your coffee, you may have noticed how around the edge of the cup, the coffee appears lighter, not quite so dark, as in the interior. The coffee is being bent upwards at the edge of the cup by the surface tension of the water in the coffee. Now, what happens if you add alcohol to the coffee? If you do this in your coffee cup you may well end up with an Irish coffee which may provide even more of an excuse to celebrate your coffee drinking, but if you were to put your coffee on a plate first (I know, why? but bear with me) you will get a quite different result. You will be able to make a hole in the middle of your coffee. The reason is that the surface tension of alcohol is much weaker than that of water. Consequently, if you try to mix a very thin layer of coffee with a small amount of alcohol, something slightly unexpected happens as this video shows:
The addition of a small amount of alcohol into the middle of a thin layer of water (or coffee) causes the water to recede. As the alcohol evaporates off, you are left with a dry ‘hole’ in the coffee. Why is this? It is effectively a liquid-tug-of-war on your plate. The higher surface tension in the coffee (or water) pulls against the weaker surface tension of the alcohol which eventually means that the water breaks away, leaving the hole. As the water molecules are continually moving, eventually they start to meet again over the dry spot and close the hole.
You can’t see this in your mug of course because the mixing occurs throughout the liquid while the plate ensures that this is only a surface effect.
You will need a strong alcohol, perhaps gin or vodka but please do try this experiment, let me know how you get on and enjoy the coffee, water (and alcohol) in UK Coffee week. And if you want to donate to Project Waterfall, you could either find a participating café here or donate online here.
Everything is connected. At least, that is part of the premise of Bean Thinking, where the physics of a coffee cup is used to explore the physics of the wider world. So it was great to stumble upon a new connection that I had not previously appreciated¹.
Like the vortices behind a spoon dragged through coffee….
The connection is between climate science and that wonderful pastime of pulling a spoon through coffee and watching the vortices form behind it. Yet the research that revealed this connection was not looking for links between coffee and the atmosphere. Instead the researchers were interested in something seemingly (and hopefully) very far from a coffee cup: rogue waves.
Rogue waves are rare and extremely large waves that have been the subject of mariners tales for many years. Nonetheless, it is only relatively recently that they have become the subject of scientific research, partly because they are so rare and so outside our usual experience that they were thought to be the stuff of myth rather than of science. So it is only now that we are developing an understanding of how it can be that, in amongst a number of smaller waves, a massive wave of 20m height can suddenly appear, apparently out of nowhere. One of the groups looking at this problem investigated the effect of a particular sort of (known) instability on a series of waves in water. However, unlike other research groups, this particular study included the effect of the air above the water as well as the waves themselves.
Rogue waves seem to come out of nowhere. A rogue wave can be 2 or 3 times the height of the other waves in the water at the time. How and why do they form?
Although this sounds a simple idea, modelling water waves in air is actually extremely complex. To do so, the authors of the study had to use a computer simulation of the air-water interface. It is not the sort of problem that can be solved analytically, instead the computer has to crunch through the numerical solutions. In order to start to see what was going on with the rogue waves, the authors had to simulate multiple waves of different amplitudes. Each simulation took weeks to perform. Given that this was only a few years ago (the study was published in 2013), you can start to see why people had previously been approximating water waves as waves in water (without worrying too much about the air interface).
Now here is where the link with coffee comes in. The group modelled waves as a function of steepness and found that, above a critical steepness, the wave breaking caused significant interaction between the air and the water layers. In addition to the bubbles that form when waves break, the movement of the air over the breaking wave formed into a vortex which, when it interacted with the back of the wave created an opposite vortex: a vortex dipole “much like the vortices that form behind a spoon dragged through a cup of coffee“.
The water droplets that form clouds are often ‘seeded’ by particles of salt or dust, such as the aerosols distributed by the vortices in this wave study. Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response
Just as with the vortices in the coffee cup, vortices were forming in the air behind the wave crest (which acted as the spoon) and travelled upwards through the atmosphere and away from the waves. As each wave broke, a train of vortex dipoles were produced that twirled off into the sky. Imagine a coffee bath and multiple spoons rather than a coffee cup. The authors suggested that these vortices could carry aerosols from the sea (salt, water droplets etc) into the atmosphere. Travelling within the vortices, these tiny particles could travel far further and far higher than we may have expected otherwise. Such aerosols can be critical for cloud formation and so the effect of these breaking waves could be important for climate modelling.
While an undergraduate, I had an opportunity to study a course in atmospheric physics. I remember the lecturer lamenting that while we (as a community, but not really as the students sitting in the lecture theatre at that time) understood atmospheric modelling quite well and that we understood how to model the oceans fairly well, we got problems when we tried to put the two sets of models together. It was clear that something wasn’t quite right. Years later, it seems that at least past of the reason for that is linked to those vortices that you see as you pull your spoon through your coffee cup.
Everything is connected indeed.
A summary of the study can be found here. The abstract (and link to the pdf) of the published paper can be found here. If you do not have access to the journal through a library, an early, but free, version of the paper is here – note though that this version may not include the amendments included after peer review.
¹A quote attributed to Jean-Baptiste Biot (1774-1862), is perhaps relevant here “Nothing is so easy to see than what has been found yesterday, and nothing more difficult than what will be found tomorrow.”
Expanding biscuits are a 2D example of a close packed crystal lattice.
Blaise Pascal once wrote of the benefits of contemplating the vast, “infinite sphere”, of Nature before considering the opposite infinity, that of the minute¹. And although the subject of today’s Daily Grind involves neither infinitesimally small nor infinitely large, a consideration of biscuits and coffee can, I think lead to what Pascal described as “wonder” at the science of the very small and the fairly large.
The problem was that my biscuits went wrong. Fiddling about with the recipe had resulted in the biscuit dough expanding along the tray as the biscuits cooked. Each dough ball collapsed into a squashed mass of biscuit, each expanding until it was stopped by the tray-wall or the other biscuits in the tray. When the biscuits came out of the oven they were no longer biscuits in the plural but one big biscuit stretched across the tray. However looking at them more closely, it was clear that each biscuit had retained some of its identity and the super-biscuit was not really just one big biscuit but instead a 2D crystal of biscuits. The biscuits had formed a hexagonal lattice. For roughly circular elements (such as biscuits), this is the most efficient way to fill a space, as you may notice if you try to efficiently cut pie-circles out of pastry.
Salt crystals. Note the shape and the edges seem cuboid.
Of course, what we see in 2D has analogues in 3D (how do oranges stack in a box?) and what happens on the length scale of biscuits and oranges happens on smaller length scales too from coffee beans to atoms. Each atom stacking up like oranges in a box (or indeed coffee beans), to form regular, repeating structures known as crystal structures. To be described as a crystal, there has to be an atomic arrangement that repeats in a regular pattern. For oranges in a box, this could be what is known as “body centred cubic”, where the repeating unit is made up of 8 oranges that occupy the corners of a cube with one in the centre. Other repeating units could be hexagonal or tetragonal. It turns out that, in 3D, there are 14 possible such repeating units. Each of the crystals that you find in nature, from salt to sugar to chocolate and diamond can be described by one of these 14 basic crystal types. The type of crystal then determines the shape of the macroscopic object. Salt flakes that we sprinkle on our lunch for example are often cubic because of the underlying cubic structure on the atomic scale. Snowflakes have 6-fold symmetry because of the underlying hexagonal structure of ice.
It is possible to grow your own salt and sugar crystals. My initial experiments have not yet worked out well, but, if and when they do, expect a video (sped up of course!). In the meantime, perhaps we could take Pascal’s advice and wonder at the very (though not infinitesimally) small and biscuits. And if you’re wondering about where coffee comes into this? How better to contemplate your biscuit crystals than with a steaming mug of freshly brewed coffee?
What is the ideal temperature at which to serve coffee?
What is the optimum temperature at which to enjoy a cup of coffee?
A brief check online for the “ideal” serving temperature for coffee suggested a temperature of around 49-60ºC (120-140ºF, 313-333K) for flavour or 70-80ºC(158-176ºF, 343.1-353.1K) for a hot drink. In my own experiments (purely to write this article you understand), I found that I most enjoyed a lovely coffee from The Roasting House(prepared by V60) at around 52ºC. My old chemistry teacher must have been one who enjoyed the flavour of his coffee too. His advice for A-level practicals was that if we wanted to know what 60ºC ‘felt’ like, we should consider that it feels the same on the back of our hand as the underside of our cup of coffee. So, for argument’s sake, let’s say that we serve our coffee at the upper end of the flavour appreciation scale: 60ºC.
But, have you ever stopped to consider what 60ºC means or even, how we arrived at this particular temperature scale? Why do we measure temperature in the way that we do? While there are interesting stories behind the Fahrenheit scale, today’s post concerns the Celsius, or Centigrade, scale. Indeed, we use “degree Celsius” and “degree Centigrade” almost interchangeably to mean that temperature scale that has 0ºC as the melting point, and 100ºC as the boiling point, of water. It is one of those things that has become so habitual that setting 0ºC at the freezing end and 100ºC at the boiling end seems obvious, intuitive, natural.
Careful how you drink your coffee if you repeat this experiment!
And yet the temperature scale that Anders Celsius (1701-1744) invented back in 1741 did not, initially, work this way at all¹. Celsius’s scale did indeed count from 0ºC to 100ºC and was defined using the same fixed points we use now. But rather than counting up from the melting point, Celsius’s scale counted up from 0ºC at the boiling point to 100ºC at the freezing point. Rather than degrees of warmth, Celsius’s scale counted degrees of cold. So, in the original Celsius scale, the serving temperature of coffee should be 40ºC: Sixty is indeed the old forty*.
Which immediately begs a question. Why is it that we count temperature up (the numbers get higher as it gets hotter)? A first answer could be that we view that temperature is a form of measurement of ‘heat’ and that heat is an energy. Consequently, something cold has less energy than something hot, “cold” is the absence of “heat” and therefore what we should measure is “heat”. This means that our thermometers need to indicate higher numbers as the temperature gets hotter, and so we are now counting the correct way. While this is good as far as it goes and certainly is our current understanding of ‘heat’, ‘cold’ and temperature, how is it that we have come to think of heat as energy and cold as the absence of heat? It was certainly not clear to scientists in the Renaissance period. Francis Bacon (1561-1626) considered that cold was a form of “contractive motion” while Pierre Gassendi (1592-1655) thought that although ‘caloric’ atoms were needed to explain heat, ‘frigoric’ atoms were also needed to explain cold.
How heat, rather than visible light, is reflected provides clues as to why we measure temperature ‘up’.
One experiment that helped to show that heat was an energy (and so lent support to the idea of measuring temperature ‘up’) was that of the reflection of heat by mirrors. In the experiment, two concave mirrors are placed facing each other, some distance apart. Each mirror has a focal length of, say, 15 cm. A hot object is placed at the focal length of the first mirror. At the focal point of the second mirror, is placed a thermometer. As soon as both objects are in place, the temperature indicated by the thermometer increases. If the mirror were covered or the thermometer moved away from the focal point, the temperature indicated decreases again to that of the room. It is an experiment which can easily be demonstrated in a lecture hall and which fitted with a view point that cold is the absence of heat.
However, around the same time as this initial demonstration, Marc-Auguste Pictet did another experiment, the (apparent) reflection of cold². The experiment was as before but in Pictet’s second experiment, a flask containing ice replaced the hot object. On repeating the experiment the temperature indicated by the thermometer decreased. Covering the mirror or moving the thermometer from the focal point of the mirror resulted in the indicated temperature increasing again. Just as ‘heat’ was reflected in the mirrors, so too (seemingly) was ‘cold’.
So, the question is, how do you know what you believe you know about heat? Are there experiments that you can design that could help to disprove a theory of ‘frigoric’? And how do you explain the experiments of Pictet? Reader, it’s over to you.
*Within ten years of Celsius’s death (of tuberculosis in 1744), his colleagues Martin Strömer and Daniel Ekström had inverted Celsius’s original temperature scale to the form we know today. A similar scale designed by Jean Pierre Christin was also in use by 1743³.
¹”Evolution of the Thermometer 1592-1743″, Henry Carrington Bolton, The Chemical Publishing Company, 1900
²”Inventing Temperature”, Hasok Chang, Oxford University Press, 2008
³”The science of measurement, a historical survey”, Herbert Arthur Klein, Dover Publications Inc. 1988
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.
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.
Artisan, on East Sheen Lane, is one café in a small chain of coffee shops in West London (four cafés at the time of writing). Although there was plenty of seating inside, most tables were already taken when I arrived shortly after lunch suggesting that this is a very popular local café. There are many details to notice in this friendly corner shop coffee house. Firstly, the counter, on the left as you enter, was decorated as if supported by a door fixed on its side, one of many quirky features. When it arrived, my black Americano came with a most fantastic crema on top which cracked to reveal the coffee beneath, appearing as if it were a meandering river. Adjacent to my table was a sliding door, presumably leading to the toilets, that had a counterweight hanging from its side, I’m sure that could have led to a series of thoughts on Greek science and Archimedes.
There was also plenty to notice on the counter itself, a sign for two tip jars suggested you either tipped in one or the other depending on whether you wanted to “see into the future” or to “change the past”. As with previous ‘honesty box’ type experiments, it would be fascinating to know which box gets more coins and whether this correlated with external events in the East Sheen area and around. Still, I digress. Also on the counter was a wheel, a bit like the wheel of the Wheel of Fortune TV show. In this café, the wheel offered different coffees or cakes rather than prizes. As the wheel is spun, it is slowed by friction acting against pins that stick out from the circumference of the wheel. When learning about angular momentum and wheels in physics we always assume the ideal of a frictionless wheel without losses. We assume that it spins forever. The wheel in Artisan was quite far from this ideal, the whole idea being that the friction eventually stops the wheel and the pin points to your ‘prize’. So how do we reconcile these two ideas of the wheel? How efficient can water wheels be? And how efficient can engines be?
The counter and wheel at Artisan, East Sheen
This was a question that occupied Sadi Carnot (1796-1832) (named after the Persian poet Sa’di of Shiraz). Carnot was interested in how to optimise steam engines. Although steam engines were being engineered to be increasingly efficient, Carnot realised that people still did not understand what the maximum efficiency of a steam engine could be. Carnot worked on the principle that heat was a fluid (caloric) and so steam engines could be understood analogously to water wheels. Even though we no longer have this understanding of heat, Carnot’s ideal engine is still relevant for today. He discovered that, for an ideal engine (that is an engine that works without frictional losses etc.), the maximum amount of work that you could extract from the engine depended only on the temperature difference between the maximum working temperature and ambient temperature of the engine (not on the details of the engine such as whether it used steam as its working fluid). In practise this means that a steam turbine (which operates between approximately 543 °C = 816 Kelvin and 23 ºC = 296 Kelvin) has a maximum efficiency of 64%. Were you able to design a frictionless engine made from a cup of coffee (typical drinking temperature 60 °C = 333 K), it would have a maximum efficiency of around 10%
A meandering coffee river and Physics World (November 2016)
Of course, a real engine made from a cup of coffee would encounter frictional losses etc. which would reduce its efficiency. So while we may think that an efficiency of around 10% is not that bad (particularly if we’re making the coffee anyway), once we’ve allowed reality to enter into our calculations, the actual efficiency is much lower. This is probably best summarised as: The best use of coffee is in drinking it, and where better than Artisan coffee if you find yourself in East Sheen (or Putney, Stamford Brook or Ealing)?
Artisan Coffee is at 139 East Sheen Lane, SW14 8LR
Last week, a new study was published that explored the mathematics behind brewing the perfect filter coffee. The research, summarised here, modelled the brewing process as being composed of a quick, surface extraction from the coffee grounds, coupled with a slower brew, where the water was able to get into the interior of the coffee grind. It was an interesting study and the authors are now looking at grind shape and the effect of how you wet the grounds. However, what struck me was that the authors mentioned scanning electron microscopy (SEM) images of ground coffee. A lovely idea, what does coffee look like when magnified hundreds (or thousands) of times?
So here are a few images that I found shared under Creative Commons Licenses. I hope you find them as fascinating as I do.
1) A green coffee bean:
A green coffee bean. Sadly no details as to magnification. Image shared under CC license from Nestle, Flickr
2) Instant Coffee
Spray dried instant coffee from the Nestle, Flickr account. Image shared under CC license.
3) Roast and ground coffee (fluorescence microscopy image)
Ever wondered what your coffee looked like when magnified many times? This image using fluorescence microscopy is of roasted coffee. Note the similarities between this image and the following one (which has a scale bar). Image shared under CC license from Nestle, Flickr
3b) More ground, roasted coffee, this time from Zeiss
Scanning electron microscope image of roast (and ground) coffee magnified 750x. Image from Zeiss, Flickr, Todd Simpson, UWO Nanofabrication Facility. Shared under CC license. (To put the scale bar in perspective, it is the size of the smallest particles in an espresso grind. Clearly, the grind here is quite coarse).
4) Finally, an image of tea, just to keep this article tea-coffee balanced:
Green tea as seen under the microscope by the scientists at Nestle. Shared under CC license Nestle, Flickr.
If you come across any great images of coffee (or tea) under the microscope, please do share them. In the meanwhile, enjoy your coffee however you brew it.
In 2018, the Institute of Physics will move to Kings Cross and into what is being called the “Knowledge Quarter”, an area incorporating the British Library, the newly opened Francis Crick Institute and the University of the Arts, among others. Coffee houses have, in the past, been integral to the development of knowledge, places where scientists, artists and the generally interested would meet to discuss new ideas or groundbreaking results. So what about the cafés in Kings Cross? Where will tomorrow’s scientists, artists and the generally interested meet?
Knowing that I would be in the Kings Cross area a couple of weeks ago, I looked up the Kings Cross coffee guide by doubleskinnymacchiato and decided, for not-quite-random reasons, to try Pattern on this occasion. I had been forewarned that the first thing that I would notice would be the colourful patterns on the wall. A good call, that was indeed one of the first things you notice as you walk in. Secondly though were the hat-lampshades on the bulbs over the table at the window (visible in the photo on doubleskinnymacchiato’s review). As anyone who has met me in autumn/winter may appreciate, the lampshades immediately made me feel right at home. It was fairly crowded when I arrived in the late-morning and so I shared the bench in the window with a couple of people who seemed to be discussing history/philosophy and how to write properly referenced argumentative essays. The Americano I had ordered was brought over and, slightly self-conscious to photograph it while sharing the table, I just had to enjoy and savour the well made coffee. There is, perhaps, almost too much to notice at Pattern. But something behind me caught my eye, something that connects coffee, patterns and this café: An old style dial telephone, fixed to the counter.
Patterns in the cord, patterns in the telephone. An unusual feature at Pattern, Kings Cross.
Although the history of the invention of the telephone is quite controversial, the bit that reminds me of coffee is not so contentious, it is to do with how the telephone works. Let me explain.
In the gallery the “Information Age” at the Science Museum in London, it is argued that the commercial success of the telephone was driven by the invention of the carbon microphone, simultaneously invented by David Hughes (1831-1900) and Thomas Edison (1847-1931). It is the Edison version that prompts me to think of espresso. Edison’s microphone worked by packing a cylinder of carbon granules between two metal plates. In my mind I think of Edison’s carbon microphone as similar to a perfectly tamped coffee block in a filter basket. In the microphone, one plate was fixed, the other was flexible and acted as a diaphragm. When somebody spoke into the microphone, the diaphragm would vibrate causing the carbon granules to move alternatively closer together and further apart. Carbon conducts electricity and so the resistance of the microphone changed if the carbon granules were closer together or further apart. The sound waves impacting on the diaphragm were being perfectly translated to electric current patterns that could be transmitted through the telephone lines. The packing of the carbon granules would need to be optimum to transmit the sound, just as the pressure used to press the espresso tablet needs to be just right, enough contact between coffee grains to prevent the water flowing straight through without producing a good coffee, but not so much that the water cannot percolate through the coffee tablet and what should be a lovely espresso becomes over extracted. The ground coffee pressed into the filter basket at Pattern must have fitted this optimum density very well. A well poured espresso revealing that they had achieved that optimum balance between compression and space in the espresso tablet. Good coffee, interesting physics, I’m sure the Institute of Physics will be pleased when it eventually moves to its new home with such great coffee neighbours.
Physics is everywhere! (But coming to Kings Cross)
Although slightly off topic, a cafe-review considering telephones would not be complete without including the story about Erasmus Darwin, the Devil and his “speaking machine”. Erasmus Darwin (1731-1802) was a fairly portly man who worked hard. So it was inconvenient for him to have to go from his study to the kitchen when he wanted something to eat. Being a bit of an inventor, he installed a speaking tube in his home that connected his study to his kitchen. Desmond King-Hele in “Erasmus Darwin, A life of unequalled achievement”* described what happened next:
“One day a local yokel who had arrived with a message for Darwin, was left alone in the kitchen. He was terrified when a sepulchral and authoritative voice from nowhere demanded ‘I want some coals’. Such a request could only come from the Devil, he thought, wishing to stoke up hell’s fires. The man fled and would not come near the house again.”
The poor local may have been bewildered by the number of telephones and ‘voices from nowhere’ that surround us now. If you’re reading this in a café, why not look around you, notice some strange connection (the very lateral ones can be particularly fun to ponder), and then let me know what you have seen. It’s always interesting to hear the science, history and connections that people notice as they sit in cafés around.
Pattern Coffee is at 82 Caledonian Road, N1 9DN
*Desmond King-Hele, “Erasmus Darwin, A life of unequalled achievement” was published by Giles de la Mare Publishers, 1999.
It was late afternoon by the time we stopped by Ginger and White in Hampstead. The warm weather meant that we could enjoy time spent sitting outdoors in the little alleyway in front of the café. We had been taking a friend around the various sights (and foodie places) of London and so stopped here before heading back home. The long black, cortado and soya latte were all very well done and, while the others had enjoyed a crepe at La Creperie de Hampstead just around the corner, I took the opportunity to try the excellent banana bread on offer at Ginger and White. There was a fairly good selection of cakes on offer, but sadly those that the staff could confidently affirm were nut free were far fewer. However, the moist and tasty banana bread was a good option anyway. Coffee was roasted by Square Mile and there were also Square Mile beans available for purchase should you wish to take some home with you. While the café was fairly busy, it was nevertheless a relaxing place to sit and watch the people of Hampstead go by.
Everything is connected. From the lights to your cup of tea.
As I was looking around, wondering what the physics part of this cafe-physics review would be, I had what you could call a “light-bulb moment”. The walls of the building opposite were reflected in the windows of the café but looking inside, I noticed the lights which appeared to be LED lightbulbs set-back into the ceiling. Along with requiring less energy to power than conventional or halogen lightbulbs, LED lightbulbs in a café offer another, more poetic advantage for the café: they have a connection to the drinks being served and particularly tea. It’s all about diffusion.
At the heart of an LED light, there are two materials that form a junction. On one side of the junction is a semiconductor material that conducts electricity by means of electrons. Electrons conduct electricity in metals and are the ‘normal’ way that we consider electrical current to be carried. On the other side of the junction is a different semiconductor, one that still conducts electricity but this time does so with carriers called ‘holes’. You can view the electrons as having a negative charge and the holes as having a positive charge.
What happens when you put a tea bag into a cup of cold water. How long until the water becomes ‘tea’?
But what happens at the junction? Is there really a sharp barrier between these two types of material? Think about putting a tea bag in a cup of cold water, does the tea bag just sit there or does it slowly, very slowly, start to diffuse tea into the cold water? It is a similar thing for the two materials. Slowly the electrons diffuse into the hole material and the holes into the electron material. In fact, mathematically, the same equations describe the process in the junction as in the tea cup. But unlike tea, in the LED, the holes and electrons have an electric charge associated with them and so, as they diffuse away from the junction, they set up an electric field across the junction. It is this electric field that eventually stops any further diffusion of electrons or holes across the junction and sets up the conditions necessary for LEDs to emit light. It would be like having a tea bag that diffuses tea into the cup until it is perfectly brewed and no further.
Of course, there is much more than this to understanding LEDs. If you’re interested, there is further information here. I find it fascinating however that what happens in your tea cup, is also happening on many different scales in many places in the universe. And of course, in the lighting of cafés and coffee houses around the world.
Ginger and Whites is at 4a-5a Perrins Court, NW3 1QS
Have you ever noticed drops of coffee skipping across the surface of your coffee as you have been preparing a V60? Or watched as globules of tea dance on the resonating surface of a take-away dragged across a table top? The dancing drops can be seen in this video of coffee being prepared in a V60:
These droplets are the result of some fascinating physics. Although we have encountered them on the Daily Grind before (here and here), the more physicists study them, the more surprises they throw up. While the droplets can be considered particles, they are guided around the coffee pot by the surface waves they create as they bounce. In a sense they are a macroscopic example of wave-particle coexistence. There is a significant temptation to explore whether they have relevance for the concept in quantum physics of wave-particle duality. But another aspect of this wave-particle coexistence has recently been shown to produce a different and unexpected connection. A connection between chaos and computing. And as you can create these droplets in coffee, perhaps we could say a connection between coffee, chaos and computing.
Drops of water can be stable on the water’s surface for much longer than 1 minute if you put the water on a loudspeaker, more info on how to create these at home here.
It is fairly simple to create these surface droplets in coffee at home. The secret to getting stable droplets on the surface is to create a vibration, a wave, on the surface of the coffee liquid. The droplets that then form on (or are introduced to) the surface ‘bounce’ on this wave. If you wanted to create surface droplets reliably at home, you would put your coffee on a loud speaker. I suspect that the reason that they appear in a V60 is that the first drops set up a standing wave on the surface of the coffee that acts to support later drops as they encounter the surface. If anyone has a different theory, please do let me know.
But how is it possible that these bouncing droplets connect chaos theory and computing? It is a consequence of the way that the globules of coffee on the surface interact with the waves that guide them around the coffee. Consider for one moment a particle bouncing around a confined space (the traditional example is of a ball on a billiards table). On an ordinary table, the billiard ball will behave quite predictably, start it off aimed roughly at the side of the table and it will bounce in an easily describable way. But if you make the ends curved or put circular objects in the middle of the table for the ball to bounce off, small differences in initial direction can result in large differences in the final path of the ball (for more details and an animation see here). The billiard ball behaves chaotically, and the initial path cannot be found from the final position, there is no way to re-trace the path of the ball, it is not “time-reversible”.
A still from the video above showing three drops of coffee on the surface.
The droplet bouncing on the liquid surface appears to move chaotically, just as the billiard ball on a circular table. However, unlike the billiard ball, the droplet is not a mere particle, but a particle linked to a self-generated surface wave. Each time the droplet bounces on the surface, it creates a small wave, like ripples on a pond. The path taken by the droplet is a complex interaction between this self-generated wave, the vibration keeping the droplet bouncing and the droplet itself. This means that if you are able to shift the phase of the bounce by 180º (meaning, that rather than bounce on an upward motion of the surface, the drop bounces on a downward motion or vice versa), the bouncing droplet not only reverses the direction it travels in, it retraces its path. Rather than behave as the chaotic billiard ball, the path taken by the seemingly chaotic globule of coffee can be exactly reversed.
Which is where the link with computing comes in. It is as if each “bounce” of the droplet “writes” information on the surface of the coffee in the form of a wave. The subsequent bounces “read” the information while the reversal of the direction of the bouncing droplet “erases” the stored information by creating a surface wave opposite to the initial one. The authors of the recent paper suggest that “in that sense [the walking droplet can] be termed as a wave Turing machine”, giving the final link to computing.
Whether or not this turns out to be useful for computing is, to me, almost irrelevant. What is interesting is that such a simple phenomenon, that anyone who makes pour-over coffee should have seen fairly often, is linked to such complex, and fundamental physics. If you would like to read more, there is a great summary article here while the actual paper is here.
