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.

Worth dying for? A glassy tale.

Pureover, pureover in packaging
The PureOver in its packaging. Glass and cardboard, no plastic in sight. The PureOver is designed to brew filter coffee but without the need for filters.

It was the middle of the afternoon and we had friends over, friends who wanted coffee but, “only a small cup”. What were our options? We could make a V60 which would be a bit of a waste or an Aeropress which, while great for a small coffee for one person, is pushing it a bit for two people (even if one only did want a “tiny” bit). It was time to dust off the PureOver. This all-glass brewing device makes approximately 2-300ml of filter coffee entirely without the need for any filters. It is my go-to brewing device for a decent sized cup of coffee for one person or a “small” and “tiny” cup for two people. The PureOver was designed by a group of glass-blowers in Portland (USA) who wanted to be able to brew drip coffee without waste filters. It is now made commercially in China and shipped around the world for people who want to brew likewise.

The PureOver works by creating a filter bed out of the coffee grounds themselves. The design of the brewer ensures that the coffee is fairly well packed at the bottom of the pot allowing the water to filter through but without (much) sediment falling into the cup underneath the brewer. I have written about the PureOver, including a “how-to” brew guide, elsewhere. The PureOver works well, brews a lovely cup of coffee and looks great. Which shows how well the hard bits have been hidden; much of life is an art where the performance hides the work behind it. In some parts of our lives this is obvious. Acting, for example needs to appear natural and not reveal the work that has gone into developing the character the actor plays. I think the same is true of teaching/tutoring* physics. Such teaching should be a seamless conversation and discussion between students and tutor, in some way hiding the work that has gone into the preparation of that conversation. The PureOver is exactly the same. There is a lot of physics that is within the filtration bed and the diffuser design, but the bit that I would like to focus on is the bit that we look straight through without noticing. It is the role of the glass.

The diffuser sitting on top of the Pour Over coffee brewer. The holes are to ensure that the water falls evenly and slowly onto the grounds below.

The PureOver is made of borosilicate glass which was first invented by Otto Schott (1851-1935) in the nineteenth century. It is made by combining silica with boron trioxide (B2O3). One of the things that makes borosilicate glass so special is that it has a really low thermal expansion coefficient. From a practical point of view, and why this matters in the PureOver, is that it means that it is not likely to shatter as you add boiling (or just off the boil) water to the glass. You can brew coffee without the brewer breaking. We just want to be able to use the coffee brewer without thinking too much about it, using borosilicate glass allows us to do this.

If we do think about it a bit more though, the thermal expansion coefficient reveals something to us of the atomic structure of the material. All atoms in a solid vibrate, as they gain more energy (in the form of heat), the amplitude of that vibration increases, so they vibrate more. But atoms within a solid structure do not vibrate symmetrically. It is much harder (it takes more energy) to push them together than it is to pull them apart. This means that as the temperature increases they can vibrate ever so slightly further away from each other than they can towards each other and the net effect is that the atoms get further away from each other and the material expands**. The thermal expansion coefficient can therefore reveal clues as to the internal energies and structure of different solids. Applying this to borosilicate glass itself gets problematic as glass is a disordered rather than a well defined crystalline structure, but the principle is there.

We often come across borosilicate glass in “Pyrex” glassware, although since the 1930s/40s “pyrex” has been made of soda-lime glass rather than the original borosilicate. Nonetheless, it is a story involving pyrex that provides the title of this post. In 1953, a chemist working at Corning Glass Works in New York State, got a surprise as he dropped a piece of experimental glass he had been working on when he removed it from the furnace. Donald Stookey had serendipitously discovered “Pyroceram” a type of glass that was not only extremely heat resistant, it had also bounced, not smashed, when he dropped it. However despite being commercialised for other specialist products, Pyroceram was not, initially, used for kitchen items because the parent company Corning, also sold Pyrex and did not want any competition with that other successful product. So more research was done on Pyroceram which did lead to new commercial opportunities, including one that we probably have with us right now. Because the toughness aspect of the Pyroceram type glasses developed into what we now know as “Gorilla Glass” which is probably the screen on your smartphone.

Perhaps not quite how the designers imagined brewing a coffee. I brew the PureOver into my V60 jug in order to avoid the few grains of coffee that get through the filter from going into the final mug of coffee.

You can read more about the story of this discovery (and how it got used in the Apple iPhones) in the June 2022 issue of Physics World. Stookey went on to be awarded the US National Medal of Technology by President Reagan and of course, Gorilla Glass is now found in many products. So you would be forgiven for thinking that this marvel of technology is a recent phenomenon as an unbreakable glass would surely have been highly valued if it had been invented earlier. The story of a Roman craftsman may provide a contrasting pause for thought. As described by Petronius (quoted in the book “The Alchemy of Glass”***):

“There was once a workman who made a glass cup that was un-breakable. So he was given an audience of the Emperor with his invention; he made Caesar give it back to him and then threw it on the floor. Caesar was as frightened as he could be. But the man picked up his cup from the ground: it was dented like a bronze bowl; then he took a little hammer out of his pocket and made the cup quite sound again without any trouble. After doing this he thought he had himself seated on the throne of Jupiter especially when Caesar said to him: ‘Does anyone else know how to blow glass like this?’ Just see what happened. He said not, and then Caesar had him beheaded. Why? Because if his invention were generally known we should treat gold as dirt.“

*I am careful to keep my comment here to tutoring as that is what I have most experience of. If you teach larger groups or in a school, please do let me know what you think, whether this applies to teaching too, in the comments.

**See for example “Thermal Physics, CJ Adkins, Hodder and Stoughton, 1976

*** “The Alchemy of Glass; counterfeit, imitation, and transmutation in Ancient Glassmaking”, Marco Beretta, Watson Publishing International, 2009

For more about glass including the question of how transparent glass is, please see this post by Bobreflected.

Reflections, deviations…. coffee

The reflections from the surface of a cup of coffee of a building opposite a central London cafe. Towards the edges of the cup, the coffee bends upwards, revealed by the lines bending that would be expected to be straight.

A “flat white” could be ordered from many a coffee shop. A “flat black” may be a physical impossibility. We can realise this by gazing contemplatively, or perhaps even longingly, at a long black while it cools. Notice that the surface of the coffee is ever so slightly curved. Leaving aside the white mists that you may see skipping across the coffee surface, the coffee is flat in the middle of the cup but rises towards the edges. If you have noticed this, it is most probable that you did so because of the different way the light is reflected over the surface of the coffee. It is most obvious if you can arrange the reflections on the cup to reflect something supposedly straight: a window frame or a beam of strip light for example. The reflection is fairly clear and fairly straight until about 5mm from the edge of the cup where suddenly it bends. You can see an example of this in the photograph on the right.

The reason for the curvature is of course surface tension, which is the same effect that makes droplets form into shapes that are close to spheres. First investigated by Agnes Pockels and Lord Rayleigh in the nineteenth century, surface tension is caused by the fact that molecules at the surface of the water (in the coffee) will feel a net attraction to the other molecules within the water. There being no molecules of water above the surface of the cup, the surface molecules are pulled back towards the liquid in the cup. At the sides of the cup something slightly different is happening. There, the molecules in the water will be pulled back towards the liquid but will also experience the uncompensated attraction (or repulsion) from the atoms in the mug material. Exactly analogous to surface tension, but in the solid, the interaction of the surface energy of the mug with the surface tension of the liquid will pull the liquid into different shapes. It is for this reason that highly waterproof surfaces, such as fresh oak leaves, will form spherical drops of water, but wettable surfaces, such as an oak leaf in autumn, will accumulate flatter, less spherical droplets on the surface.

coffee, red wine, wet coffee stain, coffee spill, coffee ring
The interaction between the surface tension of the water and the surface energy of the solid surface it sits on determines the shape of the droplet. These drops of coffee and wine on paper were for an experiment about coffee ring formation. The droplets are: Drops of coffee (left), soapy coffee (middle) and red wine (right)

We see the effects of surface tension too when a bubble, or a small bit of dust, sits on the surface of the coffee. Again, looking at the light reflections, we see how the coffee, or tea, bends near the floating object showing how un-flat the surface really is. Bubbles are usually large enough that we can see them directly. In the photograph on this page for example, you can clearly see the reflections from the surface of the bubble together with the bent reflections of light from the surface of the liquid. However in the case of the dust, sometimes the dust is small enough that the reason that we see it is because of the change of the path of the light reflected from the surface. For a similar reason, the insects that skate the surface of a pond are visible because of the light patterns they make rather than their intrinsic visibility. Each time we are using the deviation of the light from its expected path in order to deduce the presence and shape of an object hidden to our view.

A similar deviation of the expected path of light is seen in the phenomenon of gravitational lensing which has been used to infer the presence of black holes. Such a deviation even provided experimental evidence for Einstein’s (then) recently proposed General Theory of Relativity, just over 100 years ago on May 29, 1919. The idea that light had weight and would be deflected by a gravitational field was not new, indeed, even the Newtonian model of gravity predicted that light would be deflected as it went past a massive object*. The question was how much and, as an important secondary question, how to measure it. As Arthur Eddington later described in his book “Space, Time and Gravitation”*, according to Newton, any object thrown horizontally on the Earth’s surface would fall 16 feet (in his use of units, 4.88 m in SI) in one second. The same was true for light. However with Einstein’s theory, the predicted deflection of light was 32′ (9.75m). The difficulty for the experimentalist is that in the same second, the light would have travelled nearly 300 000 km. Detecting such a small deflection over such a large distance would be difficult, harder than seeing a grain of dust on the coffee surface. Which is where the light deflection comes in. Because if you watch as the light from a distant star travels past a massive and fairly large object, such as the Sun, you should be able to discern the small, but significant deflection. And on May 29th 1919 a total solar eclipse (which thereby blocked the extra and interfering light from the Sun) offered a perfect opportunity for Eddington and an expedition sent by the Royal Society and Royal Astronomical Society (to Brazil and West Africa) to attempt to measure such a deflection.

tea reflections, bubble on tea, surface tension, light bending
The way that light reflects off a surface of a cup of tea in this case, reveals the curvature of the tea surface. In this case the curvature is clearly due to the bubble in the centre. Sometimes you can see distortions on the surface caused by bits of dust which are difficult to see on their own.

Although the deflection was significant, working with large telescopes and photographic plates, the magnitude of the deflection of the light that they were looking for was still only 1/1500 of an inch on the photographic plate. Two groups at two different locations took multiple photographs of the eclipsed Sun and the stars around it in order to measure the position of the stars as seen behind the Sun and then compare that to the position of the stars when they had been photographed earlier in the year without the Sun between them and the Earth. Eddington describes the experiment:

“There is a marvellous spectacle above, and, as the photographs afterwards revealed, a wonderful prominence-flame is poised a hundred thousand miles above the surface of the sun. We have no time to snatch a glance at it. We are conscious only of the weird half-light of the landscape and the hush of nature, broken by the calls of the observers, and beat of the metronome ticking out the 302 seconds of totality.”

Finally after developing and comparing the images back in London, the team confirmed a deflection of 1″.98 +/- 0″.12 (Brazil) and 1″.61 +/- 0″.30 (W. Africa) for the stars closest to the Sun (NB. 1″ indicates 1 second of arc). Einstein’s theory had predicted a deflection of 1″.74, Newton’s theory had predicted 0″.87. The results of the light deflection were far more in agreement with Einstein’s new theory of General Relativity than with the classical Newtonian model.

The ‘wobble’ of a few of the stars on the photographic plates had confirmed a prediction of the theory of Relativity. Which could lead to the question: What do you see, or not, as the light dances off of your coffee?

*”Space, Time and Gravitation: an outline of the General Theory of Relativity”, Sir Arthur Eddington, Cambridge University Press, first printed 1920, 1968 edition.

Me time at Hétam

Iced chocolate at Hetam. The chocolate is sourced from Indonesia. At the time of visiting, drinks were only available in take-away cups, hopefully this will change as the cafe becomes more established and the pandemic restrictions that were in place at the time of visiting are eased.

In 2021, a new cafe opened up in Bangsar, Kuala Lumpur, Malaysia. Called Hetam, it is a cafe almost designed for the post-pandemic, Instagram age that we find ourselves living in. At the time of visiting, there was no ‘inside’ to this cafe, everything was outdoors: customer seating was outdoors, even the ordering and the counter were outdoors. Umbrellas provided some protection from the downpours as well as the hot sun that you can get in Kuala Lumpur. You order at a counter which is on the right of what looks like it used to be an ordinary house on the service road parallel to Jalan Maarof (between Lorong Maarof 5 and 6). The house is now the headquarters for the online section of Hetam and is where they package up their online sales. There are a small selection of edibles to the right of the cash till but the main focus is on the coffee, tea and chocolate. The coffee is roasted by Hetam. At the time of visiting, the coffee was a choice of either an Indonesian natural or a Brazilian washed coffee and available as any of the usual espresso based drinks. I found that the Indonesian worked better in the espresso but that when brewing with an Aeropress at home, the Brazilian came out on top. Various Japanese Genmaicha and Hojicha teas were available but each time, I focussed on the coffee. The chocolate also is sourced by Hetam mostly from Indonesia and is well worth trying.

The staff at Hetam were very friendly and knowledgable. When we first arrived, they talked us through checking-in using the MySejahtera (Covid-19) app when we didn’t have data on our phones (as of 1 May 2022, hopefully MySejahtera will be something you don’t need to use any more). This led to a conversation on the origins of Hetam and their hopes for the cafe for the future. We ordered a hot long black and an iced chocolate and took a seat in the side/back garden of the house. The space seems almost made for Instagram. Infact, perhaps it was. Carefully arranged bamboo adorns the sides of the garden. White pebbles form the floor while strategically placed bits of tree are scattered throughout the space leading to a certain, specific aesthetic. The first time that we enjoyed a coffee at Hetam, another couple were already there. As we sipped our coffee, the couple split into model and photographer and, with what appeared to be a well practised routine of recognisable Instagram poses, set about photographing each other against different backdrops. In subsequent visits, we enjoyed the place to ourselves.

The counter at Hetam is helpfully under a shelter, the other seats are mostly under umbrellas. You get a glimpse here of the ‘insta-ability’ of the cafe. Random dead logs form a counterpoint feature to the white pebbles of the seating area.

The name “Instagram” is apparently a derivation of a combination of “instant camera” and “telegram”. The idea being that a message is sent through an image acquired by an instant camera. The word camera is in turn derived (from both Latin and Greek) from the word for a chamber or a vault. Presumably this was a suitable name for the camera because early photographs were taken through a pin hole into a vaulted dark chamber. Which brings us into the realm of physics as the photograph is literally that which is written by light. Film cameras and even the old Polaroid instant cameras, could still, legitimately be said to take photographs. The light would fall onto a chemically active film and change it based on the exposure levels so that the image was written directly by the light. When it was developed, the negative would be the reverse of the places on the film ‘written’ by the photons of the light (for a description of the process and a recipe for developing film with coffee click here, opens as pdf). This is not true of the sort of “instant cameras” most would now use to upload an Instagram post. In the case of digital cameras, the photons of the light still activate a light sensitive electronic chip behind the camera lens, but much of the interpretation of the image is done using computer software. For example, many of the light sensitive cells in the camera are not colour sensitive, they are only sensitive to the number of photons that fall on them (the intensity of the light). Colour images are formed by considering neighbouring cells which each have a different coloured filter covering them. The relative intensity of the electronic response within each group of cells is then interpreted by the software as a different colour. At this point can it be said that the image is written by the light? The final image is a mixture of the light falling on the photoactive cells and the interpretation of that electrical data by the software in the phone or digital camera. The light directs the electrons within the device but does it write the image?

Table, pebbles and bamboo in the seating area of Hetam, KL.

There’s also the issue of what it means to have the image and to share it. The picture on the phone, the image shared through the screens, is a collection of data points that no one can hold. A photograph printed from film or even the negative is, in that sense, more tangible. In the case of the negative, what you hold is what was written by the photons, by the light, at the point at which the subject was seen. In either case though what does it mean to have, or even to share, that image? Erich Fromm in his book “To have or to be” contrasts a poem of Tennyson with a haiku of Basho*. In the former, Tennyson ‘plucks’ a flower out of a wall in order to study it. Basho in contrast looks “carefully” at the flower; paying attention to it but not possessing it. Fromm questions our mode of being, suggesting that Tennyson could be compared “to the Western scientist who seeks the truth by means of dismembering life.” Is this fair? Does our desire to possess an image, pluck a flower or to ‘capture’ a moment and thereby ‘keep’ it necessarily imply that we would seek truth by means of dismembering life?

Which may take us to a consideration of those dead tree branches on the gleaming stones. They appear like petrified wood, wood that has been preserved for years through a process of fossilisation. We cannot own such objects, they outlast us. If we photograph it we cannot keep that moment, what does it mean to us if we don’t look carefully at the instant but rather try to pluck it for posterity?

So finally back to Hetam. While it may be ideal for Instagram, and while it will definitely be worth a few good photo ‘captures’, the space is also ideal for contemplation. For sitting with a coffee, enjoying the moment, appreciating the surroundings, both aesthetic and people, and for being rather than having. A friendly, outdoor and relaxed cafe, what more could you want?

Hetam is on Jalaan Maarof just next to the Petronas petrol station on the service road to Jalan Maarof.

*”To have or to be” by Erich Fromm, Jonathan Cape publishers, 1976 (1978)

Time for tea?

Matcha, tea in Japan, frothy tea
A Matcha tea in Japan. A lot to contemplate here.

A recent article in Caffeine magazine caught my attention. Emilie Holmes of Good and Proper Tea was writing about the joys of appreciating loose leaf tea. While tea is a little diversion from coffee, January is traditionally a time to look forward as well as back and maybe, BeanThinking should occasionally cross over to the tea side. It was one line in particular of that article that puzzled me. Writing about the ‘naturally “slow” nature of the tea ritual’, Holmes observed that while brewing loose leaf tea you would be able to see “the leaves in a glass pot emit wisps of colour as they infuse…”

It was great to read someone who clearly had spent time carefully observing their tea. And yet that sentence prompted a series of questions in my mind. It was not that I doubted the observation, indeed, thinking back to teas I have made and enjoyed, I realise that I have seen these wisps before. It was more a question of why would it happen, why would the brewing tea emit lines of colour from the leaves? These lines must be telling us something.

diffusion, convection, tea brewing
A tea bag in hot water. The lines of tea are difficult to see in the photo, you’ll just have to do your own experiments, but, streaming from the bottom of the bag, you can see wisps of darker tea-water.

We need to think about how tea brews. A first mechanism would be through turbulence. Hot water poured onto a bed of tea leaves would stir them up and the resulting movement within the pot would mix the leaves with the water leading to a properly brewed cup of tea. This is very much the lazy tea brewers bag-and-cup method (which I can share). It would lead to a brewed tea, but it could not lead to a situation in which you could sit back and see wisps of colour. That requires calm and the quiet moments of a pot of tea brewing while you can enjoy the process.

A second mechanism would be through diffusion. Ultimately the same mechanism as the principle behind how LEDs work, diffusion is where the soluble parts of the tea leaves would travel, through the process of a random walk, throughout the water of the pot. This is a very slow process and we would expect that the concentration of colour would be most intense around the leaves and then fade out gradually with distance from the leaves. We would not expect ‘wisps’ nor lines of tea, that suggests something else.

It suggests the third mechanism of the tea brewing: a mix of diffusion and then convection within the hot water of the pot. The lines of tea are indicating that within the cup, regions of the hot water are at slightly different temperatures. Owing to the hot water being in contact with cooler air surrounding it, the surface of the water is cooling down and sinking, leading to a convective motion within the water inside. As the water moves it carries the diffused tea with it into new areas of the water, a movement of hot water to cooler water and back again. The tea is carried in a line because the convection patterns are occurring in small cells within the tea pot, small regions where hot tea is moving towards cooler tea which is warmed and itself moves. The convection does not happen as if the hot water is one big mass but a series of smaller ‘cells’. We see similar cells on the surface of the Sun. The lines are telling us of the movement in the tea pot and the amount and speed of their movement reveals more about how hot the water is relative to the air outside the pot.

diffusion only
A tea bag in cold water: This time, there are no wisps of tea as the drink brews. Instead, there is a slow diffusion of tea infused water from the bag outwards.

Testing this idea I required tea bags. My tea pots are opaque and so would not help me to appreciate this detail of brewing a cup of tea and so it was back to the bag-in-cup method. However, in order to avoid turbulence, I poured the water (hot or cool) into the mug before adding the tea bag. It was not the best way to make a tea, apologies to tea lovers, but it was a tea that I do not enjoy anyway, so it was good to use it up. Sure enough, when the tea bag was put into the hot water, within a very short time, wisps of coloured water formed lines curling underneath the bag. Why did they flow down? Was it because the tea in the bag was slightly cooler than the hot water and so, as the tea diffused out of the leaves it moved with convection downwards because of gravity and the fact that cooler water is denser? A tea bag in cool water however behaved differently. The water in the cup had been taken from the tap and then left in the cup for a couple of hours so that the water was definitely at the same temperature as the room. This time, the tea bag first floated and then sank to the bottom of the cup. There was no obvious infusion of the tea-coloured water into the plain water but slowly the region around the bottom of the tea cup at the bag turned browner with the tea. As time went on, this region expanded to give a tea layer and a water layer.

The wispy lines of tea only happened when using hot water. Which suggests a further experiment. How do these wisps change when brewing for black teas as opposed to green teas (which use a lower brewing water temperature)?

After about five minutes the tea brewed in hot water (left) was fairly evenly distributed throughout the cup whereas the tea brewed in cold water (right) showed a distinct layering between concentrated tea at the bottom of the cup and plain water above that layer.

One last observation with these tea bags in the hot water. Some of the tea floated within the bag, some sank, as time went on, more tea leaves fell towards the bottom of the bag (which was itself floating). What was happening there? Maybe if you experiment with your tea, you can let me know in the comments below, on Twitter or on Facebook. There are definite advantages to slowing down and brewing a proper cup of tea.

A short (lived) black

coffee at Story
A black coffee with bubbles on top. The colours on a bubble are the result of light interference. But sometimes the top of the bubble could appear black. What is happening there?

The long black can be distinguished from the Americano by the order in which the espresso and the water are added to the cup. This in turn will affect the type of bubbles on the surface of the coffee. As a guess, the long black (espresso last) will have many more but smaller bubbles than the Americano (water last) which will probably have larger, but fewer bubbles. Perhaps this guess is wrong, this could be an excuse to get out and drink more coffee.

We are used to the coffee being black and the bubbles on the surface reflecting a rainbow of shimmering colours that change with the light and with time before they finally burst. We know the physics of the colours on the bubbles: they are the result of the interference of reflections from the outer and inner surface of the bubble cancelling out certain colours and adding to others dependent on the bubble skin’s thickness. But what about black bubbles? Or, if not entirely black, perhaps the cap of the bubble can, for a short while, appear black just before the bubble bursts?

It is easier to take a short break from coffee and look for this effect in soap films. Like the bubbles on coffee, soap bubbles are caused by the surfactant in the soap solution having a hydrophilic (water loving) and hydrophobic (water hating) end. The hydrophilic end of the surfactant can point into the water (coffee) leaving the hydrophobic end to form a surface. When this is agitated with air, the hydrophilic ends remain contacted with water resulting in bubbles which are thin layers of water surrounded by these surfactant molecules. In coffee the surfactant is not soap but is formed by the lipids and fatty acids. These bubbles are therefore slightly weaker than the soap based bubbles and so while they will form on a coffee, it is not easy to make a film of a coffee bubble in the same way as you can dip a wire loop into a soap solution and come out with a soap film.

However, we can use the stability of the soap film to investigate the colours in the coffee bubbles and watch the colours evolve with time. At this point, I would strongly encourage anyone reading to grab a solution of soap and a wire loop and start playing with soap films.

Soap film in a wire loop held by a crocodile clip.
A soap film in a wire loop showing reflected horizontal coloured bands that are the result of light interference.

Holding the wire loop so that the soap film is vertical with a light source shining at it, we can watch as the film changes from being uniformly transparent to having bands of colour form and move down the film. We watch as there is a red/green band and another red/green band and then on top of the bands there appears a white, or at least pale blue, almost white, band and above that a layer that doesn’t reflect the light at all. If we view the soap film against a dark background looking only at the reflected light, this top portion of the film appears black. Rotating the loop we can see that the bands effectively stay in the same position because it is gravity pulling on this soap film that is causing the film to be thicker at the bottom than at the top. And we recognise that the coloured bands are revealing that thickness change to us by the fact that they are changing throughout the film. If we are careful as we rotate the wire, we could even see vortex like motions as the layers settle into their new position relative to the frame including at the very top where there are swirls and patches of fluid that mix the black layer with the coloured bands. What is going on there?

In fact, this black layer is one of the thinnest things that they human eye can see, and it occurs because of a subtle piece of physics. All waves have a number of properties defined by the position of the peaks and troughs on the wave. The wavelength is the distance between two equivalent points on the wave. The amplitude is the height of the peak (or trough). And the phase is the position of the wave relative to the peak (or trough). When light is reflected at a surface of a material that has a refractive index greater than that which the light is travelling through (eg. air into water, soap, or glass), the reflected wave has a 180 degree phase shift relative to the incident wave. Each peak becomes a trough, each trough becomes a peak. When light is already travelling through water, soap or glass and gets reflected at the surface of the material that is effectively air, there is no phase shift and the light is reflected back with the same phase as the incident wave (a peak remains a peak and a trough a trough).

At the top of the soap film, the layer is so thin that the light reflected from the first surface (180 degree shift) overlays that reflected from the back surface (no phase shift) so that peak and trough cancel each other out and we see no light reflected whatsoever for any visible wavelength; the surface looks black.

As bubbles ‘ripen’ or age, they will become thinner at the top of the bubble. It is at this point that you may be lucky enough to see a region of the bubble from which no light is reflected, this is the black film.

Which leads to some immediate questions. When we look carefully at the soap film, the boundary between the upper white band and the black film is quite sharp, it is not gradual as we may expect if the soap film were completely wedge shaped with gravity. It suggests that the top of the film is very thin and then suddenly gets thicker at the point where we start to see the colour bands. Moreover, the black film does not appear to mix with the thicker film just beneath it. As we watch, just before the soap film bursts, we get turbulence between the black layer and the thicker film, but the turbulent patterns appear like two fluids next to each other, not the same fluid in a continuum. And then, one final question. If we can’t measure the thickness of the black film with light (because it is all reflected as black) how can we know how thick this film is? If we rely on the light interference method, all we can say is how much thinner it is than the wavelength of light.

In fact, careful experiments have revealed two types of black film, which to us experimenting at the kitchen table would be indistinguishable. There is the common black film and the Newton black film. The Newton black film is effectively two layers of surfactant molecules only and is about 5nm thick (which is 5 millionths of a millimetre). The common black film is thicker, but is still much less than 100 nm thick. Investigating how these films behave is still an active area of research.

One last observation may prompt us to play for a bit longer with the soap films. Johann Gottlob Leidenfrost (1715-94) noted that if you put a sharp object such as a needle through the region of the soap film that showed the coloured bands, the film could self-heal and wouldn’t necessarily burst. If however you pierced the black region of the film, the film always burst entirely.

It seems that we could play endlessly with soap films, perhaps while watching the bubbles in our coffee. However you enjoy your coffee, have fun experimenting.

A couple more soap films showing reflected coloured interference bands. At the top, the film has become so thin that no light is reflected (clearly seen in the image on the right, where the lamp in the top left should be a circular reflection but is not reflected in the region above the coloured bands). In the image on the left, you can see what looks like turbulence or mixing just above the uppermost band.

To err is human…

Press Room coffee Twickenham
A smaller V60. For one cup you would use less coffee, but the errors on the measurement will always be there.

Preparing a good V60 requires 30g of coffee (for 500 ml of water)*. This can be measured using a set of kitchen scales, but a first estimate can also be obtained, if you are using whole coffee beans, by timing the passage of the grind through the grinder. Using an Ascaso burr grinder, my coffee used to come through at an approximate rate of 1g/s, so that, after 30 seconds, I’d have the perfect amount of coffee. Recently however this has changed, depending on the bean, sometimes 30g is 40 seconds, sometimes just less than 30 seconds.

Clearly there is an error on my estimate of the rate of coffee grinds going through the grinder. This may be influenced by factors such as the hardness of the bean (itself influenced by the degree of roast), the temperature of the kitchen, the cleanliness of the grinder and, the small detail that the ‘seconds’ measured here refers to my counting to 30 in my head. Nonetheless, the error is significant enough that I need to confirm the measurement with the kitchen scales. But are the scales free of error?

Clearly in asking the question, we know the answer will be ‘no’. Errors could be introduced by improper zero-ing of the scales (which is correct-able), or differences in the day to day temperature of the kitchen (not so correct-able). The scales will also have a tolerance on them meaning that the measured mass is, for example, only correct to +/- 5 % Depending on your scales, they may also only display the mass to the nearest gramme. This means that 29.6g of coffee would be the same, according to the scales, as 30.4g of coffee. Which in turn means that we should be using 493 – 507 ml of water rather than our expected 500 ml (the measurement of which also contains an intrinsic error of course).

Turkish coffee
A Turkish coffee provides a brilliant illustration of the type of particle distribution with depth that Jean Perrin used to measure Avogadro’s constant. For more information see here.

The point of all of this is that errors are an inescapable aspect of experimental science. They can also be an incredibly helpful part. Back in 1910, Jean Perrin used a phenomenon that you can see in your coffee cup in order to measure Avogadro’s constant (the number of molecules in a mole of material). Although he used varnish suspended in water rather than coffee, he was able to experimentally verify a theory that liquids were made up of molecules, by the fact that his value for Avogadro’s constant was, within error, the same as that found by other, independent, techniques. Errors also give us an indication of how confident we can be in our determination of a value. For example, if the mass of my coffee is 30 +/- 0.4 g, I am more confident that the value is approximately 30 g than if the error was +/- 10 g. In the latter case, I would get new scales.

But errors can also help us in more subtle ways. Experimental results can be fairly easily faked, but it turns out that the random error on that data is far harder to invent. A simple example of this was seen in the case of Jan Hendrik Schön and the scientific fraud that was discovered in 2002. Schön had shown fantastic experimental results in the field of organic electronics (electronic devices made of carbon based materials). The problem came when it was shown that some these results, despite being on different materials, were the same right down to the “random” noise on the data. Two data sets were identical even to the point of the errors on them, despite their being measurements of two different things.

A more recent case is a little more subtle but crucial for our understanding of how to treat Covid-19. A large study of Covid-19 patients apparently showed that the drug “Ivermectin” reduced mortality rates enormously and improved patient outcomes. Recently it has been shown that there are serious problems with some of the data in the paper, including the fact that some of the patient records have been duplicated and the paper has now been withdrawn due to “ethical considerations”. A good summary of the problems can be found in this Guardian article. However, some of the more worrying problems were a little deeper in the maths behind the data. There were sets of data where supposedly random variables were identical across several patients which suggested “that ranges of cells or even entire rows of data have been copied and pasted“. There were also cases where 82% of a supposedly random variable ended in the digits 2-5. The likelihood of this occurring for random variables can be calculated (it is not very high). Indeed, analysis of the paper showed that it was likely that these values too were either copy and pasted or “invented” because humans are not terribly good at generating properly random numbers.

A gratuitous image of some interesting physics in a V60. If anyone would like to hire a physicist for a cafe, in a 21st century (physics) recreation of de Moivre’s antics at Old Slaughters, you know how to contact me…

Interestingly, a further problem both for the Ivermectin study and for the Schön data comes when you look at the standard deviation of the data. Standard deviation is a measure of how variable is the measured outcome (e.g. duration of time a patient spent in hospital). For the ivermectin study, analysis of the standard deviations quoted on the patient data indicated a peculiar distribution of the length of hospital stay, which, in itself would probably just be a puzzle but in combination with the other problems in the paper becomes a suggestion of scientific fraud. In Schön’s data on the other hand, it was calculated that the precision given in the papers would have required thousands of measurements. In the field in which Schön worked this would have been a physical impossibility and so again, suggestive of fraud. In both cases, it is by looking at the smaller errors that we find a bigger error.

This last detail would have been appreciated by Abraham de Moivre, (1667-1754). As a mathematician, de Moivre was known for his work with probability distribution, which is the mathematics behind the standard deviation of a data set. He was also a well known regular (the ‘resident’ mathematician) at Old Slaughters Coffee House on St Martin’s Lane in London[1]. It is recorded that between 1750 and 1754, de Moivre earned “a pittance” at Old Slaughters providing solutions to games of chance to people who came along for the coffee. I wonder if there are any opportunities in contemporary London cafes for a resident physicist? I may be able to recommend one.

*You can find recipes suggesting this dosage here or here. Some recipes recommend a slightly stronger coffee amount, personally, I prefer a slightly weaker dosage. You will need to experiment to find your preferred value.

[1] “London Coffee Houses”, Bryant Lillywhite, 1963

Up in the air with a Pure Over Brewer

The diffuser sitting on top of the Pure Over coffee brewer. The holes are to ensure that the water falls evenly and slowly onto the grounds below.

The Pure Over is a new type of coffee brewer that is designed to brew filter coffee without the need for disposable paper filters. The brewer, which is completely made of glass, is a perfect size for brewing one cup of coffee and, as promised, makes a lovely cup without the need for wasteful paper filters. Generally, for 1-cup filter coffees, the Pure Over has become my go-to brewing method, although it does have a few idiosyncrasies to it that are helpful to be aware of while brewing.

An advantage of this brewing device is that it provides a large number of opportunities for physics-watching, including a peculiar effect that connects brewing coffee to an air balloon crash into the garden of a London Coffee House. It concerns a feature of the Pure Over that is specific to this particular brewing device: the ‘diffuser’ that sits on top of it.

The glass diffuser has five small holes at the bottom of it which are designed to reduce the flow of the water onto the coffee bed so that it is slower and more gentle. In order to avoid the paper filters, the Pure Over features a filter made of holes in the glass at its base. This filter does surprisingly well at keeping the coffee grounds out of the final brew, but it works best if the coffee bed just above it is not continuously agitated. The idea of the diffuser is that the coffee grounds are more evenly exposed to the water, with the grounds closest to the filter being least disturbed and so the coffee is extracted properly.

As water is poured from a kettle through the diffuser, the water builds up in the diffuser forming a pool that slowly trickles through the holes. Initially this process proceeds steadily, the water is poured from the kettle into the diffuser and then gently flows through and lands on the coffee. At one point however, the pressure of the steam within the main body of the brewer builds until it is enough to push the glass diffuser up a bit, the steam escapes and the diffuser ‘clunks’ back onto its base on top of the pure over. Then, this happens again, and again, until there is a continuous rattle as the steam pressure builds, escapes and builds once more.

The ideal gas laws, such as that found by Jacques Charles, relate the volume and pressure of a gas to its temperature. The application of the laws helped to improve the design of steam engines such as this Aveling and Porter Steam Roller that has been preserved in central Kuala Lumpur, Malaysia.

The pressure of the steam builds until the force exerted upwards by the rising steam is greater than the weight of gravity pulling the diffuser down. Once enough gas escapes, the pressure is reduced and so the steam no longer keeps the diffuser aloft which consequently drops with a clunk. The motion could take our thoughts to pistons, steam engines and the way that this steam movement was once exploited to drive our industrial revolution. Or you could go one stage earlier, and think about the gas laws that were being developed shortly before. There’s Boyle’s Law which relates the pressure of a gas to its volume (at constant temperature). That would perhaps partially explain the behaviour of the pure over. But then there’s also Jacques Charles and his observation that the volume of a gas is proportional to its temperature (at constant pressure). This too has relevance for the pure over because as we pour more water in from the kettle, we warm the entire pure-over body and so the temperature of the gas inside will increase. Consequently, as the amount of hot water in the pure over increases, the temperature goes up, the volume of that gas would increase but is stopped by the diffuser acting as a lid. This leads to the pressure of the gas increasing (Boyle) until the force upwards is high enough, the diffuser lid rises upwards on the steam which escapes leading the pressure to once again drop and the diffuser top to go clunk and the whole cycle begins again.

Of course, we know that Boyle’s law is appropriate for constant temperature and Charles’s law is appropriate for constant pressure and so the laws are combined together with the Gay-Lussac/Amonton law into the ideal gas laws which explain all manner of things from cooling aerosols to steam engine pistons. And yet, they have another connection, which also links back to our pure over, which is the history of hot air balloons.

Charles discovered his law in around 1787, a few years after the first non-tethered hot air balloon ascent, in Paris, in June of 1783. The hot air balloon is a good example of the physics that we can see in the pure over. Although Charles must have suspected some of the physics of the hot air balloon in June, he initially decided to invent his own, hydrogen filled balloon which he used to ascend 500 m in December of 1783. Hydrogen achieves its lift because hydrogen is less dense than air at the same temperature. However, it is the hydrogen balloon that links back to coffee and coffee in London.

hot air balloon
The ideal gas laws also contribute to our understanding of the operation of hot air balloons. We are familiar with them now, but how would such an object have been perceived by observers at the time of the first flights?

The first balloon flight in England took place using a hydrogen, not a hot-air, balloon in 1785. The balloon was piloted by Vincenzo Lunardi who was accompanied by a cat, a dog and, for a short while, a pigeon (before it decided to fly away). But it was not this successful flight that connects back to coffee, it was his maiden flight on 13 May 1785. On that day, Lunardi took off from the Honourable Artillery Company grounds in Moorgate, flew for about 20 minutes and then crashed, or as they said at the time “fell with his burst balloon, and was but slightly injured”(1) into the gardens of the Adam and Eve Coffee House on the junction of Hampstead Road and, what is now, Euston Road. In the 1780s the Adam and Eve coffee house had a large garden that was the starting point for walks in the country (in the area now known as Somers Town)(2). Imagine the scene as, quietly appreciating your tea or coffee, a large flying balloon crashes into the garden behind you.

The Adam and Eve is no longer there, in fact, its original location now seems to be the underpass at that busy junction, and the closest coffee house is a branch of Beany Green. However there is one, last coffee connection and it brings us back to the pure over. The pressure of the steam under the diffuser needs to build until the upwards force of the steam can overcome the gravitational force down of the weight of the glass diffuser. In the same way Lunardi had to have enough lift from the hydrogen balloon to compensate for the weight of the balloon and its passengers. Lunardi had wanted to be accompanied by another human on the day of his successful flight. Unfortunately, the mass of two humans in a balloon was too much for the balloon to accommodate which is why, the human was replaced by the dog, the cat and the pigeon.

Which may go some way to illustrate how far the mind can travel while brewing a cup of coffee, particularly with a brew device as full of physics as the Pure Over.

1 London Coffee Houses, Bryant Lillywhite, George Allen and Unwin publishers, 1963

2 The London Encyclopaedia (3rd edition), Weinreb, Hibbert, Keay and Keay, MacMillan, 2008

Viewing an eclipse, the coffee way

NASA image of annular eclipse from space
A different perspective? This is the view looking towards Earth of the 2017 Annular solar eclipse over South America. Taken by the EPIC DSCOVR project of NASA.

This week, on Thursday, June 10th, 2021, there will be a solar eclipse. If you are at high latitudes in the Northern Hemisphere including parts of Canada, Greenland and Siberia, you will see a so-called ring of fire as the moon moves in front of the Sun. At lower latitudes the eclipse will be much more partial and in London we are expecting to see 20% of the Sun obscured by the Moon.

You can read more about solar eclipses on other websites such as here or here, on Bean Thinking, we are going to focus on the coffee links to the eclipse.

The first coffee link comes in how to view it. This website suggested a number of ways of viewing the eclipse, one of which was to use a colander. This suggests a perfect adaptation to a view via coffee: the Aeropress filter cap. The idea behind the method is that each of the holes provides a type of pin-hole camera to image the Sun. Knowing roughly where the Sun will be at 10.06am (BST = UTC+1), we can construct a device to hold the aeropress filter cap so that we can see 97 images of the Sun projected onto a piece of paper: 97 images of the Sun to be eclipsed over the following 2hours 18 minutes. The maximum eclipse is around 20% of the solar disc and occurs at approximately 11.15 (although the exact fraction obscured and timing depends on your location). The Aeropress Eclipse viewing device shown in the photo here has an added (smaller) pin hole which should provide a more focussed image of the Sun and so will provide a second way of imaging the eclipse.

A second coffee link comes with thinking about why this particular solar eclipse is not ‘total’ anywhere on earth but is instead described as annular. And to do this, we’ll think about a coffee bean. The amazing visual spectacle of a total solar eclipse occurs because the moon is 400 times smaller than the Sun but is (on average) about 400 times closer to the Earth. So when we think about looking at a coffee bean, held at arms length from our eye (about 60cm), it would totally obscure (eclipse) an object 3.2 m tall, 233.5 m away*.

Eclipse viewer
An aeropress based device for viewing the eclipse. The strings attached to the cardboard flap at the top allow the angle of the aeropress filter cap to be fixed at different points. The camera is at the approximate point where the images will be projected onto paper.

The word “average” though hides an important detail that neither the Moon’s orbit around the Earth, nor the Earth’s orbit around the Sun are completely circular. On the 10th June 2021, the Moon will be two days past its maximum distance (apogee) from the Earth, and while the Sun is also nearly at its maximum distance, the distance ratio will mean that the Moon does not entirely obscure the Sun. Instead, if we return to our coffee bean analogy, it is the equivalent of stretching our arm 2 more centimetres and noticing that the object that was obscured is no longer completely obscured.

This will still make for a fantastic view if you are in Greenland, Siberia or happen to be at the North Pole where you will see a dark disc surrounded by a ring of Sun. For those of us further south, we will only see the Sun partially obscured by the Moon. Nonetheless, such an opportunity in any one particular location doesn’t come super-often (although worldwide there are often several eclipses per year, in London there will only be 42 partial eclipses in this current century). And in London, we have to worry about the weather too. So, if the weather is good for you, why not have a go viewing it, particularly if you adapt a piece of coffee brewing equipment to do so, and post your pictures of the effect here, or to Bean Thinking on Twitter or Facebook.

Finally, the timing of the eclipse is perfect for a mid-morning coffee, though maybe you’ll have to brew with something other than the Aeropress. Have fun.

*These figures have been calculated using a ratio of the size of the Moon to the Sun as 1:400.8 and an average distance of 1:389.2 (calculated from the average values). The distances on June 10 2021 mean that the distance ratio is closer to 1:377

Update to post, the day before (9 June 2021): This is the Aeropress viewing device in action, but 24h before the eclipse. Will the clouds stay away tomorrow?

The Aeropress Eclipse viewer in action. The images of the Sun are projected onto the cardboard behind the filter cap.

Update 10 June 2021: It was cloudy in London and I couldn’t get the Aeropress filter cap method to work in the brief periods of sunshine during the eclipse. Suspect it was a problem with focus-distance/angle/remaining cloud cover at points. However, the smaller pinhole did work (see the blurry image below) and the clouds did mean that there was a natural filter that made a direct photograph possible (see below). Do share your images here if you managed to view it.

Although there were brief periods without cloud, focussing issues etc. meant that I couldn’t get the Aeropress filter cap viewing method to work. Maybe for the next one!
A smaller pinhole did give an image of the Sun being eclipsed (lower blurry bright image)
The fact that it was cloudy did mean however that I could take a photograph of the eclipsed Sun directly. This was at about 11.10am (5 minutes or so before the maximum point of eclipse)

Pure Percolation

Pure over boxed
The Pure Over in its box. The glass base is designed with an inbuilt filter, avoiding the need for disposable paper filters but making the physics of percolation unavoidable.

It was entirely appropriate that the first coffee I tried in the Pure Over coffee brewer was the directly traded La Lomita Colombian from Ricardo Canal via Amoret Coffee. Ricardo was a special guest at one of the Coffee and Science evenings we held at Amoret Coffee in Notting Hill (pre-pandemic) where, among other things, he spoke about how he is using Biochar on his coffee farm. Biochar is a porous, charcoal based material that can help to provide the coffee plants with nutrients as well as water, thereby reducing the amount of fertiliser the plants need. To understand how it works, we need to understand a bit about percolation, which of course we also need to understand in order to brew better coffee in the Pure Over. Indeed, there are enough similarities, and an extension to a quirk of how espressos are brewed, that it is worth spending a little more time thinking about this process and the connections revealed as we brew our coffee.

Percolation recurs in many of the brew methods we use for making coffee. The V60, Chemex, Kalita wave, percolators and the espresso itself, all rely at some point on water flowing through a bed of ground coffee. The flavour of the resultant cup is dependent on the amount of coffee surface that the flowing water is exposed to together with the time that it is in contact with the coffee. What this means is that grain size, or the degree to which you grind your coffee, is critical.

Playing with brewing coffee, we know some things by experience. Firstly, frequently, the flow through a coarse grind of coffee will be quite fast (probably too fast to make a good cup). Secondly, we know that for any particular brew method, the more water we pour into the brewer, the faster the water initially comes through. We also know that we can affect the flow rate of water through the coffee if we increase the area of the coffee bed, or decrease its thickness. These observations were quantified into an equation by Henri Darcy in 1856. Darcy’s work had been as an engineer, designing and building public works such as the aqueduct that brought drinking water into the city of Dijon in the 1840s. Darcy received significant recognition at the time for his work including the Légion d’honneur, but it is more for a later set of experiments and particularly for his equation that we remember him today. In the 1850s Darcy was working on the problem of water purification. Passing water through a bed of sand is still used as a method of purifying the water today. Darcy used a series of cylinders filled with sand to investigate how quickly water trickled through the sand bed in order to come up with a proper quantification of those things that we too know by experience with our coffee filters. You can read about the mathematics of Darcy’s equation here.

espresso puck
An espresso puck. The compact structure nonetheless allows water to percolate through it at high pressure.

Darcy found that the flow rate of water through the sand bed increased when the porosity of the bed was higher (fine, dense sand would delay the flow of the water more than coarse, loosely packed sand). If there was a greater pressure on the water at the top of the bed (ie. more water is on top of the sand), the flow rate through the bed would increase too. Conversely the flow would get slower as the water was made more viscous. This is something we too know from experience: try to pour honey through the coffee grounds and it just won’t work.

For us to apply Darcy’s insights into making better coffee, it means that we need to think about the grind size. Too coarse and there will be lots of empty space through the bed of grounds: the porosity is high, and the water will flow straight through. Too fine and the flow rate will decrease so much that rather than just the sweet and slightly acidic solubles that first come out of any coffee extraction*, there could be too much of the bitter organic compounds that come out later, changing the character of the cup. With coffee we have an additional concern. Unlike sand, coffee grinds will swell, and splinter, as water is added to them, closing up any narrower paths and lengthening the brew time. This also means that, unless we properly wet the grounds prior to filtering our coffee, the extraction will be non-uniform and not reproducible. Another reason to bloom coffee thoroughly before brewing.

There is one more factor in brewing our coffee however that Darcy’s equation, which is valid for more stable systems, overlooks. Darcy assumed a constant flow rate of water through the sand bed, but coffee is different. In his book about espresso*, Illy showed that the flow of the water through an espresso puck was not constant over time. Something really interesting was happening when you looked carefully at an espresso puck. Ground coffee can come in a large distribution of sizes. In addition to the grind that we are aiming for, we also get a whole load of smaller particles called ‘fines’. Sometimes this is desirable, but with espresso, and by extension with our filter coffees, these fines add a twist to the physics of the percolation. As the espresso water is pushed through the coffee puck, the fines get pushed down through the puck between the ‘grains’ of the coffee grinds. This reduces the flow rate of the water until the point at which they get stuck. This will have the effect of increasing the contact time between the coffee and the water and so allowing more flavour solubles to be extracted. But crucially, these fines remain somewhat mobile. If you were to turn the whole espresso puck upside down (and Illy had a machine that allowed him to do this in-situ), the fines would again go on the move. Migrating from the new top of the puck to the new bottom. Filling the voids between the slightly too coarse grains. Complicating the simplifications in Darcy’s equation, but adding flavour to our brew.

Watch House coffee Bermondsey
There is a fountain on the wall (right hand side) of the Watch House cafe in Bermondsey. Many public fountains in London date from the 1850s emphasising just what a problem access to drinkable water once was.

Which leaves the connection between the farming method and the coffee. Biochar is formed by burning carbon containing waste (such as plant matter) in a low oxygen environment. Burying the resultant charcoal is therefore a way of storing carbon, and preventing its release into the atmosphere, for many years. But it is not just good for carbon storage. The buried charcoal is highly porous and traps nutrients within its structure so that the plants growing near it can be fertilised more efficiently. Moreover, the fact that it is porous, just like the coffee or sand beds, means that it traps water for a long time. Consider how long it takes a used filter full of coffee grounds to completely dry out! The water gets trapped within the porous structure and does not evaporate easily. This aspect of the biochar means that, as well as nutrients, the plants that grow nearby get a good source of reliable water. The ancient civilisations of the Amazon region used something similar to biochar in their farming techniques resulting in soil now known as “Terra Preta”, an extremely rich form of soil that improves plant growth. On his farm, Ricardo is going fully circular and making his biochar out of old coffee trees. The old trees thereby giving new opportunities to the fresh growth. It is a carbon capture scheme that reduces the need for fertilisers and that relies on percolation physics to work to best effect for the plants.

It seemed a moment of perfect coffee-physics poetry to use coffee grown on a farm using these techniques while initially experimenting with my own, percolation sensitive, Pure Over brewer. Percolation physics and interconnectedness all in one cup.

*Illy and Viani (Eds), “Espresso Coffee”, 2nd Edition, (2005)