Tag: coffee

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General Home experiments Observations Science history Tea

Coffee and Pluto

Three billion miles away, on an object formerly known as the planet Pluto (now sadly demoted to the dwarf planet Pluto), there exists a plain of polygonal cells 10-40 km across, extending over a region of about 1200 km diameter. Last year, the New Horizons mission photographed this region and these strange shapes (see photo) as the probe flew past Pluto and its moon Charon. But what could have caused them, and perhaps more importantly for this website, can we see the same thing closer to home and specifically in a cup of coffee? Well, the answer to those questions are yes and probably, so what on Earth is happening on Pluto?

Plutonian polygons
What is causing these strange polygons on the surface of Pluto. Image © NASA

Pluto moves in an highly elliptical orbit with an average distance to the Sun of 5.9 billion km (3.7 billion miles). Each Pluto year is 248 Earth years but one day on Pluto is only 6½ Earth days. As it is so far from the Sun, it is very cold on Pluto’s surface, somewhere between -238 to -218 ºC. The polygons that were photographed by New Horizons are in the ‘Sputnik Planum’ basin where the temperatures are at the lower end of that scale, somewhere around -238 ºC. At this temperature, nitrogen gas (which makes up 78% of the Earth’s own atmosphere) has not just liquified, it has solidified; turned into nitrogen ice. These polygons are made of solid nitrogen.

But solid nitrogen is a very odd type of solid and in fact, at the temperatures on Pluto’s surface, solid nitrogen is expected to flow with a very high viscosity (like an extremely gloopy liquid). And it is this fact that is the clue to the origin of the odd polygons (and the link to fluids like coffee). Pluto is not just a cold dead rock circling the Sun, but instead it has a warm interior, heated by the radioactive decay of elements in the rocks making up Pluto. This means that the base of the nitrogen ice in the Sputnik Planum basin is being heated and, as two groups writing earlier this summer in Nature showed, this leads to the nitrogen ice in the basin forming convection currents. The warmer nitrogen ‘ice’ at the bottom of the basin flows towards the surface forming convection patterns. It is these nitrogen convection cells that appear as the polygons on the surface of Pluto.

Rayleigh Benard cells in clouds
Rayleigh-Benard cells in cloud structures above the Pacific showing both closed and open cell structures. Image © NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Of course, convection occurs in coffee too, we can see it when we add milk to the coffee and watch the patterns form or by observing the dancing caustics in a cup of tea. So why is it that we see stable polygons of nitrogen on the surface of Pluto but not coffee polygons on the surface of our coffee? The first point to note is the time-scale. Although the polygons on Pluto are moving, they are doing so much more slowly than the liquid movement in a cup of tea or coffee, at a rate of only a few cm per year. But secondly, the type of convection may be different. Although both of the papers in Nature attributed the polygons on Pluto to convection, they differed in the type of convection that they considered was happening. McKinnon et al., suggest that the viscosity of the nitrogen on Pluto is much greater on the surface of the basin than in the warmer interior and so the surface flows far more slowly. This leads to cells that are much wider than they are deep. We would not expect such a drastic change in the viscosity of the coffee between the (cool) top and (warm) bottom of the cup! In contrast, Trowbridge et al., think that the cells are Rayleigh-Bénard convection cells,  circular convection cells that form such that the cells are as wide as they are deep. This sort of convection is seen in a coffee cup as well as in the sky on cloudy days: On the Earth, clouds often form at the top (or bottom) of Rayleigh-Benard cells, where hot humid air meets cold dry air (more info here). But to form cells that you can see in your coffee (such as are on the surface of Pluto) you would need the coffee to be in a fairly thin layer and heated from below. You would also need some way of visualising the cells, either with an infra-red camera or with powder suspended in the liquid, it would be hard I think to see it in coffee alone. However, you can see these cells in cooking oil as this video shows:

As well as providing the link to the coffee, the different types of convection on the surface of Pluto hypothesised by Trowbridge and McKinnon have consequences for our understanding of the geology of Pluto. If the cells are formed through Rayleigh-Bénard convection (Trowbridge), the basin has to be as deep as the cells are wide (meaning the basin has to be 10-40km deep with nitrogen ice). If McKinnon is correct on the other hand, the basin only needs to be 3-6 km deep. It is easy to imagine that an impact crater could cause a shallow crater such as that needed for McKinnon’s mechanism. A deeper crater would create another puzzle.

If you do manage to heat coffee (or tea) from below and form some lovely Rayleigh-Bénard cells while doing so I’d love to see the photos or video. Please do contact me either by email, Facebook or Twitter. Otherwise, if you just enjoy watching the patterns form on your coffee, it’s worth remembering that there could be an entire cosmos in that cup.

Categories
cafe with good nut knowledge Coffee review Home experiments Observations Tea

Electrifying coffee at the Black Penny

Black Penny coffee London
The Black Penny on Great Queen St

Back in the seventeenth and eighteenth centuries, coffee houses were places to go for debate, discussion or even to learn something new. The Grecian was known for science. Maths instruction (particularly for gambling) could be found with Abraham de Moivre (1667-1754) at Old Slaughter’s on St Martin’s Lane. Other coffee houses were meeting centres for literature, politics, philosophy or even espionage*. Coffee houses became known as “Penny Universities”. The Black Penny on Great Queen St is a café that wants to continue this tradition, with a downstairs “seminar pit” ready to host such discussions. Although the events page still says “coming soon”, if the events do indeed come, this is very much something that’s worth keeping an eye on.

Even without the seminars though, The Black Penny is definitely worth a visit. Entering from the street, the bar is on the left and is stocked with a good looking selection of cakes. We were shown through to the relatively large, bright and airy seating area at the back where a jar of water (infused with cucumber and mint) had been put on the table for us. I had a very good long black and a lovely apple and blackberry muffin with which to take in my surroundings. The muffin was confidently asserted to be nut-free, and so the Black Penny gets a tick in the ‘good nut knowledge’ section on the Daily Grind. The coffee beans were roasted by the Black Penny themselves and while it still says that they serve ‘Alchemy’ coffee on their website, this no longer appears to be the case.

Duracell batteries as coat hooks, battery, batteries
A strange form of coat hook? The things that catch your eye in cafes

Inside, there are some very interesting architectural features to notice, the remains of a ceiling for example (now removed to reveal the roof) and the acoustics introduced by the speaker positioning. Downstairs in the seminar pit there is apparently a very old stove, though I didn’t get to see that on my visit. However, what immediately struck my eye was what appeared to be a series of coat hooks that looked very similar to a well known brand of battery. Quite what these hooks were for or why they looked like batteries I didn’t manage to ascertain, however, it did get me thinking, can you use coffee-power to light an LED?

You may have heard of a potato battery, or a lemon battery. These are often used in science outreach experiments in schools to demonstrate electricity, or the concepts of current/voltage. Made from an ordinary potato (or a lemon), a copper wire is stuck into one end of the potato and a different metal (usually zinc) is stuck into the other end of the potato. At the Black Penny, there were three things left on the table. My coffee, the mint and cucumber infused water and the tea of my accomplice in many of these reviews (I’d eaten the muffin). Which of these would perform better as a battery?

coffee power
Can 6 coffee ‘cells’ with aluminium and copper electrodes light up an LED? (The answer may be in the photo)

Although people suggest using galvanised screws as the source of the zinc electrodes, I didn’t have many of those to hand and so had to manage with aluminium foil for one electrode, copper wire for the other. By putting the aluminium on one side of a shot glass, the copper wire on the other and then filling the glass with coffee, I was able to get 0.5-0.8V across the electrodes when I measured it with my digital multimeter (DMM). Fantastic you may think, almost an AA battery, but then if you were to measure the voltage across the water rather than coffee, you will find that you get a voltage of 0.6-0.7V. The result for tea was, perhaps unsurprisingly, about 0.6V.

But voltage is not the whole story. A battery does not just supply a voltage, it gives a current. The current depends on the electrical conductance of the liquid that the electrodes are in. In the case of the potato or the lemon battery, the acid (phosphoric or citric respectively) means that there are free hydrogen ions in the ‘battery’ between the electrodes which mean the electric current can flow through the circuit. Coffee consists of many acids (chlorogenic, quinic, citric etc etc.) and so it seems sensible to ask if coffee could be used to produce a battery with a current that could power an LED? LEDs require both voltage and current, (1.6V and 10mA for the LEDs used here). Hooking up a series of coffee battery-cells meant that, by 6 ‘cells’, I had 3V across the contacts. However the electric current through the coffee battery was very low (the maximum current I recorded using the low acidity Roasting House Sierra de Agalta Honduran coffee prepared in a cafetière was 155 μA). Although this was higher than the current through water (max 81 μA), it is much lower than the current through white vinegar (770 μA under the same conditions). Consequently, in order to light the LED connected to my coffee battery, I had to add salt to each coffee cell which serves as a way of massively boosting the current through the coffee (salt forms a solution of Na+ and Cl- ions that conduct electricity through the coffee). Though even then, my LED only lit dimly and intermittently.

battery, Volta, Como museum, Como
How it should be done. The “Alessandro Volta Temple” in Como, Italy, is a fantastic place to learn about the history of electricity

Sadly then, I do not see coffee power as a future for lighting in our cafés, (unless you want to use bulletproof coffee with salted butter). However, it has started to make me wonder, could we use a single coffee-cell to monitor the acidity of our coffee? If you find a method of brewing or a particular coffee especially acidic, it should produce a higher current for the same voltage through the cell, or equivalently, the resistance of the coffee-cell should decrease as the acidity of your coffee increases. Although obviously, it would be a bad idea to drink the coffee after putting it into a cell with copper and zinc (or aluminium) electrodes, you could pour a small amount of your coffee into a shot glass to test it while you were drinking the rest of the coffee. I intend on testing this hypothesis over the next couple of weeks but in the meanwhile, if you have thoughts on this to share (or the results of your experiments), please let me know either via the comments section, email, Facebook or Twitter.

The Black Penny is at 34 Great Queen St, WC2B 5AA

* A history of coffee houses can be found in “London Coffee Houses”, Bryant Lillywhite, (1963)

 

Categories
Coffee review Observations Science history slow

Reflections at Store St Espresso, Bloomsbury

Store St Espresso, coffee, Bloomsbury, UCL, London
Store St Espresso, Bloomsbury

I finally got around to visiting Store St Espresso two weeks ago while visiting the nearby Institute of Making’s 3rd birthday science-outreach party. Although the café was crowded, we managed to find a place to perch while we enjoyed a soya hot chocolate, caffé latte and my V60. Beans are from Square Mile while the V60 and filter coffee options featured guest roasters. Despite the narrow frontage, there is actually plenty of seating inside and people were happy to share tables with other customers when it got particularly busy. The café is well lit with sunlight streaming in through the sky lights above (indeed, the extra electric lighting indoors seemed a bit unnecessary given the amount of sunlight coming through the windows on such a good day). On the walls of the cafe were pieces of artwork, including quite a large pencil/charcoal piece right at the back of the cafe.

I was meeting a friend for coffee before going to the science event and so thought it would be good to combine a cafe-physics review with a visit to the science. It is always interesting to hear other people’s observations of the same space that you are ‘reviewing’. In this case, I was taken by the floor which showed some very interesting crack structures but what fascinated my friend (who was enjoying her caffe-latte) was the way that the sound from the stereo was reflecting from the bare walls, floor and ceiling. While cracks and fracture processes can be very interesting, perhaps it is worth following her observations as it leads, in a round about way, back to the coffee that she was drinking.

latte art, hot chocolate art, soya art
A caffe latte and a soya hot chocolate at Store St Espresso

While studying for my physics degree, a lecturer in a course on crystallography told us an anecdote. The story concerned a physicist walking past an apple orchard. As he was walking past, he noticed that at certain points he could hear the church bells from a distant church. As he walked on, the sound of the bells faded, before suddenly, he could hear them again. The physicist went on to derive the laws of X-ray diffraction, a technique that is now used routinely in order to understand the arrangement of atoms in crystals (like salt, diamond or caffeine). X-rays are part of the electromagnetic spectrum (just like visible light) but they have a very short wavelength.  The orchard had been inspirational to the physicist because, just as a crystal is a regular array of atoms, so the apple orchard is a regular array of trees; as you travel past an orchard (on the train, in a car or on foot), there are certain angles at which you can see straight through the trees, they have been planted in a 2D lattice. The church bells could only be heard at certain angles because of the way that the sound was being reflected from the multiple layers of the trees. The effect occurs because the sound made by church bells has a similar wavelength to the spacing of the trees (eg. ‘Big Ben’ chimes close to the note E, which has a wavelength of approximately 1m). The distance between atomic layers in a crystal is similar to the wavelength of the X-rays (the wavelength of X-rays frequently used for crystallography = 1.54 Å, size of the repeating structure in a salt crystal: 5.4 Å, 1 Å = 1/100000 of the smallest particle in an espresso grind). The physicist realised that the orchard affected the church bells in exactly the same way that the atoms in a crystal, be it salt, diamond or caffeine, will affect the deflection of X-rays. Suddenly, it became possible to actually ‘see’ crystal structures by measuring the angles at which the X-rays were scattered from substances.

bubbles on a soap solution
Not quite a regular 2D lattice. By controlling the size of the bubbles and the number of layers, you can simulate the crystal structure of different metals. Seems I need more practice in making bubbles of a similar size.

We can perhaps imagine an apple orchard but what do crystals look like? Crystals can come in many forms, all they need to be is a repeating structure of atoms through the solid. Some crystals are cubic, such as salt, some are hexagonal, others form different shapes. Metals, such as that making up the shiny espresso machine in the cafe are often a certain form of cubic structure and to visualise it, we can return to my friend’s caffé latte (via some soap). Two people who were instrumental in understanding X-ray diffraction were the father and son physicists, William Henry and William Lawrence Bragg. While attempting to make a model of crystal structures, William Lawrence Bragg found that the bubbles that could be formed on top of a soap solution were a very good approximation of the sort of crystal structures observed in metals (his paper can be found here). As they form, the soap bubbles (provided they are of similar size) form a regular cubic structure on the surface of the soap solution held together by capillary attraction, a very good model for the sort of bonding that occurs in metals. By controlling the size of the bubbles, the number of layers and the pressures on the layers of the bubbles, all sorts of phenomena that we usually see in crystals (grain boundaries, dislocations etc) could be made to form in “crystals” formed from soap bubbles. Why not look for such crystal structures in the foam of your cafe latte, though be careful to see how the size of the bubbles affects the arrangement of the bubbles through the foam structure.

Sadly, I have never found a reference to the story of the physicist and the apple orchard and it may even have been apocryphal. The closest reference I can find is that W. Lawrence Bragg (after whom the laws of X-ray diffraction are named) had a “moment of inspiration” for how X-rays would ‘reflect’ from multi-layers of atoms while he was walking in an area called “The Backs” in Cambridge. If any reader of this blog does know a good reference to this story I would be very much obliged if they could tell me in the comments section (below). To this day, I have been unable to pass by an orchard (or even a palm oil estate in Malaysia) without thinking about crystal structure, X-ray diffraction and church bells!

It seems that taking time to appreciate how sound is reflected (or diffracted) from objects, either in Store St Espresso or in an apple orchard, could be a very fruitful thing to do. If you have an observation of science in a cafe that you would like to share, please let me know here.

Store St Espresso can be found at 40 Store St. WC1E 7DB

The physics of X-ray diffraction and some great bubble crystal structures can be found in the Feynman Lectures on Physics, Vol II, 30-9 onwards.

Categories
General Home experiments Observations Sustainability/environmental

Clouds in my coffee

clouds over Lindisfarne
How do clouds form?

Does your coffee appear to steam more next to a polluted road than in the countryside?

This is a question that has been bothering me for some time. Perhaps it seems an odd question and maybe it is, but it is all about how clouds form. Maybe as you read this you can glance out the window where you will see blue skies and fluffy white clouds. Each cloud consists of millions, billions, of water droplets. Indeed, according to the Met Office, just one cubic metre of a cloud contains 1 hundred million water droplets. We know something about the size of these droplets because the clouds appear white which is due to the way that particles, including water droplets, scatter sunlight. Clouds appear white because the water droplets scatter the sunlight in all directions. In contrast, the particles in a cloudless sky scatter blue light (from the Sun) more than they scatter red. Consequently, from our viewpoint, the scattered light from the clouds appears white while the sky appears blue. The sort of directionless light scattering that comes from the clouds happens when the scattering sites (ie. the water droplets) are of a size that is comparable to, or larger than, the wavelength of light. This means that the water droplets in a cloud have to be larger than about 700 nm in diameter (or approximately just less than a tenth of the size of the smallest particle in an espresso grind). The particles in the atmosphere on the other hand scatter blue light more than they scatter red light because they are smaller than the wavelength of the blue light. You can find out more about light scattering, blue skies and cloudy days, with a simple experiment involving a glass of milk, more details can be found here.

glass of milk, sky, Mie scattering
A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself

So each of the one hundred million water droplets in a cubic metre of cloud is at least about a micron in diameter. We can then estimate how many water molecules make up one droplet by dividing the mass of a droplet of this size by the mass of one water molecule. This turns out to be more than 1000 million water molecules that are needed to make up one droplet of cloud. So, 1000 million water molecules are needed for each of the 100 million drops that make up one, just one, cubic metre of cloud. These numbers are truly huge.

But can so many molecules just spontaneously form into so many water droplets? Unlike a snowball, the water droplet in a cloud cannot start very small and accumulate more water, getting larger and larger until it forms a droplet of about a micron in size. Water droplets that are much smaller than about a micron are unstable because the water molecules in the drop evaporate out of it before they get a chance to form into a cloud (precise details depend on the exact atmospheric conditions). Water droplets need to come ‘ready formed’ to make the clouds which seems unlikely. So how is it that clouds can form?

Condensation on mug in CGaF
Look carefully at the rim of the mug. Do you see the condensation?

It turns out that the water droplets form by the water condensing onto something in the atmosphere. That something could be dust, or salt or one of the many other sorts of aerosol that are floating around in our skies. Just as with a cold mug filled with hot coffee, the dust in the air gives the water molecules a cold surface onto which they can condense. This sort of water droplet can ‘snowball’ into the bigger droplets that form clouds because the water is now condensing onto something and so does not evaporate off again so easily. At the heart of each water droplet in a cloud is a bit of dust or a tiny crystal of salt. Which brings me back to my question. It is much more dusty along a polluted road  than it is in the clean air of the countryside. Is this going to be enough of an effect to affect the probability of cloud formation? Does your coffee steam more as you cross the road than when you walk through the park?

It is a question that demands an experiment (and associated video). Last year, the Met Office suggested this simple experiment for observing clouds in a bottle. Unfortunately however, I have yet to make this experiment work in a way that would allow me to test whether polluted air produces thicker clouds than cleaner air. If you have any suggestions as to a good experiment (that will work on camera!) please let me know either in the comments section, by emailing me, or on Facebook. In the meanwhile, I’d be interested to know what you think, so if you think this post is about you, please let me know.

 

 

Categories
Coffee review General Observations

Setting standards at Brill, Exmouth Market

Brill, Exmouth Market, neon, architectural history
The neon lit “Brill” from the back of the cafe. You can also see evidence of an old arch in the brickwork, an old doorway?

Brill on Exmouth Market has quite a history. Originally a record store, it has evolved into a music shop/cafe more recently. On my recent visit, I ordered a very good Americano (beans from Officina Coffee Roasters) and although cakes were on sale, it was a small bar of Green & Blacks chocolate that appealed to me a bit more that day. It is a small cafe and so the few seats that are upstairs were occupied. This turned out to be a good thing though because I noticed a sign indicating that there were more seats downstairs, which actually meant that there was seating in a lovely little courtyard/garden at the back of Brill. Although it was originally locked (it was February and fairly dismal when I visited, who in their right mind would want to sit in the garden?), the friendly staff unlocked it and quickly cleaned one of the tables so that I could enjoy my coffee and chocolate in peace in central London. Indeed, the occasional (inevitable?) sound of sirens in the distance only served to emphasise the tranquility of the courtyard. The courtyard has four tables and a glitter-ball in the corner hanging from a tree. There was a lot to appreciate outside, both in terms of the science and the history of the place: Leaves deposited by vortices in corners of the yard with brickwork that suggested a significant re-build has occurred to this cafe.

But from my vantage point, it was the word ‘Brill’, lit up in neon lighting inside the cafe, that caught my attention. Neon lights are always interesting to me because their colour is so suggestive of the atoms that make up the light. The colour of a neon light is determined by the energy levels of the atoms that make up the light, the gas ‘neon’ shines red, hence neon lights. But if you wanted blue ‘neon’ lights you could use mercury as the vapour in the tube instead of neon, it is all about the energy levels of the atoms in the gas in the tubes.

glitter ball, disco at Brill Exmouth Market
A glitter ball in the corner of the courtyard at Brill

Under certain conditions, cadmium also emits a red light which brings us to the subject of this cafe-physics review: The definition of length. How is it that we can all agree on what ‘one metre’ is, or even one ‘inch’? Perhaps you are wondering how the red light emitted by cadmium, (or neon), relates to the definition of the metre? It’s about standards and definitions. Up until about 1960, the standard unit of length (the metre) was measured with reference to an actual, physical, metal rod kept in Paris with two scratches carved into it, one metre apart. Any arguments about the precise length of a metre could be settled by referring to the metre, this metal bar in Paris. But of course there were problems, the first of which was that the metre was in Paris. Perhaps you would think it easy to make copies? Yet in the nineteenth century this was already becoming a problem, the measurements that were being made were becoming too precise. Anders Ångstrom’s pioneering work with spectroscopy (investigation of elements by the colours that they emit/absorb) revealed a small difference between the metre kept in Uppsala (where Ångstrom was based) and that kept in Paris. Although the difference was tiny, when it was compared with what people had started to measure, it became significant. Then there was the question of the scratches: Would you measure the metre between the furthest two points of the scratch? Or the closest? Then an even worse problem was discovered: The rod was shrinking! If you’re tempted to abandon metric units and hark back to Imperial units, bear in mind that the UK Imperial Yard was shrinking even faster. No, something had to be done and that something involved changing the definition of the metre fundamentally.

neon sign, light emission
Neon signs have characteristic colours due to the electron transitions in the ionised gases

It is here that cadmium comes in to the story. Rather than use a physical length that we could all measure, the people whose job it is to define our base units decided that the definition of the metre would be with reference to the wavelength of the red light of Cadmium. I do not know why they did not want to use the red of neon lights but even with cadmium it quickly became apparent that there was a problem. The problem was that cadmium exists as several isotopes, all having a very slightly different ‘colour’ of red light that they emit. So, rather than cadmium, in 1960 they settled on the orange line of Krypton as the definition of the metre. One metre was then defined as 1650763.73 vacuum wavelengths of Krypton. That was the definition for over twenty years before the definition of the metre was updated again in 1983. It is now defined as “the length travelled by light in a vacuum during a time interval of 1/299792458 of a second”.

Perhaps it is not a definition that you or I could use, we’d probably still refer to our metre rule! Nonetheless this definition does allow people to perform experiments that need very precise and very accurate measurements of lengths. These standards are important for extremely sensitive measurements such as that needed to detect gravitational waves with the LIGO experiment, reported a few weeks ago. The neon lights at ‘Brill’ do indeed suggest a story that goes way back in time, both for the cafe and for the science.

Brill is at 27 Exmouth Market, EC1R 4QL

Spectroscopy information from “Spectrophysics”, by AP Thorne, Chapman and Hall Ltd, 1974

Categories
General Home experiments Observations Science history Tea

Caustic Coffee

A post that applies equally to tea, just swap the word “tea” for “coffee” throughout!

A cusp caustic in an empty mug of coffee
Have you seen this line?

Look deep into your coffee. Do you see the secrets of the cosmos being revealed? Well, neither do I usually but there is something in your coffee that could be said to have ‘cosmic implications’ and I’m sure it’s something that you’ve seen hundreds of times.

Now, admittedly it is easier to see this effect if you put milk in your coffee. Imagine drinking your (milky) coffee with a strong light source (the Sun, a lightbulb) behind you. You see that curved line of light that meets in a cusp near the centre of the cup? You can see various photos of it on this page. Yes, it is indeed the reflection of the light from the curved mug surface but it is far from just that. It is what prompted a professor at Duke University to say “It’s amazing how what we can see in a coffee cup extends into a mathematical theorem with effects in the cosmos.” To understand why, perhaps it is worth reflecting a bit more on our coffee.

The shape of the curve is called a ‘cusp’  and the bright edge is known as a ‘caustic’. It is fairly easy to play with the angle of the cup and the light so that you can see the first cusp curve but you can go further and create caustics that are the result of multiple reflections. Such multiple reflections can give heart shaped curves or “cardioids” so, in a certain sense adding milk to your coffee is good for (seeing) the heart.

caustic in a cup of tea or coffee
A cusp reflection is just visible in a cup of (soya) milk tea

Caustics were first investigated by Huygens and Tschirnhaus in the late 17th century. Mathematically, the cusp curve is termed an epicycloid, you can draw one by tracing the shape made by a point on the circumference of a circle rotating around a second circle, as this graphic from Wolfram mathematics demonstrates. There is a lot of maths in milky coffee. But just how is it that these curves reveal the “Cosmos in a cup of coffee“? It turns out that once you start to see caustics you start to see them everywhere. Caustics are not just going to be formed on the inside of your coffee mug, they can be formed by light waves getting bent by ripples on the surface of a stream or even by gravity, in a phenomenon known as “gravitational lensing”.  Gravitational lensing is when a massive object, such as a black hole or a galaxy, bends the light travelling past it so that it acts analogously to a lens in optics (but a very big one). It is this last type of caustic that prompted the headline quoted above. In a series of papers published in the Journal of Mathematical Physics, Arlie Petters of Duke University and coworkers calculated how light from distant objects was focussed through gravitational lensing and the effects of caustics. Their predictions (and in particular any exceptions to their predictions) could lead to a new way to search for the elusive dark matter, which is thought to contribute to much of the Universe’s mass. They are now waiting for the Large Synoptic Survey Telescope (LSST) to start mapping the sky in order to test their theories.

multiple caustics from multiple LEDs
Multiple light sources are being reflected in this cup.

Before concluding this discussion of cosmic coffee, it is worth taking another look at the mathematician Tschirnhaus. As well as maths, he was known for his philosophy and his chemistry. In fact, it seems that he was responsible for the invention of European porcelain. As noted elsewhere, it has been argued that it was the ability of Europeans to start making their own porcelain that explained the rapid rise in consumption of tea and coffee during the eighteenth century in Europe. Interestingly, one of the tools that allowed Tschirnhaus to succeed in manufacturing porcelain in Dresden where others elsewhere failed was his use of “burning mirrors” to focus the heat and to achieve higher furnace temperatures than were otherwise available. He was using those caustics that he and others had so thoroughly studied mathematically in order to produce the type of cup in which we most often encounter the easiest caustics. A lovely little ‘elliptical’ story on which to end this Daily Grind.

In order to see the caustics in your coffee, it is necessary that the coffee reflects the light incident on it. Meaning, you need to add milk to your coffee. I knew there had to be a good reason to add milk to coffee at some point. Please do share your photos of caustics in your coffee either here or on Facebook or Twitter.

 

 

Categories
General Home experiments Observations Science history Tea Uncategorized

Predicting the weather with a cup of coffee?

What do the bubbles on the surface of your coffee tell you about the weather?

weather, bubbles, coffee, coffee physics, weather prediction, meteorology
There is a lot of physics going on with the bubbles on this coffee, but can they be used to predict the weather?

You have just poured a cup of freshly brewed coffee into your favourite mug and watched as bubbles on the surface collect in the middle of the cup. It occurs to you that it is going to be a good day, but is that because you are enjoying your coffee or because of the position of the bubbles?

There are a large number of sayings about the weather in the English language. Some of the sayings have a basis in fact, for example the famous “red sky at night, shepherd’s delight, red sky in the morning, shepherd’s warning“. Others though seem to verge on the superstitious (“If in autumn cows lie on their right sides the winter will be severe; if on their left sides, it will be mild”), or unlikely (“As August, so the next February”).  In 1869, Richard Inwards published a collection of sayings about the weather. “Weather Lore” has since undergone several new editions and remains in print although Inwards himself died in 1937. Amongst the sayings contained in the book is one about coffee:

“When the bubbles of coffee collect in the centre of the cup, expect fair weather. When they adhere to the cup forming a ring, expect rain. If they separate without assuming any fixed position, expect changeable weather.“

A quick search on the internet shows that this example of weather lore is still circulated, there is even a ‘theory‘ as to why it should be true. But is it true or is it just an old wives’ tale? Although I have consumed a lot of coffee I have never undertaken enough of a statistical study to find out if there could be an element of truth in this particular saying. The number of bubbles on the surface of the coffee is going to depend, amongst other things, on the type of coffee, the freshness of the roast and the speed at which you poured it. While the position of the bubbles will depend on how you poured the coffee into the mug, the surface tension in the coffee and the temperature. It would appear that there are too many variables to easily do a study and furthermore that the mechanism by which coffee could work as a weather indicator is unclear. It is tempting to write off this particular ‘lore’ as just another superstition but before we do that, it is worth revisiting another old wives tale which involves Kepler, Galileo, the Moon and the tides.

tides, old wives legends, Kepler, Galileo, Lindisfarne, bubbles in coffee
The pilgrim path between Lindisfarne and the mainland that emerges at low tide is marked by sticks. But what causes the tides?

Back in the mid-17th century, Newton’s theory of universal gravitation had not yet been published. It was increasingly clear that the Earth orbited around the Sun and that the Moon orbited around the Earth, but why exactly did they do that? Gilbert’s 1600 work De Magnete (about electricity and magnetism) had revealed what seemed to be an “action at a distance”. Yet the scientific thought of the day, still considerably influenced by Aristotelianism, believed that an object could only exert a force on another object if it was somehow in contact with it. There was no room for the heavenly bodies to exert a force on things that were found on the Earth. Indeed, when Kepler suggested that the Moon somehow influenced the tides on the Earth (as we now know that it does), Galileo reproached him for believing “old wives’ tales”: We should not have to rely on some ‘magical attraction’ between the moon and the water to explain the tides!

The point of this anecdote is not to suggest that a cup of coffee can indeed predict the weather. The point is that sometimes we should be a little bit more circumspect before stating categorically that something is true or false when that statement is based, in reality, purely on what we believe we know about the world. We should always be open to asking questions about what we see in our daily life and how it relates to the world around us. It will of course be hard to do a proper statistical study of whether the bubbles go to the edge or stay in the centre depending on the weather (whilst keeping everything constant). Still, there are a lot of people who drink a lot of coffee and this seems to me to offer a good excuse to drink more, so perhaps you have some comments to make on this? Can a cup of coffee predict the weather? Let me know what you think in the comments section below.

 

Weather legends taken from “Weather Lore”, Richard Inwards, Revised & Edited by EL Hawke, Rider and Company publishers, 1950

Galileo/Kepler anecdote from “History and Philosophy of Science”, LWH Hull, Longmans, Green and Co. 1959

Categories
General Observations slow

The coffee cave

Americano, Caravan coffee, Skylark, Wandsworth
Gazing into a coffee you can see the reflection of your face looming back at you.

Have you ever gazed into your coffee as you take a mouthful only to get disturbed to see a distorted view of your face looming back at you from the coffee? Has it struck you that while you often see such reflections, you rarely see shadows? Try it first with water and then coffee. Can you, perhaps, see a shadow on the coffee where you cannot see shadows on the water? Why would this be?

For a shadow to be visible on a surface, the surface must scatter enough light so that the contrast between shadow (where there is no light to scatter) and non-shadow (where the surface is illuminated) can be seen. Although a shadow (or at least the relative lack of light) is always going to be present behind any obstacle, it is whether or not it can be seen on the surface of the water/coffee that is at issue here. Pure water is of course quite transparent. Without anything in the water to scatter the light (such as mud for example), the light passes straight through the water to the other side. Overall, not enough light is scattered back from the surface of the water to generate the contrast required for seeing shadows. Seeing shadows on pure water is going to be hard.

Chemex, 30g, coffee
The concentration of suspended particles will depend on how you make your brew

By contrast, coffee contains suspended particles, in fact they are part of the very essence of the drink. These particles offer a surface to scatter the light back towards the observer and so highlight the shadows formed by the object between the coffee and the light. It strikes me that different brew methods will result in different amounts of sediment and suspended particles in the coffee and therefore a greater or lesser tendency of the coffee to reveal shadows. Perhaps if anyone does notice that it is harder to form shadows on coffee prepared by a Chemex  than a French Press (for example) they could let me know using the comments section below.

Shadows have been used by philosophers to illustrate by allegory how we perceive the world around us. In the tale of Plato’s cave a group of prisoners are held in a cave such that they can only ever see the shadows playing on the cave’s wall. The shadows are formed by a fire behind the prisoners that the prisoners cannot see. As they can only see the shadows, they start to think that it is the shadows themselves that are ‘real’. It is a tale questioning the reality of what we currently see and also our inability to adjust to the differences between looking directly at the Sun or discerning shadows in the dark. In the story of the cave, it is the fire, or the Sun that causes the shadows that deceive the prisoners. No consideration was given to the role played by the wall on which the shadows dance. Yet we can see from our coffee that to understand the world of shadows we do not merely need a light source. To understand shadows, we need a surface from which to reflect the shadows. Perhaps we need to spend some time contemplating our coffee, the shadows and what they can tell us about the world and how we see it.

For details about this and other phenomena involving light and its interaction with the world around us, see: “Color and Light in Nature”, David K. Lynch and William Livingston

 

Categories
Coffee review Observations Science history

Enlightenment at Timberyard, Seven Dials

coffee, Timberyard, wooden tray
Great coffee at Timberyard

It is not often that you come across an independent café in central London that has great coffee, a good deal of space and seats available and so I found myself very happy to have come across Timberyard near Seven Dials. As I ordered my long black, I was presented with a choice of bean for the espresso base. Should I have the “fruity and acidic” Jabberwocky, or the “chocolate” Climpsons? I was trying Timberyard for the first time and so the choice was easy. For me ‘chocolate’ will win over ‘fruity’ every time. However having the choice was a nice touch. Being in central London, it was of course crowded when I tried it, but there were still seats around, including some stools outside. I took a seat outside, ready to watch the people and the cars going by. After a short while, the coffee was brought over, served on a wooden tray together with a complementary bottle of water.

crema on coffee, Timberyard
The patterns as the crema breaks up are reminiscent of the coastlines of Norway and of fractal mathematics.

It was a very pleasant location to sit and enjoy my coffee while I watched people rushing by on their way to various meetings and tourists milling around, taking their time to soak in the city. As I waited for the coffee to cool, the crema on the surface started to break up and I was reminded of the coastline of Norway. It struck me that the same mathematics of fractals describes the coastlines as would describe the patterns in the crema. It was then that I noticed the street lighting. A light converted from an old style gas lamp was attached to the wall of a shop just across from where I was having my coffee. In the other direction, there was a modern lamp-post of one particular design and then, just slightly further down the road, a lamp-post of a different design. This prompted me to think about the history of street lighting and also the problems with it.

One of the first roads in England to be lit at night was the Route du Roi (nowadays known as Rotten Row) that ran from Kensington Palace to St James Park. Three hundred lamps were hung from trees along the route. These first street lights produced light by burning fuel, a method of street lighting which existed in one form or another until fairly recent times (as evidenced by the oldest street lamp visible from Timberyard). They were installed, as now, to try to reduce crime; it seems that the park used to be frequented by highwaymen. One of these had been hanged for the killing of a woman in the park in 1687. Though it wasn’t quite murder: Rather than be robbed of her wedding ring, the unfortunate lady had attempted to swallow it and so choked to death.

gas lamp, Monmouth St
An old style street lamp on Monmouth St. visible from Timberyard

A more recent type of street light was based on sodium. Applying an electric voltage across a gas of sodium caused the sodium to emit light in the yellow region of the visible spectrum. If rather than sodium, the lights had been based on neon gas, the colour of the light emitted would have been different as the colour corresponds to the different energy levels in the atoms, (for more info click here). In an effort to find increasingly efficient light sources, there is now a move into street lighting based on LEDs (Light emitting diodes). Rather like the sodium lamps, such devices work by applying a voltage over a material but in the case of the LEDs, the material is a semiconductor junction (where the energy gap can be manipulated to have the same size as the energy of visible light). LEDs have the significant advantage that the voltage supplied to produce sufficient lighting can be much less than is the case for sodium lights. This increase in efficiency is a small but effective way to limit our carbon dioxide emissions, especially when used together with sensors on the lamp post to detect when it is dark enough to actually necessitate the light being turned on.

Such a combination of energy saving measures benefits not just the planet but the public wallet. Perhaps in a few years time we’ll see such a set of eco-friendly lamp-posts spring up near Timberyard to add to the collection of street lights there.

In the meanwhile, if you visit Timberyard and notice some interesting physics or history, or if you just slow down and see something interesting, please let me know using the comments box below.

Timberyard is at 7 Upper St Martin’s Lane, Seven Dials, WC2H 9DL (and Old St, EC1V 9HW.)

London info taken from The London Encyclopaedia (3rd Ed), Hibbert et al.

Categories
General Observations Tea

Dynamical similarity

vortices in coffee
A vortex … (Dragging a spoon through a cup of coffee)

Science involves designing experiments to test theories. I do not want to get distracted here by how a theory is defined or the precise ways in which a theory is tested by experiment. The point of this week’s Daily Grind is to look at the role of experiments in physics, where they can be used, where it is more difficult to use experiments to test hypotheses and, how this can be connected with coffee. Some physics can be relatively easily tested by observation or experiment: we can for example take photographs of distant no-longer-planets to test theories about the evolution of the solar system or measure the viscosity of a liquid as we add something to it. Yet there are some areas of physics where it is not immediately obvious how you would test any theory that you develop. One such area is atmospheric physics where the limitations of living on one planet with one atmosphere where many different things all happen at once, could potentially be a bit of a problem for doing experiments on the theories of atmospheric physics.

vortices, turbulence, coffee cup physics, coffee cup science
… is a vortex… (What happens if you put a coffee on a record player?)

Fortunately, there is a way in which atmospheric physicists can test their theories with experiment and, perhaps unsurprisingly for the Daily Grind, that way involves a cup of coffee (or tea). The route out is called “dynamical similarity” and it is a consequence of the fact that the same mathematics describes much of that which happens in a cup of tea as it does the atmosphere. It is true that a tea cup is a lot smaller than the atmosphere but a vortex in a tea cup is the same as a vortex in the atmosphere even if one is only a centimetre across while the other has a core size of many kilometres. The mathematics will be the same. This allows people to test hypotheses formed about the atmosphere in an environment that they can control and repeat.

A vortex in the atmosphere
… is a vortex.
(Typhoon Nangka, Image Credit: NASA image courtesy Jeff Schmaltz, LANCE/EOSDIS MODIS Rapid Response Team at NASA GSFC. Caption by Kathryn Hansen)

A couple of months ago, I wrote an article in Physics World about the connections between coffee and physics. Shortly after it came out, I got an email from Paul Williams alerting me to an article that he had written in the journal Weather called “Storm in a tea cup“. It turns out that the subject of his research had been to study the impact on the weather of the interaction of two types of atmospheric waves: Rossby Waves and Inertia-gravity waves. The method that he had used to test this was, if not quite a tea cup, a bucket which he could rotate. Rossby waves and inertia-gravity waves are both present in the atmosphere and can be induced, albeit on a smaller scale, in a bucket. He was using the concept of dynamical similarity to explore what happens in our atmosphere. And the experiment was important. Before his experiments, it had been thought that the effect of the interaction of these two sorts of waves was minimal. His experiments revealed that this may not be the case, the inertia-gravity waves can significantly affect the Rossby waves. Given that Rossby waves are responsible for cold/warm fronts and weather phenomena in mid-latitude regions of the world (such as the UK) his results, and his cup of tea, were potentially very important.

I’m always very happy to hear about what others are doing with science in a tea cup or a coffee mug. Please share any thoughts in the comments section below.

Paul Williams “Storm in a tea cup” can be found in Weather, 59, (4), p.96 (2004) 

With apologies to Gertrude Stein.