Coffee and the stars

cold mug
There are many ways that gazing at a cup of coffee can help with sky gazing.

There is a problem looming on the horizon concerning how astronomers can continue to look at the sky as the effects of global climate change become more pronounced. Some of these issues are an extension of those that have been affecting amateur astronomers since the invention of telescopes. Fortunately for those with portable telescopes, many of the issues can be minimised, but some effects will be a problem for our larger observatories. And of course, for this website, we can gain an insight into what the problems are by gazing more closely at our coffee.

It’s time to make a hot coffee. Or a tea. In fact, for some of the following observations a cup of green tea or a herbal tea would be perfect. You are after a brew that is light and allows you to see through to the bottom of your mug. But if you want to keep with coffee, worry not, there are still important clues to be seen above the coffee (and you can always use the spare brewing water to pour plain hot water into a cold cup).

If you have made a tea, you should be able now to look into your tea to the bottom of the cup. If it is a sunny day, or if you have a light on behind you, you will hopefully be able to see lines of light starting to form and then dancing around the base of the cup. If you have made a coffee, this will be more difficult for you to see. In addition to pouring any spare brew water into a cup to see the same effect in plain water, you could also look at the top of your cup and notice how the steam is making the air above more turbulent, changing the way you see things on the other side of the mug (is there an allegory there?).

The dancing light patterns and turbulent steam clouds are similar to conditions in the atmosphere that can make observing the stars difficult for amateurs and professionals alike. It is perhaps easier at first to think about the keen amateur astronomer who takes their telescope from the warmth of their indoors to the cold of a cloudless night. We can perhaps immediately see analogues with the (hot) tea in the (cold) cup and the steam clouds above the coffee.

Shortly after pouring hot tea into a cool cup you should be able to see these bright lines dancing over the base of the cup. They indicate how the refractive index of the tea changes as a function of temperature and so show the convection zones within the tea cup.

We can start by thinking about the turbulence in the air movement of the atmosphere being similar to the turbulence in the steam clouds above the cup. It is hard to focus on point objects through the steam clouds; the star light twinkles as it travels through our atmosphere. But then, just as we see the light patterns form in our tea cup as regions within the tea that have ever-so-slightly different temperatures mix in a convective pattern, so the hot air within the tube of the telescope will mix with the air at the edge of the tube that has been cooled by contact with the night-temperatures. The refractive index of air and water varies as a function of temperature (fluid density). And so with the telescope as with the tea cup, these regions of hotter and cooler fluid (air and tea respectively) have different refractive indices, meaning that any light travelling through those regions gets bent by different amounts as a function of the temperature of the medium it flows through. In the tea cup, this means that we see bright lines dancing across the bottom of the cup that trace the convection zones in the tea. In the telescope we would get a wobbly image.

For the amateur with their portable telescope the solution to the convection problem, if not the atmospheric turbulence, is relatively simple. Take your telescope outside for a good amount of time so that the air inside the tube can reach a similar temperature to the air outside. Convection will subside and the image will be more stable. If we wanted to drink cold tea, we could see the same thing with our tea cup: leave the tea to cool to room temperature and those dancing light lines on the bottom of the cup should subside (this is admittedly a thought experiment on my part. I have generally finished the tea before reaching this point).

But unfortunately, similar phenomena also affect professional observatories, and a recent study suggests the problems are likely to get worse as the effects of global climate change become increasingly apparent. One of the first problems is exactly the same as for the portable telescopes: the telescopes are frequently warmer than their surroundings. Observatories such as the European Southern Observatory facility in Cerro Paranal, Chile, have in the past compensated for this by cooling the domes housing the telescopes during the day to match that of the air outside. The problem is that the feedback circuits do not work to cool to a temperature higher than 16C and, as the atmospheric temperatures rise, so it becomes harder to maintain the temperature equilibrium between the telescope and the atmosphere. As the atmosphere becomes warmer, it also becomes more turbulent, causing further problems for observations done with ground based telescopes.

Edmond Halley, Canary Wharf, Isle of Dogs, view from Greenwich
The view towards the Isle of Dogs (and Canary Wharf) from Greenwich. In the 17th century it was thought that the Isle of Dogs floated on the tidal Thames because of how it seemed to rise and fall with the tide. The reality is far more interesting and involves the same physics that affects tea and telescopes. You can read about that aspect here.

More difficult however is the effects of water vapour in the atmosphere for observations being made in the infra-red. As the atmospheric temperature increases, so the water vapour content in the atmosphere will increase. One measure of the water vapour in the atmosphere is known as the integrated water vapour (IWV). The IWV is the total water vapour in a column of air stretching vertically from the Earth’s surface to the top of the atmosphere. High IWV levels affect observations in the infra-red and are particularly frequent during El Nino events. It is not just that climate change will cause there to be, on average, more water vapour in the atmosphere. It is known that the frequency of El Nino events is increasing as a consequence of the effects of the climate change we are already seeing. This will lead to more frequent occasions when the observing conditions are unfavourable for ground based telescopes.

The authors of the study conclude that we will need to think about the effects of climate change on the local conditions before we can build any new ground based observatories. We will need to adapt to the new conditions that climate change forces on us. As to how we can minimise the effects of climate change altogether, that will require gazing into our coffee and tea and thinking a lot more deeply. There are things we can do, individually and collectively. Is it too much wishful thinking to wonder if we will start to do them in 2021?

A coffee balancing act

Coffee Corona

Sometimes you can infer the existence of a thin (white) mist over your coffee by the corona pattern around reflected light fittings.

Clouds of steam hover just above your brew, dancing on the surface in sharp, almost violent, sudden movements. You can see it almost every time you drink a long black, cup of tea or even a glass of hot water. But what on earth is going on?

Back in 2015, a paper by Umeki and others showed that these dancing white mists were levitating water droplets, a common manifestation of something that had been noticed in lab experiments a few years earlier. Hundreds of water droplets, each about 10 μm diameter (the size of the smallest grains in an espresso grind) somehow just hover above the coffee surface. You can read more about that study here. Yet there remain questions. How do the water droplets levitate? What causes those violent movements in the cloud? Can contemplating your coffee help to understand these questions?

To explore what is happening with the white mists, we need to view them in an environment that we can control so as to change one or other of the parameters in the ‘coffee’ and see what happens to the mists. And this is what Alexander Fedorets and co-workers have been doing for a few years now (even before the work of Umeki). What Fedorets has noticed is that when you heat a small area (about 1mm²) of a thin layer of liquid, it is not just possible to create these white mists, you can see the droplets levitating and they form hexagonal patterns of droplets. This is quite astonishing because whereas we are used to solids forming crystals (think of water and snowflakes for example), a formation of liquid droplets in a “self-organised” pattern is an unusual phenomenon.

floating, bouncing drops

You can stabilise much larger droplets of water (up to a couple of mm diameter) by vibrating the water surface. This is a very different phenomenon but is also an interesting effect you can create in your coffee.

Then we can ask, what is it that causes these droplets of water to levitate above the surface? According to a recent paper of Fedorets, the answer is indeed as simple (in the first approximation) as the fact that these droplets are in a delicate balance between being pulled into the coffee by gravity and pushed upwards by a stream of evaporating water molecules. This balance suggests that we can do a ‘back of the envelope’ calculation to estimate the size of the droplets and also to understand what happens when the coffee cools down. We start by thinking about the gravitational pull on the droplet, the force on that is just F↓ = mg (where g is the gravitational acceleration and m is the mass of the droplet) so, if we write this in terms of the density of water, ρ, and the radius, r, of the droplet:

F↓ = ρ (4/3)πr³.g

Similarly, we know how to calculate the upwards force on a particle created by a flow of liquid (steam). It is the same expression as Jean Perrin used to understand the layering of water colour paint in a droplet of water (which is the same as the layering of coffee in a Turkish coffee) and so proved experimentally Einstein and Langevin’s theories of Brownian Motion (which you can read about here). If the steam has a velocity U and the dynamic viscosity of the steam is given by μ, the upwards force given by the steam is:

F↑ = 6πμUr

For the droplet to ‘balance’ (or levitate) above the surface, F↓ = F↑ so with a bit of re-arrangement we get the radius of the droplet as given by:

r = √[9μU/(2ρg)]

Plugging in sensible numbers for μ (2×10^-5 kg/ms) and U (0.1 m/s), and using the density of water (10³ kg/m³) and g = 9.8 m/s² gives a radius for the droplet of 17 μm which fits very well with what is observed.

Rayleigh Benard cells in clouds

The white mists often seem to vanish as if they were sustained by Rayleigh Benard cells in the coffee. Rayleigh Benard cells can also be found in the clouds in the sky, in fact, anywhere where there is convection.
Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

But does the expression tell us anything else? Well, the radius is proportional to U; the velocity of the steam. So if you increase the temperature, you should increase the radius of the levitating droplets. This is exactly what is seen. Also, as the temperature of your coffee drops and there is less steam coming off the surface, it will become harder to stabilise these white mists; the mists will disappear as the coffee cools. This is something you can test for yourself: what is the optimum temperature at which to see the white mists (and drink your coffee)?

But the study by Fedorets showed something else. Something quite intriguing and perhaps relevant to your experience. Fedorets had stabilised the droplets on the surface by using an infra red laser and held them into a fixed area by only heating a small region of the liquid. In that sense the study is quite far from our physical experience with a coffee. But what Fedorets noticed was that these stabilised droplets grew with time. As the droplets grew, the bottom of the droplet got closer and closer to the liquid surface until, suddenly, the droplet collapsed into the liquid. This collapse caused a capillary wave on the water surface which is a small wave regulated by the surface tension of the water. And this wave then caused the surrounding droplets to collapse into the liquid interior. Because this happened very quickly (the wave travels at about 1m/s which is equivalent to a slow stroll at 3.6km/h), to us, looking at our coffee, it would appear that a violent storm has momentarily erupted over the surface of the white mists.

As the wavelength of a capillary wave is determined by the surface tension of the liquid, this suggests that if you change the surface tension of the coffee you may change the speed or perhaps the appearance of the collapse of these white mists. You can change the surface tension of your coffee by adding either soap or alcohol to your long black. Umeki did add a surfactant (to reduce the surface tension) and didn’t notice a significant difference to the speed of the wave but maybe other factors (such as temperature) were dominant in that experiment. It certainly seems a good excuse to investigate. Let me know if you experiment with your coffee and if the white mists move faster or slower in your Irish coffee compared with a morning V60, you may want to film the results if you intend to drink the coffee afterwards.

The work of Fedorets and of Umeki were both published under ‘open-access’ meaning that anyone can read them (without paying). You can read Umeki’s study here and Fedoret’s study here.

Why politicians should drink loose leaf tea

Coffee Corona

Notice the rainbow pattern around the reflected light spot?
The universe is in a cup of coffee but to understand rising sea levels, it’s helpful to look at tea.

The universe is in a glass of wine. So said Richard Feynman. It has been the focus of this website to concentrate instead on the universe in a cup of coffee, partly because it is much easier to contemplate a coffee over breakfast. However there are times when contemplating a cup of tea may be far more illuminating. Such was the case last week: if only a politician had paused for a cup of tea before commenting on rising sea levels.

There are many reasons to drink loose leaf tea rather than tea made with a bag. Some would argue that the taste is significantly improved. Others, that many tea bags contain plastic and so, if you are trying to reduce your reliance on single-use plastic, loose leaf tea is preferable. Until last week though, it had not occurred to me that brewing a cup of tea with a mesh ball tea infuser (or a similar strainer) was a great way to understand the magnitude of our problem with rising sea levels. If a stone were to enter a pond, the pond-level would rise; if a spherical tea strainer (full of loose leaf tea) were to be placed in a cup, the soon-to-be-tea level would rise.

Clearly, because we know our physics, we would not place a strainer of tea into an existing cup of hot water as we know the brewing process relies on diffusion and turbulence, not just diffusion alone. So what we more commonly observe in the cup is actually a tea-level fall as we remove the straining ball. Fortunately, we can calculate the tea level decrease, h:

A schematic of the tea brewing process

My cylindrical tea mug has a radius (d) of 3.5cm. The radius (r) of the mesh ball is 2cm. We’ll assume that the tea leaves completely expand filling the mesh ball so that the ball becomes a non-porous sphere. Clearly this bit is not completely valid and would anyway create a poor cup of tea, but it represents a worst-case scenario and so is good as a first approximation.

Volume of water displaced = volume of mesh ball

πd²h = (4/3)πr³

A bit of re-arrangement means that the height of the tea displaced is given by

h = 4r³/(3d²)

h = 0.87 cm

This answer seems quite high but we have to remember that the mesh ball is not completely filled with tea and so the volume that it occupies is not quite that of the sphere. Moreover, when I check this answer experimentally by making a cup of tea, the value is not unreasonable. Removing the mesh-ball tea strainer does indeed lead to a significant (several mm) reduction in tea level.

Earth from space, South America, coffee

Assuming we are truly interested in discovering more about our common home, we can gain a lot through contemplating our tea.
The Blue Marble, Credit, NASA: Image created by Reto Stockli with the help of Alan Nelson, under the leadership of Fritz Hasler

What does this have to do with politicians? Last week a congressman from Alabama suggested that the observed rising sea levels could be connected with the deposition of silt onto the sea bed from rivers and the erosion of cliffs such as the White Cliffs of Dover. If only he had first contemplated his tea. Using a “back of the envelope” calculation similar to that above, it is possible to check whether this assertion is reasonable. As the surface area of the oceans is known and you can estimate a worst-case value for the volume of the White Cliffs falling into the sea, you can calculate the approximate effect on sea levels (as a clue, in order to have a significant effect, you have to assume that the volume of the White Cliffs is roughly equal to the entire island of Great Britain).

Mr Brooks comments however do have another, slightly more tenuous, connection with coffee. His initial suggestion was that it was the silt from rivers that was responsible for the deposition of material onto the sea bed that was in turn causing the sea level to rise. About 450 years ago, a somewhat similar question was being asked about the water cycle. Could the amount of water in the rivers and springs etc, be accounted for by the amount of rain that fell on the ground? And, a related question, could the amount of rain be explained by the amount of evaporation from the sea?

The initial idea that the answer to both of those questions was “yes” and that together they formed the concept of the “water cycle” was in part due to Bernard Palissy. Palissy is now known for his pottery rather than his science but he is the author of a quote that is very appropriate for this case:

“I have had no other book than the heavens and the earth, which are known to all men, and given to all men to be known and read.”

Reflections on a cup of tea.

Attempts to quantify the problem and see if the idea of the water cycle was ‘reasonable’ were made by Pierre Perrault (1608-80) in Paris and Edmond Halley (1656-1742) in the UK. Perrault conducted a detailed experiment where he measured the rain fall over several years in order to show that the amount of rain could account for the volume of water in the Seine. Halley on the other hand, measured the amount of evaporation from a pan of heated water and used this value to estimate the evaporation rate from the Mediterranean Sea. He then estimated the volume of water flowing into that sea from a comparison to the flow of the water in the Thames at Kingston. Together (but separately) Perrault and Halley established that there was enough water that evaporated to form rain and that this rain then re-supplied the rivers. Both sets of calculations required, in the first place, back of the envelope type calculations, as we did above for the tea-levels, to establish if the hypotheses were reasonable.

If you missed the coffee connection, and it was perhaps quite easy to do so, the question that Halley studied concerned the rate of evaporation as a function of the water’s temperature. This is something that is well known to coffee drinkers. Secondly however, one of Halley’s experiments about the evaporating water was actually performed at a meeting of the Royal Society. It is known that after such meetings, the gathered scientists would frequently adjourn to a coffee house (which may have been the Grecian or, possibly more likely, Garraways). As they enjoyed their coffee would they have discussed Halley’s latest results and contemplated their brew as they did so?

What this shows is that sometimes it is productive to contemplate your coffee or think about your tea. Notice what you observe, see if you can calculate the size of the effect, consider if your ideas about the world are consistent with your observations of it. But in all of it, do pause to slow down and enjoy your tea (or coffee).

Would you like plastic in that?

Straws with viscous liquid (milkshake) in them

Do you need that straw?

Plastic Free July starts in just a few days time. Each year this initiative encourages us to eliminate, or at least reduce, our use of single use plastic throughout the month of July. It is a great way to increase our awareness of our plastic use by attempting not to use any.

There are numerous reasons that we may want to reduce our plastic consumption. In addition to the problems of litter associated with plastic waste, there are problems for wildlife caused by ingesting our rubbish. Even if we dispose of it responsibly, plastic takes a long time to degrade. It is thought provoking to consider that the take-away cup that we discarded yesterday may still be lying in some landfill site years after we have forgotten about drinking that coffee. So what can be done about it and what are the specific issues for coffee drinkers?

air valve, plastic, environmental coffee packaging

Air valves and metallised plastic are common packaging materials for freshly roasted coffee, but can we avoid them?

One way to start to reduce our dependence on single use plastic is to understand how much we actually use on a day by day basis. Registering for a plastic free July is one way of doing this. As a result of attempting a Plastic Free July last year, I have found some plastic-free habits that have stuck with me all year. Loose leaf tea is one such improvement (teabags can also contain plastic). Although initially it seemed a bit of a pain to use a basket to brew the tea, as I kept with the habit I found it easy to compost the tea leaves after making a brew and the tea tastes better too. Things like shampoo bars and tooth ‘paste’ tablets (from Lush) have also been better and longer lasting than similar products packaged in plastic bottles.  Although some plastic habits are hard to break, living as plastic free as possible for one month did deepen my awareness of the plastic that I take for granted.

But perhaps living plastic free for a month is too daunting? An alternative challenge sadly emphasises just how linked coffee drinking can be to single-use plastic consumption. The Top 4 challenge asks you to eliminate, just for July, the target take-away items. Of these 4, at least 2 (and arguably 3) are linked to coffee drinking or cafés. The top 4 are plastic bags, bottles, take-away coffee cups and straws. Could you avoid these for just one month? Take the challenge.

blue tits, mint water, mint infusion, mint leaves in water

Enjoying a glass of water in a cafe can be better than running with a bottle of water anyway.

If you are ready to go plastic-free in your coffee habits, here’s a list of where we frequently encounter single-use plastic while drinking in cafés or even at home, together with suggestions of how to avoid the plastic where appropriate. Please let me know in the comments section below if you can think of further examples (and how you are avoiding them either in July or more permanently).

  • Disposable take-away coffee cups – get and use a re-usable one. You can find a helpful comparison of different types of re-usable coffee cups on Brian’s Coffee Spot.
  • Tea bags – yes they can contain plastic, see more information here. To avoid them, get hold of a metal tea basket, or even a tea pot and strainer and start investigating loose leaf tea.
  • Water bottles/soft drinks bottles – if in a café, why not enjoy the moment by staying with a glass of water rather than grabbing a bottle? If you are in a hurry though, a flask (such as klean-kanteen) is a great investment. In some parts of London (and perhaps elsewhere?) chilled tap water is available on tap for use in re-usable bottles
  • Air valves on your roasted coffee bag – do you really need these? The Nottingham based coffee roaster, Roasting House, did a taste test on freshly roasted coffee packaged with and without air valves, you can read their results here. If the coffee roaster that you normally purchase coffee from insists on using air-valves, why not write to them to request that they reconsider their packaging or try a more environmentally conscious roasting company to see how their coffee compares?
  • Coffee packaging – What type of material did the last bag of coffee that you purchased come in? Chances are it was metallised plastic, why not find a roaster with alternative packaging? Who knows, you may find another great coffee roaster to add to the ones that you buy from.
  • Straws – why would you use these anyway?
  • Milk bottles – Some companies still supply milk in glass bottles, otherwise you could consider non-dairy milks that can be home-made such as oat or almond. Some cafés also offer home-made non-dairy milks which would be a way of going plastic free while enjoying a latte in a café.
  • Cakes/sandwiches packaging – in larger chains these may come in packaging. However, if they are coming in packaging then they are not likely to be that fresh, find somewhere else with better cakes or sandwiches or make your own!
  • Spoons/cutlery
  • Packaging for sugar etc – ditching the sugar is supposed to be good for you anyway. If you cannot resist sweetening your coffee, try to find a sugar that is packaged in paper rather than plastic.
  • Washing up liquid – switching to a re-fillable washing up liquid reduces (but does not eliminate entirely) plastic waste.

Good luck if you take the challenge. There are still a few days left to plan how you can reduce the plastic in your life before the start of Plastic Free July 2017. Please do let me know how your attempts to be plastic free go and whether you find, as I did last year, that you enjoy your tea (or even coffee) more when you do so.



Reading tea leaves with Einstein and my great-grandmother

tea pot science

It’s not just tea, Einstein is famous for some other physics too

Ask anyone what Albert Einstein is famous for and you’ll probably (hopefully) hear that he came up with the theory of relativity (special and general). Perhaps you may also be told that he came up with a little theory explaining the photoelectric effect for which he won the Nobel prize in 1921. Maybe, if you have read this website before, you will know that he contributed to our understanding of Brownian motion, which is a phenomenon that is frequently found in a coffee cup. But it turns out that Einstein wrote another paper, far more important than any of these others, which was about tea. Or at least, I suspect my great-grandmother would have found it more important than any of these others as it coincided with a special hobby of hers, reading tea leaves.

It seems that my great-grandmother used to enjoy reading tea-leaves. Whether it was something she had learned as a child or merely used as an interesting trick to perform at family functions, stories of her examining the patterns formed by swirling tea leaves in a cup have come down to us in younger generations. Einstein too had noticed the patterns formed by the tea leaves in the cup and had observed a problem. The problem is this: If you drink a cup of (inadequately filtered) loose leaf tea and stir it, the tea leaves collect in a circle in the middle of the base of the cup. At first this may appear counterintuitive. When we stir things, don’t things fly outwards towards the edge of the cup rather than inwards to the centre of the circle? Why is it that the leaves collect in the middle?

Thames, NASA image

How do rivers erode? What causes a river to meander? The meandering Thames, photographed by NASA, Image courtesy NASA/GSFC/MITI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team

For Einstein, this tea leaf problem was connected to another phenomenon, the erosion of rivers. But it turns out that the problem is also linked to issues found in beer brewing and blood tests, and it seems, in how to poach an egg. To see the solution and therefore the connections, we need to think a bit more about how water flows. One of the brilliant lines in Einstein’s paper starts “I begin with a little experiment which anybody can easily repeat.” This experiment is to obtain a flat bottomed cup of tea with some tea leaves at the bottom of it. Now stir the tea and watch how the leaves settle, Einstein continues “the leaves will soon collect in the centre of the bottom of the cup“.

The explanation is connected with the fact that at the walls of the cup, the liquid (tea) is being slowed down by the friction between the walls and the tea. Secondly, as the tea is stirred, the surface of the tea becomes concave with a distinct dip in the centre of the swirling tea. The result of all this is that a secondary rotation is set-up where the tea flows down the sides of the cup, along the bottom and then back up in the centre and once more to the sides (have a look at the diagram, some things are easier with pictures). As they are carried along with the water, the tea leaves move towards the centre of the cup but then, being too heavy to rise again with the tea up to the centre of the cup, they stay on the bottom forming a circular patch of tea leaves.

adaptation from Einsteins paper

The secondary circular flow set up in a tea cup when it is stirred leads to a circular deposition of tea leaves (figure adapted from Einstein’s 1926 paper).

When you think about how water flows as it goes around a bend in a river, you could perhaps imagine a similar secondary flow being set up but this time from the inner edge of the bend to the outer edge and back down (so, like half a tea cup). As the water is going to be moving fastest at the outer edge, just before it plunges down towards the bottom of the river in this secondary cycle, any river erosion is going to be most noticeable on the outer edge of the bend.

It seems the effect is also used in beer brewing in order to introduce a greater concentration of hops into the brew, and to separate different types of blood cell in blood tests. So this just leaves the poached eggs. How do you poach eggs? If you have a proper poacher perhaps you get neat eggs each time but for those of us without them, poached eggs tend to be a messy cooking project. But worry no longer! Just as tea leaves collect in the centre of a tea cup, so will the egg if you ensure that your pan of boiling water is swirling around the central axis before you put your egg in. Cooking helped by physics, perfect.

For reasons of full disclosure, I should emphasise that I have only recently found this suggestion for cooking eggs ‘theoretically’ and not yet tested it. So, if you were looking for reasons to drink loose tea, or wanted to poach an egg without a poacher, perhaps you could try Einstein’s little experiment and let me know how you got on, I’d love to hear your tea leaf readings and see your poached egg results.




Reflections on physics and coffee

BeanThinking started as a way of slowing down and appreciating connections, often between a coffee and the physics of the wider world but also in terms of what can be noticed in any café. Perhaps, for this first post of 2017, it’s worth spending five minutes looking at your coffee while you drink it to see what you notice. Here are a few coffee connections that occurred to me recently:

reflections, surface tension

Reflections on a coffee.

Parallel lines and surface reflection: The parallel lines on the ceiling of a café were reflected in a long black. Surface tension effects on the coffee meant that the reflections were curved and not at all parallel. A piece of dust on the surface of the coffee was revealed in the reflection by the curved reflections of the ceiling. Astronomers can use similar effects (where images of a star appear in a different location to that expected) to infer the presence of dark objects between distant stars and their telescope. This gravitational lensing can be used to detect quasars or clusters of galaxies.




layering of coffee long black

Layers of coffee

Layering of crema as the coffee is consumed: The coffee stain effect and this layering of the crema suggests a connection between a coffee cup and geology. It used to be my habit to take a mug of tea with me when I taught small groups of undergraduates. In the course of one of these tutorials, a student (who had been observing similar layering in my tea mug) said, “You drink your tea faster when it is cooler than when it is hot”. Full marks for observation, but not sure what it said about his attention during my tutorials! Similar observations though can help geologists estimate the age of different fossils.


interference patterns on coffee

Bubbles in coffee

Bubble reflections: An old one but the interference patterns caused by bubbles on the surface of the coffee are full of fascinating physics. The fact that the bubbles are at the side of the cup and seem to be grouped into clusters of bubbles may also be connected with surface tension effects (although there is a piece of weather lore that connects the position of the bubbles to the weather. If anyone ever does any experiments to investigate this particular lore, I’d love to hear about them).



Coffee, Van Gogh

Art in a coffee cup

Van Gogh’s Starry Night: The effects of vortices and turbulence caused the crema of a black coffee to swirl into patterns reminiscent of this famous painting by Van Gogh. As a result of posting this image on Twitter, @imthursty sent me a link to this preprint of a paper submitted to the arxiv: the connections between Van Gogh’s work and turbulence. A great piece of coffee combining with art and science.


So many connections can be made between tea, coffee and science and the wider world, I’d love to see the connections that other people make. So, if you see some interesting physics, science or connections in your coffee cup, why not email me, or contact me via FB or Twitter.


An easy way to get a halo

The other day I was talking to a primary school child about condensation, what it was, where to see it etc. So I asked,

“Do you drink coffee?”


“Do you drink tea?”


(I started to worry about the future generations). Nonetheless, I pulled out my cup of steaming coffee and pointed to the water droplets around the edge of the mug (which are very common if you haven’t warmed your cup before pouring your hot coffee into it) and noticed a sudden expression of recognition cross the child’s face.

“Like when you breathe on a mirror?”

Kettle drum at Amoret

Condensation on around the top of the jug on this V60

Yes, exactly so (and probably a much better example for a kid anyway, the problem of being an adult with a one track mind!). As the child had realised, the science in your coffee cup is connected to phenomena that occur elsewhere in the world. In the case of condensation, it occurs when the temperature of the surface onto which condensation happens is below what is called the “dew point”. Determined by the relative humidity in the environment, the dew point is the temperature below which water vapour in the air will condense into liquid water.

Of course the dew point gets its name from the dew that can form after a chilly night. Which brings us to another property of those water droplets that form around the rim of your coffee mug. Although it is not easy to see on the mug, each droplet is acting as a lens, focussing the light that falls onto it. As the surface of the mug is fairly flat, rather than form spherical droplets, the drops that form on the side of the mug are squashed hemispheres. This is not the case when dew forms on grass. Tiny hairs on the surface of the grass protrude from the leaf meaning that the water droplets form into spheres (which is, incidentally very similar to the reason that a duck is so waterproof). When the sun comes up, each sphere of water focusses the sunlight onto the grass behind it which reflects it back, right in the direction it came from.

heiligenschein, self portrait

Self-portrait with weak heiligenschein. Share your photos with me on FB or Twitter.

This means that if you stand with your back to the sun and look at your shadow on dew covered grass, you will very probably see a region of bright light surrounding your head, your heiligenschein. German for “Holy light”, heiligenschein is the effect of all of those spherical dew lenses reflecting the sunlight back towards you. You can only see the effect around your ‘anti-solar’ point (a position defined as being 180º from the Sun from the viewpoint of the observer, see here for what this means visually). This means that while you will see heilgenschein around your head, or around the shadow of the camera that you use to photograph it, you will never see the halo around someone else’s head even while they themselves can clearly see it.

I’m sure there’s some sort of metaphor there, perhaps one to contemplate next time you’re drinking a hot, steaming coffee.


Coffee: The mathematical and the beautiful

Last week, a new study was published that explored the mathematics behind brewing the perfect filter coffee.  The research, summarised here, modelled the brewing process as being composed of a quick, surface extraction from the coffee grounds, coupled with a slower brew, where the water was able to get into the interior of the coffee grind. It was an interesting study and the authors are now looking at grind shape and the effect of how you wet the grounds. However, what struck me was that the authors mentioned scanning electron microscopy (SEM) images of ground coffee. A lovely idea, what does coffee look like when magnified hundreds (or thousands) of times?

So here are a few images that I found shared under Creative Commons Licenses. I hope you find them as fascinating as I do.

1) A green coffee bean:

Green coffee bean under the microscope

A green coffee bean. Sadly no details as to magnification. Image shared under CC license from Nestle, Flickr

2) Instant Coffee

Instant coffee from Nestle

Spray dried instant coffee from the Nestle, Flickr account. Image shared under CC license.

3) Roast and ground coffee (fluorescence microscopy image)

ground coffee, fluorescence image

Ever wondered what your coffee looked like when magnified many times? This image using fluorescence microscopy is of roasted coffee. Note the similarities between this image and the following one (which has a scale bar).  Image shared under CC license from Nestle, Flickr

3b) More ground, roasted coffee, this time from Zeiss

Zeiss roast coffee

Scanning electron microscope image of roast (and ground) coffee magnified 750x. Image from Zeiss, Flickr, Todd Simpson, UWO Nanofabrication Facility. Shared under CC license. (To put the scale bar in perspective, it is the size of the smallest particles in an espresso grind. Clearly, the grind here is quite coarse).

4) Finally, an image of tea, just to keep this article tea-coffee balanced:

Green tea under the microscope

Green tea as seen under the microscope by the scientists at Nestle. Shared under CC license Nestle, Flickr.

If you come across any great images of coffee (or tea) under the microscope, please do share them. In the meanwhile, enjoy your coffee however you brew it.

A cup of tea for a light bulb moment at Ginger and White, Hampstead

Coffee, Ginger and White, Hampstead

Coffee at Ginger and White, Hampstead

It was late afternoon by the time we stopped by Ginger and White in Hampstead. The warm weather meant that we could enjoy time spent sitting outdoors in the little alleyway in front of the café. We had been taking a friend around the various sights (and foodie places) of London and so stopped here before heading back home. The long black, cortado and soya latte were all very well done and, while the others had enjoyed a crepe at La Creperie de Hampstead just around the corner, I took the opportunity to try the excellent banana bread on offer at Ginger and White. There was a fairly good selection of cakes on offer, but sadly those that the staff could confidently affirm were nut free were far fewer. However, the moist and tasty banana bread was a good option anyway. Coffee was roasted by Square Mile and there were also Square Mile beans available for purchase should you wish to take some home with you. While the café was fairly busy, it was nevertheless a relaxing place to sit and watch the people of Hampstead go by.

The interior of Ginger and Whites

Everything is connected. From the lights to your cup of tea.

As I was looking around, wondering what the physics part of this cafe-physics review would be, I had what you could call a “light-bulb moment”. The walls of the building opposite were reflected in the windows of the café but looking inside, I noticed the lights which appeared to be LED lightbulbs set-back into the ceiling. Along with requiring less energy to power than conventional or halogen lightbulbs, LED lightbulbs in a café offer another, more poetic advantage for the café: they have a connection to the drinks being served and particularly tea. It’s all about diffusion.

At the heart of an LED light, there are two materials that form a junction. On one side of the junction is a semiconductor material that conducts electricity by means of electrons. Electrons conduct electricity in metals and are the ‘normal’ way that we consider electrical current to  be carried. On the other side of the junction is a different semiconductor, one that still conducts electricity but this time does so with carriers called ‘holes’. You can view the electrons as having a negative charge and the holes as having a positive charge.

tea bag, tea cup, diffusion, turbulence

What happens when you put a tea bag into a cup of cold water. How long until the water becomes ‘tea’?

But what happens at the junction? Is there really a sharp barrier between these two types of material? Think about putting a tea bag in a cup of cold water, does the tea bag just sit there or does it slowly, very slowly, start to diffuse tea into the cold water? It is a similar thing for the two materials. Slowly the electrons diffuse into the hole material and the holes into the electron material. In fact, mathematically, the same equations describe the process in the junction as in the tea cup. But unlike tea, in the LED, the holes and electrons have an electric charge associated with them and so, as they diffuse away from the junction, they set up an electric field across the junction. It is this electric field that eventually stops any further diffusion of electrons or holes across the junction and sets up the conditions necessary for LEDs to emit light. It would be like having a tea bag that diffuses tea into the cup until it is perfectly brewed and no further.

Of course, there is much more than this to understanding LEDs. If you’re interested, there is further information here. I find it fascinating however that what happens in your tea cup, is also happening on many different scales in many places in the universe. And of course, in the lighting of cafés and coffee houses around the world.

Ginger and Whites is at 4a-5a Perrins Court, NW3 1QS


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.