Home experiments

Noticing at Artisan, Ealing

coffee Artisan Ealing

A good coffee is a solid foundation for any afternoon’s noticing.

A cafe-physics review with a difference. In that, it’s not so much a review as an invitation. What do you notice in a café?

Last week, I had the opportunity to try Artisan’s Ealing branch. Although I had found a lot to notice on my previous visit to the East Sheen branch, I had a very specific reason for visiting the Ealing location of this small chain of four cafés. The coffee (espresso) was reliably good. Smooth and drinkable in a friendly atmosphere. Just as with the café in East Sheen, there were a good selection of edibles at the counter and plenty to notice. The light shades were immediately outstanding as something to notice while a framed ‘hole in the wall’ provided a conversation point. The café was very busy and while there was plenty of seating with many tables, we were still lucky to have got a table for two near the back. Behind us there was a lesson going on in the coffee school while on the wall was the calendar for the space booking downstairs. And it was this that I had come here for.

A couple of months ago, Artisan announced that this space would be available to rent to provide a friendly space (with coffee) for the meetings of local small businesses or charities. This stayed in the back of my mind for a while as it came about at roughly the same time as an idea for Bean Thinking.

Lampshades at Artisan Ealing

First the obvious. Immediately striking, these lampshades could provide several avenues for thought.

There are a couple of us who are interested in meeting, about once a month, to discuss science. As ‘science’ is quite a big subject, we thought we would limit it to science that is associated with coffee or with the café at which we are meeting. Perhaps readers of this website may realise that this is not such a restriction, it is quite easy to connect coffee to the cosmic microwave background radiation of the Universe or to chromatography and analytical chemistry. If we were to meet in a location such as Artisan, there should be plenty more food for thoughts. The lampshades prompted me to consider what made substances opaque or transparent? Where is the link to coffee and methods for measuring the coffee extraction? The hole in the wall suggested thoughts about the algorithms behind cash machines. I’m sure that there is plenty more to notice if we take the time to see it.

And so this is an invitation. Would you like to join us in exploring what we each notice about the science of our surroundings? The plan would be to meet once a month, probably starting late January 2019 or early February (date and location to be confirmed). An afternoon on the weekend is probably better than an evening and we’d probably stay for an hour or two. You do not have to be a practising scientist to come along indeed, it would be great if we could have people from a variety of walks of life. The idea is not (necessarily) to answer scientific questions that we each may have but instead to explore the science behind the questions, to find the connections that form our ideas of the universe. To really notice our surroundings and our coffees (tea drinkers would also be welcome). As a consequence of this, mobile phones/laptops etc. will be discouraged during the afternoon. We’d like to notice things around us and not be distracted by what a search engine suggests about it; if we think a search engine could help us, we’ll use it after we’ve left and come back the following month to discuss the issues further. So, if you are curious, would like to explore what you notice and can tolerate keeping your phone on silent and in your pocket for an afternoon, please do come along, it would be great to meet some of you.

menus and lampshades in Artisan

You may like to look more closely at this photo. How are the menus supported? What does that tell us about the history of science?

In order to understand whether there would be any interest in this idea and to hear your input about the format, content, location, time etc. I have set up a mailing list for these cafe-science-spaces. Please do sign up to the mailing list to hear the latest announcements concerning these events and also to email me back to contribute your opinion. You can sign up to the mailing list using the sign up form below. Alternatively, if you don’t want to sign up to the mailing list but do want to hear more, I will be advertising the events on Twitter and Facebook so please do feel free to follow me there.

 

Please enter your email address here if you would like to hear about future Bean Thinking events.

 

21 years of the coffee stain

dried coffee stains, alcohol and coffee

Happy 21st birthday to the coffee stain. But there is still much for us to learn 21 years after the first paper on the coffee stain was published.

On the 23rd October, 1997, a paper was published in the journal Nature titled “Capillary flow as the cause of ring stains from dried liquid drops.” The title is in the dry style that scientific papers can be written. An alternative title could have been “How coffee stains form”*. Perhaps you would think, surely someone had known how coffee stains formed before 1997? And maybe you would go on to think: certainly 21 years later in 2018, we’d know all there was to know about the coffee stain? I hope that readers of Bean Thinking would not think “who cares about coffee stains?”, but I wonder whether it was the combination of disinterest and assuming that someone somewhere surely knew how they formed that meant it took until 1997 for anyone to ask the question: well how do they form?

Coffee is a very popular drink among scientists, though even this does not explain how popular this paper has become. A paper’s popularity can be measured in ‘number of citations’ which tells you how many times other authors have found this piece of work important enough to reference it in their own published paper. As of early November 2018, this paper has been cited nearly 3300 times. Why? Well, there seem to be at least two reasons. Firstly, it turns out that the coffee stain effect is of enormous technological relevance; it may even have been used in the manufacture of the device you are using to read this website. But secondly even now, 21 years later, we still don’t understand what is going on, there is still much to learn and some of it is some very subtle and very beautiful physics.

the droplets ready to dry

What happens when you form coffee stains using drops containing two liquids (alcohol and water) compared to just one (water)?

Very recently for example, a new paper was published in Physical Review Letters. This one was titled “Density-driven flows in evaporating binary liquid droplets“. Another exciting title, another time we’ll retitle it for the purposes of this post: “what happens when you mix alcohol with a coffee type suspension, dry it at different angles and film it drying.” Arguably this time the given title is more succinct. Why does it make a difference if you add alcohol to your coffee rather than just drink it straight (the coffee, not the alcohol)? And what happens to the resulting coffee stain?

Maybe of an evening you’ve been relaxing with a glass of wine, or something stronger, and noticed the “legs” rising up the glass. Their formation and appearance is due to the differing surface tensions between alcohol and water and the fact that alcohol evaporates more easily than water, you can read more about that effect here. The point is that because of the difference in surface tension between alcohol and water, you get a flow of liquid from areas of low surface tension (higher alcohol content) to high surface tension (high water content). And it was this that had been thought to drive coffee stain formation in droplets which were a mix of liquids, water and alcohol for example. But how do you isolate this effect from the other effect in which alcohol evaporates more quickly than water and so there are changes in density and buoyancy of the droplet?

pendulant droplets

Drying droplets upside down. The things we do for coffee science.

To answer this you could add n-butanol to the water (or coffee) rather than alcohol. Just like ethanol based alcohol (the sort you may get in gin), n-butanol has a much lower surface tension and lower density than water but unlike alcohol, it evaporates much less readily than water. So, in a water-butanol mix it will be the water that goes first, while exactly the opposite will happen for an alcohol-water mix. In a drying droplet, the liquid evaporates most quickly from the edge of the drop. Therefore, after an initial, chaotic stage (imaginatively called stage I), you will end up with a droplet that is water rich around its rim in the alcohol-water mix but n-butanol rich around the droplet edge in an n-butanol-water mix (stage II). This suggests a way that you can distinguish the flows in the drop due to surface tension effects from those due to the differences in density between water and alcohol/n-butanol.

How would you test it? One way would be to compare the droplets evaporating as if you had spilled them on the table top with droplets evaporating ‘upside-down’, as if you had tipped the table by 180° after spilling your coffee. You can then watch the flow by taking many photographs with a camera. In this way you would be able to test whether it was surface tension flow (which should be in the same direction within the drop whether the droplet is upright or suspended) with gravity driven flow which should be opposite (the drop is upside down after all).

schematic drops upright and upside down

A cartoon of the flow found in droplets of alcohol and water mix. When upright, the flow is up through the centre of the drop and down the sides. This is expected for both surface tension based flows and flows due to gravity. When upside down, the flow is still upwards through the centre of the drop but this time the drop is upside down. So this is what you’d expect if the dense water at the edge of the drop flowed downwards (gravity based) but not if the flow were dominated by surface tension effects which should be the same, relative to the drop-interface as if the drop were upright.

The authors of the study did this and found that the flow in upright drops of alcohol-water was opposite to that in n-butanol-water drops. This is what is expected both in surface tension dominated flow and in gravity dominated flow. But, when the drops were inverted, the flow within the droplet did not change absolute direction, instead it changed direction relative to the substrate (it may be helpful to see the cartoon), in both droplet types. Expected for a gravity driven flow (dense liquids move downwards), this is exactly the opposite to what would be expected with surface tension driven flow. It is sensible to conclude that the flow in drying droplets containing two liquid types is dominated by gravity, or as the authors phrased it “density-driven flows in evaporating binary liquid droplets”.

dried upside down drops

The resultant coffee stains of drops that had been suspended upside down. They seem fairly similar to the upright ones with the exception of the central dot in many of the stains. The arrow shows some coffee that spilled down the surface as the tray was flipped over.

While the authors did a lovely job of watching the flows within the droplet, what happened to the the actual coffee stain? It could prompt us to do an experiment at home. How does adding alcohol affect the appearance of a coffee stain if the drop is upright compared to if you turned the drops all upside down? What happens if the droplet is not held upside down but instead at an angle to the vertical? There are many ways you could play with this result, see what happens, have a glass of wine and see if that gives you any insight into what you see with your coffee. As ever, have fun and if you do get any interesting results, please do let me know here, on twitter or over on FB.

 

*The dry scientific author in me wants to point out that although catchier, the title “how coffee stains form” does not actually capture the extent of the physics nor what the paper was about (the fact that this happens more often than just in coffee) and the given title was much better. The coffee drinker in me thinks yes, but, surely we could make it all about coffee anyway…

Air raising

Small waves seen from Lindisfarne

How do clouds form? How does temperature vary with altitude, and what does coffee have to do with any of it?

You put a drop of alcohol on your hand and feel your hand get cooler as the alcohol evaporates, but what has this to do with coffee, climate and physics?

Erasmus Darwin (1731-1802) was the grandfather of Charles of “Origin of the Species” fame. As a member of the Lunar Society (so-called because the members used to meet on evenings on which there was a full moon so that they could continue their discussions into the night and still see their way home) he would conduct all sorts of scientific experiments and propose various imaginative inventions. Other members of the Lunar Society included Matthew Boulton, Josiah Wedgwood and Joseph Priestley. The society was a great example of what can happen when a group of people who are interested in how things work get together and investigate things, partly just for the sake of it.

One of the things that Darwin had noticed was that when ether* evaporates from your hand, it cools it down, just as alcohol does. Darwin considered that in order to evaporate, the ether (or alcohol or even water) needed the heat that was provided by his hand, hence his hand started to feel cooler. But then he considered the corollary, if water (ether or alcohol) were to condense, would it not give off heat? He started to form an explanation of how clouds form: As moist air rises, it cools and expands until the moisture in the air starts to condense into droplets, clouds.

hole in water alcohol

There are several cool things you can notice with evaporating alcohol. Here a hole has been created in a thin layer of coffee by evaporating some gin. You can see the video of the effect here.

As with many such ideas, we can do a ‘back of the envelope’ calculation to see if Darwin could be correct, which is where we could also bring in coffee. The arabica growing regions are in the “bean belt” between 25 °N and 30 °S. In the sub-tropical region of that belt, between about 16-24°, the arabica is best grown at an altitude between 550-1100 m (1800-3600 ft). In the more equatorial regions (< 10º), the arabica is grown between 1100-1920m (3600-6300 ft). It makes sense that in the hotter, equatorial regions, the arabica needs to be grown at higher altitude so that the air is cooler, but can we calculate how much cooler it should be and then compare to how much cooler it is?

We do this by assuming that we can define a parcel of air that we will allow to rise (in our rough calculation of what is going on)¹. We assume that the parcel stays intact as it rises but that its temperature and pressure can vary as they would for an ideal gas. Assuming that the air parcel does not encounter friction as it rises (so we have a reversible process), what we are left with is that the rate of change of temperature with height (dT/dz) is given by the ratio of the gravitational acceleration (g) to the specific heat of the air at constant pressure (Cp) or, to express it mathematically:

dT/dz = -g/Cp = Γa

Γa is known as the adiabatic lapse rate and because it only depends on the gravitational acceleration and the specific heat of the gas at constant pressure (which we know/can measure), we can calculate it exactly. For dry air, the rate of change of temperature with height for an air parcel is -9.8 Kelvin/Km.

contrail, sunset

Contrails are caused by condensing water droplets behind aeroplanes.

So, a difference in mountain height of 1000 m would lead to a temperature drop of 9.8 ºC. Does this explain why coffee grows in the hills of Mexico at around 1000 m but the mountains of Columbia at around 1900 m? Not really. If you take the mountains of Columbia as an example, the average temperature at 1000 m is about 24ºC all year, but climb to 2000 m and the temperature only drops to 17-22ºC. How can we reconcile this with our calculation?

Firstly of course we have not considered microclimate and the heating effects of the sides or plateaus of the mountains together with the local weather patterns that will form in different regions of the world. But we have also missed something slightly more fundamental in our calculation, and something that will take us back to Erasmus Darwin: the air is not dry.

Specific heat is the amount of energy that is required to increase the temperature of a substance by one degree. Dry air has a different specific heat to that of air containing water vapour and so the adiabatic lapse rate (g/Cp) will be different. Additionally however we have Erasmus Darwin’s deduction from his ether: water vapour that condenses into water droplets will release heat. Condensing water vapour out of moist air will therefore affect the adiabatic lapse rate and, because there are now droplets of water in our air parcel, there will be clouds. When we calculate the temperature variation with height for water-saturated air, it is as low as 0.5 ºC/100 m (or 5 K/Km), more in keeping with the variations that we observe in the coffee growing regions†.

We have gone from having our head in the clouds and arrived back at our observations of evaporating liquids. It is fascinating what Erasmus Darwin was able to deduce about the way the world worked from what he noticed in his every-day life. Ideas that he could then either calculate, or experiment with to test. We have very varied lives and very varied approaches to coffee brewing. What will you notice? What will you deduce? How can you test it?

 

*ether could refer to a number of chemicals but given that Erasmus Darwin was a medical doctor, is it possible that the ether he refers to was the ether that is used as an anaesthetic?

†Though actually we still haven’t accounted for microclimate/weather patterns and so it is still very much a ‘rough’ calculation. The calculation would be far better tested by using weather balloons etc. as indeed it has been.

¹The calculation can be found in “Introduction to Atmospheric Physics”, David Andrews, Cambridge University Press

 

 

Exploring the sound of coffee

coffee at Watch House

We’re used to thinking about the aroma of coffee and how it looks, tastes, even how it feels, but what about how it sounds?

How much attention do you pay to your brewing coffee? You know the aroma, how the coffee blooms, you anticipate the taste and feel the warmth of the steam rising off the brew. But what about the sound? Admittedly this depends on your brew method, but what about the sounds as you filled the kettle or prepared a pour over brew? It turns out that the sound of dripping water was the subject of a recent paper in Scientific Reports.

Perhaps take time to watch a tap dripping into a bowl of water. Or maybe use this as an excuse to make another coffee by drip brewing. Each drop falling onto the water (or coffee) below first deforms the water’s surface then, as far as we can see, rebounds up with a splash of a returning drop or droplets. The phenomenon of what causes the characteristic sound of the drip has been investigated for over 100 years but in 1959 it was established using high speed photography that there were four key phases to any drip sound. First, the drop fell on the liquid, then a cavity formed just under the water surface and an air bubble formed just under that. Finally the water surface recoiled leading to a jet of droplets returning from the surface. It has been thought that the sound, that ‘plink’ of the dripping tap, was caused by that trapped air bubble expanding and contracting as it moved through the water under the water’s surface¹. But this has now been confirmed, along with some other interesting, coffee related, observations using ultrafast video recording (30 000 fps for most of the work, 75 000 fps for some of the extra details).

lilies on water, rain on a pond, droplets

Like the sound of falling rain? What causes the dripping sound of a tap?

The authors of this recent paper describe what must have been a fun experiment to do, dripping water into a tank below. You can see some of the videos of the droplet entering the water by scrolling down to the “supplementary information” in the paper. Two microphones (one above, one below the water surface) recorded the sound waves coming from the dripping ‘tap’ simultaneously with the video recording so as to match the timing of the sound with what was happening in the video. The microphone above the water surface largely recorded the same sound waveform as the microphone under the water with one crucial exception. When the authors lined the tank with MDF wood, the underwater sound was ‘damped’ quite quickly, in comparison the bare tank amplified the sound and so the sound wave took much longer to decay. Above the surface however, it didn’t matter whether the tank was lined or not, the sound signal remained the same. This may sound somewhat insignificant, but it means that it cannot be the sound created by the wobbly bubble itself merely propagating through the surface of the water. If this were the case, the microphone above the water surface should show the same signal as the microphone under the water’s surface. Instead the authors suggest that the oscillating bubble causes the surface of the water immediately above it to vibrate (in the bit that is depressed owing to the droplet having fallen into it) and it is this that we hear above the water surface.

science in a V60

Droplets on the surface of a brewing V60 may also form owing to a temperature difference between the dripping drops of coffee and the coffee ‘bath’ underneath.

It is a beautiful set of experiments but how can it link to coffee (apart from with the dripping)? It is in the way that it gives us the chance to experience our coffee with experiments involving more of our senses than just smell, touch and taste. Firstly, the study emphasises the connection between the drop’s diameter and speed to the sound of the drip (the best sounds are for drops between 1mm and 5mm diameter). This suggests that by changing the brewing parameters (whether you prepare your V60 in a jug or a mug or change the filter paper to a metal kone for example), you may hear a change in the sound of the drips. Do you? Secondly, it has been suggested that the sound that is formed is dependent on the temperature difference between the dripping drop and the water bath underneath. A temperature difference between drop and bath would also explain an odd phenomenon I noticed in the V60 a while back. Do you notice a difference in the sound of the brewing coffee when you prepare cold brew pour over as opposed to a standard breakfast brew? Lastly, the authors of this study found that they could suppress the sound of the plink by reducing the surface tension of the water bath that they were dripping water into. In their case they added washing up detergent to the bath. This seems an awful waste of coffee but is it possible that something intrinsic to our coffee brew could do the same thing? Oil will also change the effective surface tension of the water and different coffees (and different roast strengths) change the oil content of the brewed coffee. Have you noticed any change in the sound of the drips of the coffee depending on how dark a roast coffee you use?

It may not make ground-breaking science but it does offer us an opportunity to pay even more attention to our coffee. Does the sound of your coffee reveal the beauty of the physics at work just under its surface?

¹ Some history of the investigation into the dripping sound as well as the experiments can be found in: Phillips et al., “The sound produced by a dripping tap is driven by resonant oscillation of an entrapped air bubble”, Scientific Reports, 8, 9515 (2018)

Half way through…

talesfromthewormbin

What packaging does your coffee come in? Is it paper, compostable? The bits of packaging here are part of an experiment to see how long they will take to break down in a worm composting bin #talesfromthewormbin

The problem is oat milk. If you are having a go at living plastic free (or even reducing your reliance on single use plastic) during Plastic Free July, you have probably encountered at least one sticking point. Something that you are finding a little tricky to let go of. There are things that are too difficult to eliminate right now (meat/fish packaging is one example although there have been efforts to change this in some locations) but these are not necessarily sticking points. No, sticking points are things that seem that they should be easy to eliminate but for some reason are not. For me this is oat milk.

For the past three years, I have been participating in Plastic Free July with the aim of trying to find ways of living that reduce my plastic waste. And for the past three years, the problem has been oat milk. It is becoming a bit of a nemesis. Although proper, dairy based milk is available in glass bottles, this does not appear true for non-dairy based milks. Although some packaging can be recycled, it is a significant contributor to my waste pile. So, how about home made oat milk? It should be easy shouldn’t it?

oat milk, kone, filtering

Oat milk filtering through the Kone filter.

You can find plenty of recipes for oat milk online (a few are here, here and here) but I’ve always found it messy and, well, wasteful. The worms have enjoyed the oats in the past but surely there’s something better that can be done with them? Well, this year, things seem a bit different. And part of that is because of a coffee filter.

Years ago I tried the coffee Kone filter as an attempt to reduce my use of paper filters in the chemex. Sadly, I didn’t get on with the Kone. Unlike a paper filter, some sediment made it through the filter leading to more of an immersion type coffee drink rather than a filter. Consequently it went to the top of a cupboard and lay forgotten for a few years. Until this June when I re-discovered it as a filter for the oat milk. Rather than a muslin bag, the Kone can be cleaned easily and the whole process is significantly less messy (and slightly quicker – stirring the contents of the Kone with a spoon is easier encouragement to get the oat milk through than squeezing the muslin bag). Although there remains significant work before this can start to be a habit rather than just for a month, this July’s oat milk is a lot more promising than previous years. I’ll keep you updated as to whether the oat milk remains being home made in August.

pitch drop oat milk

Preparing your own dairy-free milk also offers new opportunities for watching physics such as the pitch-drop experiment here.

In the meantime, do let me know how you are getting on with your own Plastic Free July. Do you have any sticking points? On the other hand, are you finding that you are enjoying taking your re-usable cup around with you when you get a take-out coffee? Also, if you have any recipes for things that can be done with these left over blended oats. I’d love to hear of your culinary experiments.

In the following recipes, because I do not know how much oat milk you are making, I’ll call the amount of blended oats X g. In my experiments X has been either 115g or ~60g.

 

Oat and Apple Tarts

Xg blended oat left overs

Xg sugar

X/2 g flour

Pinch cinnamon and nutmeg to taste

teaspoon baking powder

Cooking apple (peeled and cut into smallish chunks)

 

Mix the blended oat left overs with the sugar and then stir in the flour, baking powder and spices. Spoon onto a greased baking sheet so that they make circular blobs of about 3cm diameter. Place the apple pieces into the mixture and bake at 180C for about 15 minutes until risen and slightly browned.

 

Sort of Flapjacks

X g blended oat left overs

X g sugar

X/2 g flour (but this isn’t really necessary).

Oat flakes, spelt flakes, sunflower seeds, pumpkin seeds, dried fruit, whatever you would like to put in a flapjack

Mix everything together, spoon into a lined and greased baking tin, bake at 190C for 15 minutes until firm. Keeps in an airtight container for days.

 

Hobnobby biscuits

home made oat biscuits

Not quite there yet. If you have a better recipe or can improve this one, please let me know.

A work in progress – the quantity of oats is not right yet and perhaps they need to be toasted oats or even spelt flakes.

X g blended oat left overs

X g sugar

X/2 g flour

teaspoon baking powder.

X-2X g oats

Mix the blended left overs, sugar, flour and baking powder together. Stir in the oats. Spoon on a lined and greased baking sheet so that you get ‘biscuit sized’ portions. Bake for 25 minutes at 190C or until brown.

 

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.

Tales from the worm bin

the cup before the worm bin

How it all began.
“Completely compostable”
But how compostable is it?

It is hard to believe but it was one year ago this week that the composting experiment that became #willitcompost started. The idea was to test just how “compostable” a coffee cup described as “completely compostable” really was. The problem is that “compostable” has a legal definition but it is not one that you or I may immediately recognise. Legally for a take-away coffee cup to be described as compostable it has to completely disappear within 6 months in an industrial composting facility. Industrial composting is quite different from home composting. In the former, the temperature is kept at (58±2)ºC while in my composting worm bin, it can get very cold indeed.

As has been written about elsewhere, in the absence of better industrial composting facilities, there is very little virtue involved by swapping a disposable cup for a compostable one, to combat the problem of waste it would be far better to remember your re-usable. However, what if you had a composting bin at home? How long would it take the cup to compost? And even, would it compost?

So every week for the past 52 weeks, I have posted a photo of the cup, composting away, in the worm bin. It seems clear that although it will eventually compost, more than 52 weeks is a long time to wait and not practical if you are drinking multiple take-away coffees.

willitcompost

51 weeks later, the lining and part of the rim of the cup are still in the worm bin. Clearly the worms have better things to eat.

In the meanwhile, other questions have been raised. What about other coffee packaging such as the bags for roasted coffee beans? What about the compostable “glasses”? Can anything be done to speed up the composting of the cup?

Last month, the opportunity came to start a new experiment testing these questions. A compostable coffee roasting bag from Amoret Coffee (which was reviewed on Bean Thinking here) was placed in the second shelf of the worm bin together with a cup, a compostable “glass” and a section of food packaging. The cup and the ‘glass’ were cut in half before being placed in the worm bin. One half of each was left as it was but the other half was soaked in (initially boiling) water for 12 hours. The idea of this was that part of the problem that has slowed the composting of the original cup was the lining that is designed to hold hot liquids without leaking. If we could somehow weaken that lining before placing it in the worm bin, perhaps the composting process would be accelerated?

talesfromthewormbin

A roasted coffee bag, a cup (split in two, see main text), a compostable glass and some food packaging, but will they compost?

Starting in late March provides the best chance of a quick composting process due to a particular aspect of worm behaviour. Although the composting worms will continue to eat the waste put into the composting bin throughout the winter, they do slow down quite a lot. If you have a worm bin, you may notice that the amount of waste that you can put into the bin decreases during the winter months. On the other hand, as the weather improves, the worms seem to eat everything very quickly so, to provide the best conditions for composting, the weather has to be reliably warm (or at least, not freezing).

Rather than once a week, updates will be approximately once per month both on social media and in the Bean Thinking newsletter. So keep your eyes on #talesfromthewormbin on twitter or subscribe to the newsletter. Do we really take our environmental responsibility seriously by using compostable packaging or, ultimately, is a more radical approach to waste, single use packaging and consumerism necessary?

A tense moment for a coffee…

capillary bridge

A bridge formed by water between a cup and a cafetière.

Each and every coffee represents an opportunity to uncover an unusual bit of science. Sometimes the connections between what happens in your cup and the wider world are fairly obvious (e.g. the steam above your coffee and cloud formation), but sometimes the connections seem a little more obscure. On occasion, your observations may lead to philosophical speculations or stories from history. Every coffee is an opportunity to discover something, if you just slow down and ponder enough.

It was with this in mind that I looked at my freshly made French Press coffee a few weeks ago. I had positioned my cup very close to the cafetière such that a small water bridge had formed between the cup and the cafetière (see photo). Such “capillary bridges” have been studied for a couple of centuries and yet there is still more work to do. Caused by the surface tension of the water, understanding the way these bridges form and the shape of the surfaces produced is important for fields such as printing and powder processing. Yet it is only in the last 150 years or so that we have started to understand what surface tension is. Moreover, much of the pioneering work on this subject was done by an amateur scientist who just noticed things (and then designed some very clever experiments to discover more).

Agnes Pockels (1862-1935) is now regarded as a surface science pioneer but in 1891 she was a complete unknown. Although she had wanted to study physics, she was prevented from going to university because she was female. Consequently, all her study of the subject had to be through her brother Friedrich’s books and letters. It is not known what prompted her investigations but from 1880 she had been experimenting with a device to measure the surface tension of water. The device used a sliding weight to measure the force required to pull a 6mm diameter wooden disk off of the surface of a trough of water.¹ The design of this device was so successful that, a few years later, Irvine Langmuir adapted it slightly in order to study the surface of oils. He went on to receive the Nobel Prize for his work in 1932. Yet it is a device that could also be built in your kitchen, exactly as Agnes Pockels did².

reflections, surface tension

The effects of surface tension can be seen in the light reflected from a coffee

Pockels measured the surface tension of water contaminated by oil, alcohol, sugar, wax, soda crystals and salt (amongst other things)¹. She discovered how the surface tension of the water could be affected by pulling the surface or introducing metal objects onto it. She discovered the “compensating flows” that occurred between regions of different surface tension (you can see a similar effect with this soap boat). Yet all of this remained hidden from the wider world because Pockels was unable to publish. Not having access to the contemporary literature about surface tension and moreover unknown, unqualified and female, no journal would look at her work let alone publish it. Nonetheless, she was clearly a brilliant experimentalist and capable physicist.

Things changed when Pockels read a paper by John William Strutt (Lord Rayleigh) in about 1890. Rayleigh was quite the opposite of the unknown Pockels. As well as his work on sound, electricity and magnetism and the (co-) discovery of Argon, Rayleigh is known for his work on understanding why the sky is blue. (Which is another phenomenon that you can see while preparing your coffee if you drink your coffee with milk.) In his paper on surface tension, Rayleigh had come to similar conclusions as Pockels’ work but Pockels had gone further. Unable to publish herself, she instead wrote to Rayleigh, in German, detailing her experimental technique and results. Rayleigh responded by forwarding her letter to the scientific journal Nature together with an introductory paragraph:

“I shall be obliged if you can find space for the accompanying translation of an interesting letter which I have received from a German lady, who with very homely appliances has arrived at valuable results respecting the behaviour of contaminated water surfaces. The earlier part of Miss Pockels’ letter covers nearly the same ground as some of my own recent work, and in the main harmonizes with it. The later sections seem to me very suggestive, raising, if they do not fully answer, many important questions. I hope soon to find opportunity for repeating some of Miss Pockels’ experiments.”¹

Coffee Corona

You may have seen white mists form over the surface of your coffee (seen here by the rainbow effect around the light reflection). But what are they and how do they form? This is still not really known.

Rayleigh’s introduction and Agnes Pockels’ letter were published in Nature on 12 March 1891. The paper enabled Pockels to publish further results in both Science and Nature as well as in other journals. In 1932 she received an honorary doctorate in recognition of her work.

It seems that this coffee-science story has two main messages. The first is to emphasise how much we gain by ensuring everyone has access (and encouragement) to study physics (or indeed whatever subject they are motivated by). What would we have lost if Agnes Pockels had not had the books of her brother and made the decision to write to Rayleigh? But the second message is that Agnes Pockels managed all this, at least initially, by merely noticing what was going on in the liquids around her. Being curious she designed and built a piece of equipment that enabled her to measure what she was intrigued by and by taking a systematic series of data she discovered physics that was unknown to the wider community at the time. So the question is, what do you notice when you look at your coffee? How does it work, what can you discover?

Please do share any interesting physics that you see in (or around) your coffee either here in the comments section below, on Facebook or on Twitter. Tea comments would also be welcome, but whatever you do, slow down and notice it.

 

¹Rayleigh, Nature 1891, 43, 437-439, 12 March 1891 (full text here)

²Reference to the kitchen is here.

A lawyer, an accountant and and emperor walk into a cafe…

Strata, geology

This is not a resonance in a coffee cup but the concentric circle pattern is similar to a resonance that you could frequently see.

Have you ever noticed concentric rings on the surface of your coffee, forming as the table under the coffee cup vibrates slightly? Perhaps you have seen more complicated patterns. You may have observed, as you have played with your coffee, that some patterns are more stable than others. The one that is formed from concentric circles is fairly easy to form and to see. A more complex one looks like a chequer board, you may perhaps of seen others. These patterns are what are known as ‘resonances’ on the surface of the coffee and they are the consequence of standing waves being set up on the coffee surface. Many people who have gone through an undergraduate physics degree will immediately be reminded of Chladni figures and there is a good reason for this. Ernst Chladni (1756 – 1827) was a pioneer in investigating such resonances, one of the reasons that he has been described as “the father of experimental acoustics”.

And yet Chladni was not a physicist in the way that we now think of the term. In fact, by training he was a lawyer, a consequence of following his father’s rather insistent ‘advice’. Obediently, Chladni had trained in law and had started working as a lawyer in 1782 when his father died. Chladni appears to have taken this event as an opportunity to start to investigate the scientific problems that he was actually interested in and so re-invented himself as an acoustician testing the theories of music developed by people like Bernoulli and Euler¹.

transmission lines, electrical noise

Like strings on a guitar. Resonances on a string can be used to make musical notes.

Did Chladni drink coffee in eighteenth century coffee houses while admiring the resonances in the cup? Sadly what comes down to us in history is not his coffee habit but his experiments with sand covered metal plates secured onto wooden rods. Chladni caused resonances on these plates by rubbing them with a violin bow. By exciting resonances similar to those you can see on the surface of your coffee, Chladni was able to test theories about the sounds made by curved metal surfaces (e.g. bells). Indeed, these experiments became so important to understanding acoustic theory that Chladni started a European tour demonstrating his plates and their relevance to designing musical instruments. It was presumably through one of these tours that he met an Emperor of the time, Napoleon Bonaparte.

But despite this great experimental progress, the mathematics used to understand these resonance patterns, was developed by another physicist with a non-typical career path, Friedrich Bessel (1784-1846). Bessel had trained as an accountant but with the good fortune of timing, he had apprenticed into an exports company. At this time, such companies would have been interested in the problem of longitude and so Bessel gained an opportunity to indulge his interest in astronomy. As a consequence of this work, particularly his work on the orbit of Halley’s comet, Bessel secured a job in an astronomical observatory and it was there that he started the work that would eventually lead us to be able to describe, mathematically, the resonances on the surface of your coffee.

Did Bessel drink coffee? Had he seen Chladni demonstrate his plates? We don’t know the answer to those questions and in many ways it is not relevant because Bessel’s mathematics did not concern such resonances at all. Instead, almost to underline the idea that everything is connected, particularly with physics and coffee, Bessel was working on the problem of how to calculate the gravitational attraction between multiple objects.

Kettle drum at Amoret

The note made by a drum is a function of the size and shape (therefore resonance pattern) of the drum and also the gas filling the drum. Would this drum-table sound the same if banged on Venus as on Earth?

Perhaps you remember from school Newton’s famous description of the gravitational attraction between two bodies as being F = GMm/r² (where F is the force, G the gravitational constant, M and m the masses of the two bodies and r the distance between them). That’s all very good but what if there were three bodies, or four, or…

It was this problem that Bessel was working on and by so doing he solved the problem of Chladni’s patterns. The maths that describes the many body problem also describes the way that these resonances form. Those patterns in your coffee are described by the same maths as allows us to calculate complex gravitational problems.

And so perhaps it is not quite correct to title this post as a lawyer, an accountant and an emperor walk into a café, but it would be fair to say that each time you catch those resonances in your coffee cup, the  influence and interests of these investigators of nature are infused within the brew.

You can find a sketch of Chladni entertaining Bonaparte with his metal plates here.

¹Harmonius Triads, Physicists, musicians and instrument makers in nineteenth century Germany, MIT Press, 2006

 

Freezing point

coffee and ice in New Cross on a wooden table

Isn’t it a fact that water boils at 100C and freezes at 0C?

Water boils at 100ºC and the ice in your iced latte is at 0ºC. These are facts that we think we know about water: it boils at 100ºC and it melts at 0ºC. A sharp observer may point out that these are pressure dependent and that if we were at the top of a mountain, the water would boil at a slightly lower temperature (I once had a student argue that this was a good reason to only ever drink green tea at high altitude). But if we are at ground level and it is a normal day, we will be fairly certain that the water for our coffees would boil at 100ºC and ice would form at 0ºC.

Yet these ‘facts’ hide some complicated physics and some oddities about our planet. Pure water, that is, water without any impurities in a clean vessel (such as a clean, scratch free glass) does not boil at 100ºC but at temperatures significantly higher than that. Nor does pure water freeze at 0ºC but at temperatures significantly below that. These are phenomena known as superheating and supercooling respectively and, if you are observant, you could see them occasionally in your coffee cup. To see why, and how, we need to think a bit more about how water freezes.

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

If you put pure water into the freezer, you may find that it freezes at a temperature considerably lower than 0C

If you fill an ice cube tray with water and put it in your freezer, you would expect ice cubes to start forming at about 0ºC. We expect the freezing temperature to be the same as the melting temperature, that is the temperature at which the ice cubes would melt. And yet, if you make the water very pure (even distilled water would be a start) and put that in a clean, defect free container (such as a clean glass jar) in the freezer, the freezing process will not begin until much lower temperatures. It’s because the water has to crystallise and change state from a liquid to a solid and to start this process, there needs to be a seed, a surface on which the ice can form. Called a “nucleation site”, this seed could be a piece of dust, a small impurity in the water, a scratch on the surface of the container holding the water, or in fact anything that allows the bonds of ice to start to form. The same is true at the other end of the temperature scale. When the liquid water turns into steam, nucleation sites are needed so that the gas bubbles can start to form at those sites. In the absence of impurities in the water, the water will not boil until temperatures high above 100ºC.

Fortunately in tap water, or in your super-filtered water that you make your coffee with, there are plenty of such nucleation sites so the water boils and freezes at roughly the temperatures you’d expect them to. The same is not true however for clouds in the sky where some (high altitude) clouds have been shown to contain water droplets that are at -35ºC, well below the “freezing temperature”. Exactly why this occurs is still puzzling and a topic of research, but when you stop and think about it, how would you actually measure this temperature? If you supercooled a cup of water and then put a thermometer into it, the thermometer would provide a nucleation site and the water would immediately freeze. How can you measure the water’s temperature without a thermometer?

kettle, V60, spout, pourover, v60 preparation

You are unlikely to see superheating when you boil the water for your coffee in a kettle like this.

Recently a study reported in Physical Review Letters used a laser to measure the diameter of a series of supercooled liquid droplets by determining the energy of a resonance that depended on the droplet’s size. To calculate the temperature of the droplet, the authors then used the principle that as water evaporates, the droplet from which it is evaporating will become colder at the same time that it shrinks in size. Measuring the size of the droplet allowed them to calculate the evaporative loss and therefore the temperature of the drop. They double checked this new technique by measuring (with the same laser) the energy of a particular atomic bond in water that has a known temperature dependence (at higher temperatures). The temperature determined from the drop’s size corresponded with the extrapolation of the energy of this atomic bond and so the team were fairly confident that they had measured liquid water to very cold temperatures indeed. In fact, the authors suggested that it was still possible to have liquid water at 230.6±0.6 K which, in more every-day units corresponds to -42.55ºC, well below the nominal ‘freezing point’.

So pure, liquid, water can get very cold indeed. But could you ever see this in your coffee cup? Although you may like to try some experiments with freezing ultra-pure water, it is easier to see the phenomenon of superheating in your coffee. However, given the possibility of an accident, it may be safer to watch the effect on the video below. The idea is that if you put very pure water in a clean cup into a microwave, it is possible to superheat it well above 100ºC without it boiling, because there are no nucleation sites in the cup or the water on which the steam bubbles could start to form. When you take the cup out and put a nucleation site in (perhaps a spoon or maybe even instant coffee granules), the water will boil suddenly as a result of those new nucleation sites and can even explode. Obviously if you were anywhere near the water when this happened you could get seriously burnt and so it is probably safer to watch the Mythbusters do it with their robotic arm. Enjoy the video, enjoy your coffee, preferably far from superheated: