Filling a re-usable water bottle from the tap, the sound starts off as a low hum, then rises in pitch before a sudden change in note as the water spills over the spout because you have over-filled it. Texturing milk in a pitcher, the sounds change as the bubbles form and break, ready for pouring as latte art. How often do we know what is happening by listening to the sound something makes?
And yet these sounds are revealing more than just when the bottle is full or the milk can be poured. They are teaching us, if we listen carefully, about the physics of what is going on within the water bottle, within the milk pitcher and even within coffee grinds as we bloom the coffee. Consider the water bottle. It is a classic resonator, the basis of many musical instruments. As we fill the bottle, the liquid level acts as an end point to the bottle, reducing the volume of air in the bottle as the water fills it. The note that we hear coming out of the bottle corresponds to the frequency of the sound wave that is resonant in the empty volume of space. As the frequency is inversely proportional to the (square root) of this volume, when the volume decreases (ie. the bottle is filled) the frequency increases, so the note that we hear will go up. The bottle is acting as an approximation to a Helmholtz resonator. You can read about how this can be used for experiments with coke bottles here, or more of the physics (and the maths behind it) here.
Similarly with the milk pitcher, the changing musical note is telling us about the changing conditions within the pitcher, though in this case it gets quite complex. Firstly, as the steam wand is introduced to the pitcher, air is introduced to the milk which “stretches” it. This builds the volume of the milk in the pitcher and introduces air bubbles into the liquid. The combination of the volume change and the introduction of air is going to affect the sound that the jug would make, but the sound you hear, the ‘hiss’ is most probably dominated by the sound of the steam leaving the steam wand. After a short while, the barista will lower the steam wand further into the milk in order to heat the milk in the pitcher. Treating the pitcher again as an approximation of a Helmholtz resonator, we know that the frequency that we hear from the pitcher increases as the speed of sound inside the resonator increases. As the speed of sound in the milk increases with temperature (assuming that it is mostly made of water), to a first approximation we expect the note that we hear to increase in pitch with time. So after the hiss, we will hear a note which rises in pitch as we continue to warm the milk. Is this what we hear?
Together with other species, we use the information that sound gives us to understand much of the world around us. “Listening” famously helps bats to navigate and hunt and also, helps us to understand more about what occurs in the ocean. Indeed, it has even been suggested that we should listen to the sounds recorded as space probes land on different planets or moons in order to gain further information about what could be hidden just out of view of the camera. Of course, the sounds on another planet may not sound exactly as they do on Earth. Prof. Tim Leighton of the University of Southampton has calculated (and then synthesised) what a methane-fall (like a waterfall but of liquid methane) would sound like on the surface of Saturn’s moon Titan. You can hear the recorded waterfall on earth here, and the simulated methane fall on Titan here. Provided we know what we are listening for and to, better listening can improve our understanding of our surroundings.
An example of where better listening may improve our understanding of our surroundings comes with bread. One common way of knowing when bread is properly cooked is to tap its base and listen to when it sounds hollow. We can assume that this is because the bread crust acts as the walls of a resonator with the large number of air bubbles that form during cooking (and which make the structure of the crumb) being the bit where the sound wave resonates. The hollow sound shows that what is inside is solid, whereas if it were still dough-y, it would damp the resonance (no pun intended) and make it dull sounding. If this assumption is correct, the note that is made by tapping the bread will decrease as the bread cools and the speed of sound in the air in the bread decreases. But can we also get information about the crumb structure of our loaf by listening to the pitch of the loaf as we tap it? Would not the frequency of the resonance (ie. the sound) change depending on how open the bread structure is (a large, open loaf would perhaps have a lower ‘note’ than a loaf with a small crumb which may have a higher note). Is the bread ‘telling’ us more than just that it is cooked? Experimenting bakers, it’s over to you.
One of the great moments while brewing coffee happens as you add a small amount of hot water to the coffee grounds and an intense aroma rises towards you. Together with the sight of the bubbles of carbon dioxide escaping the just-ground coffee and the sounds as the grind expands, cracks and the bubbles pop, it is a multi-sensory experience.
It is also a very good point to stop what we are doing, and think for 30 seconds, or a minute. Which means also that it’s a perfect time to experiment with your coffee. Istobiii is inviting us all to an experiment to try what he is calling “cold bloom”. You can watch his invitation to the experiment here.
Does blooming your coffee with cold (or tepid) water produce better coffee? What would be the difference between blooming with colder water compared with just boiled? And why do we bloom anyway?
Given that Istobiii is suggesting extending the bloom time with the colder water to 1.5-2.5 minutes, we have plenty of time to think. Do give it a try, and have fun experimenting.
Last week, I revealed the results of an experiment into an odd observation while brewing coffee in my Aeropress: why was it that the bubbles formed on the opposite side to the hand I used to pour the water from the kettle? On the face of it, it was an easy experiment, with a simple explanation and a fairly clear set of results. But behind this story is a series of decisions and psychology that can illustrate, on a small level, some of how experimental science is done. It’s not for nothing that there’s the saying, the devil is in the details.
Theory, experiment and the impartial observer
There can be an erroneous idea about the progress of science, repeated even among people who should realise the fallacy. A theory, with testable predictions is proposed, which is subjected to experiment by a series of dispassionate observers in order to provide evidence that either supports the theory or disproves it. We dehumanise the theoreticians and experimentalists to observers who can emotionally disconnect and observe the results from an objective distance.
There are countless examples against this within the history of science (both for theories that have now been rejected but also for theories that we still consider good models) but I want to keep to the example that we can all have in front of us in our kitchen: that of the bubbles in an Aeropress.
With the Aeropress it was an odd experimental result that prompted a theory that then fitted the odd observation. The theory came with some extra ‘predictions’, but theory and experiment evolved together. Again, there are examples of this in the history of science but the experiment prompted the theory that prompted further experimental tests.
The problem then is that the experimenter (in this case me) was well aware of the theoretical predictions. Could I dispassionately, and completely subconsciously, pour a kettle as I had always poured the kettle, or would part of me, however much my conscious was opposed, change how I poured the kettle subsequent to my idea of how the bubbles formed?
For the case of the experiment with the Aeropress, this remains an open question. Generally though, many experimentalists will aim to try to reduce conscious or unconscious biases by putting procedures in place to prevent them coming in. When Isaac Newton and John De Saguliers investigated the role of air resistance on falling masses from inside the dome of St Paul’s Cathedral, London, they dropped them from a trap door system. This meant that the masses (which in the first instance included glass balls filled with mercury) fell at the same time; the quiet suspicions of the experimentalist investigators could not influence the results. It created a mess on the floor of that great Cathedral, but it did eliminate this component of bias from the experiment. You can read more about their experiment here.
A need for peer review
Assuming that we are collecting data in a neutral way, what happens then? On the face of it, seeing if the bubbles appeared on the left hand side or the right hand side should be an easy question to answer. And in some cases, such as the pictures that I chose to illustrate my post about the results last week, the answer is clear. But are those photos representative of the whole data? And, for more ambiguous photos, such as the one shown here, how do you define which bubbles to count?
One problem here is that each photo is very slightly different. Either the angle is different, or there is steam on the lens, or the focus is not there. But even so, sometimes it is harder to see all the bubbles on an image. For this experiment I defined a minimum bubble size (which you can see as the white square in the image) which I used to decide which features on the surface of the coffee to ignore: after all, when viewing the image, it is not clear whether items smaller than this are bubbles or just a different colouration to the coffee crema.
You may notice that I did not mention this detail in last week’s post, but one of the images includes the square. This is one of those things that would (most likely) be picked up in what is known as ‘peer review’. When we write results up and submit it to a journal for publishing, the journal will typically send the paper out to 2 or 3 ‘referees’. These are people, who ideally work on similar experiments, who will read the paper and think “hang on a minute, what if it is not the bubbles but the bubble size that shows an effect, how have these authors counted the bubbles?” The example is admittedly a somewhat trite one, but the point is that the paper is read by someone who also does this sort of experiment and knows where problems can be encountered. The ideal is not to trip the authors up, or to show that they did anything wrong, but to see things from a new angle, a different set of obsessions and so ask the original authors to address points that improves the paper in the sense that we can all start to see what is going on*.
Peer review also of course helps to stop the publication of results that are wrong, or statistically invalid (see below). We therefore need some form of peer review in order that we can be collectively, as a society, happy that this science is being done robustly. So if you see a newspaper report that “the study, which has not yet been peer reviewed…” treat it with a very large pinch of salt and please don’t tweet it (unless you happen to also research that area and so can read the paper as if you are writing it).
We have attempted to eliminate our biases, we have been open and transparent about our methodology, what could possibly go wrong now? It is in not taking enough data. Say I made a coffee pouring from my right hand and the bubbles formed on the left, then with my left hand and the bubbles formed on the right, we can know that this is not enough to be sure that the bubbles ‘always’ form on the alternative side. For that bit of the experiment I made 22 coffees. Not enough to be statistically certain (more on that here), but probably enough for an observation on a coffee blog.
But the bit I want to focus on here is the part of the experiment where I counted the number of bubbles versus the bubble size. I was investigating any similarities with a study that measured thousands of bubbles over 225 images documenting 14 events. I counted the number of bubbles on one small portion of one coffee that may not be representative of the coffee generally. Can we accept that as a valid procedure?
While I may not have counted enough bubbles here, one experiment (that can involve coffee) where there certainly were enough objects counted was in the determination of the mechanism behind Brownian motion. Brownian motion is the phenomenon by which small particles of dust or bits of coffee move in random directions on the surface of your cup. It happens because the molecules within the water of the coffee hit against the dust and impart a small momentum to the particles. Because there are many molecules moving in all sorts of directions, the resultant movement appears random. If we look through a microscope we can see the particles moving but there is no way that we could see the molecules that move them. Back in the nineteenth century this became an exceedingly controversial topic: could you form a scientific theory for a phenomenon (such as Brownian motion) which relied on assuming an underlying reality (molecules) that you could not hope to see or measure directly? The question was (partly) resolved only in the early twentieth century with the very careful experiments of Jean Perrin (you can read more about Perrin’s experiments and their relation to coffee here). When Perrin summarised his results he wrote:
“I have counted about 11, 000 granules in different regions of different preparations to obtain the figure 21.2 of the first column.”
Which is slightly more than the number of bubbles I counted last week.
A way forward – truth and integrity
What does this mean for science and how science is done and reported, especially in this era of rapid research and in which everyone has an opinion? Is science discredited by the fact that we are humans, and not fully dissociated and objective, when we do it?
Although I ran out of space to discuss Michael Polanyi’s comments on statistics and pattern recognition, he does have something extremely relevant to say about the progress of science. For Polanyi, how we do science and how we behave as a society were (and are) intimately linked. He considered that for science to prosper, we needed “fairness and tolerance” in discussion. By fairness he meant the requirement to state your case, your experimental result or theory, openly, separating fact, from opinion and emotional involvement and openly allowing them each to be critiqued. By tolerance he meant that we needed to listen to the other, even while we disagree, in order to see where they may have a point. He linked this behaviour within science to the behaviour required of the public in listening (and sharing) science. As he said:
“Fairness and tolerance can hardly be maintained in a public contest unless its audience appreciates candour and moderation and can resist false oratory. A judicious public with a quick ear for insincerity of argument is therefore an essential partner in the practise of free controversy…“
Science and society move together.
And so an invitation. Keeping in mind the idea of Polanyi about honesty and integrity in discussion, I would like to invite any reader of this blog to become a peer reviewer of the experiment reported last week. Please go and enjoy a coffee, carefully preparing and noticing your brewing technique and then work out how you would have made the experiment and tested any results. Perhaps you have a different theory that would require a slightly different counting method than the one chosen? Perhaps you think that more experiments are necessary? Become my peer reviewer! Feel free to comment below, or on Facebook or Twitter. Or, if you would prefer, email me through the contact form here. Bear in mind I am human, and so I will react to your report. But if you and I keep can Polanyi’s warning in focus, perhaps we can together improve our understanding of the science behind bubbles in an Aeropress. And, by extension, improve our understanding of how science, and society, can work.
I genuinely do look forward to reading your comments.
*I have worked in academia long enough to know that this is not always how the peer review process works in practise. There are many cases where peer review falls short of the ideal, for all sorts of reasons. But it remains a necessary part of the publication process as many referees (and authors) do try to approach the process in this way. Obviously emotion gets in the way when we receive the referee’s report initially, or, on the other side, if we think that the authors have seriously misunderstood their experiment, but if we take a few days to sit with the report/paper, we do try to get towards the ideal.
I am a very lazy Aeropress brewer, but this very laziness resulted in an unexpected observation and coffee connection. Why was it that the bubbles that formed on the top of my coffee were always on one side of the Aeropress cylinder?
First some background. I had been brewing the coffee using an adaptation of the “inversion method“, perhaps it should be called the Bean Thinking inversion method, or BTiM. You can read a good brew guide for preparing coffee properly using the inversion method here. The method I used follows.
After the usual steps of rinsing the filter and blooming the grounds, I filled the Aeropress cylinder using (just boiled) water poured from a standard kettle. Owing to the configuration of the kitchen and the fact that I am right hand dominant, I used my right hand to do this. This generally results in a fantastic bubble pattern on the surface of the coffee, as you can see in the picture, but one that is generally asymmetric – the bubbles appear on the left hand side of the well.
Subsequent repetition of the technique showed that the adverb “always” was a bit of an over statement. However, without recording the bubble patterns after each brew, it is easier to remember the unexpected results, which tend to be asymmetric, and not notice the more even distributions. Michael Polanyi comments on this at length in his book on science and scientific theory/practise “Personal Knowledge” (and while it seems a strange title at the start of the book, the reasoning behind the title becomes clearer throughout the text).
Nonetheless, out of 11 brews, 7 had bubbles primarily on the left hand side of the cylinder, with 3 brews of a more even distribution and 1 with a right hand side distribution.
What could be happening? A discussion on Twitter led to a theory by @baristapierre that air was effectively being pulled into the Aeropress during the pour. Because of the way that water from a kettle spout would flow into the Aeropress, this trapped air, the bubbles, would appear primarily on the opposite side of the Aeropress cylinder from the pour. What would happen if I poured using my left hand?
Here I need to put a note on the method. While I am right hand dominant, I write with both hands and use each hand fairly interchangeably (while tending to favour the right). There may be some effect of my handedness on the pour, but this should not necessarily be too significant. What happened as I changed the handedness of the pour?
Sure enough, the bubbles appeared on the right hand side of the well. And again, but then a run of more ambiguous results. Finally, after 11 brews with the left hand, 5 had bubbles on the right hand side but 4 had bubbles on the left hand side and 2 had a more even distribution (You can see a graph of the final results below).
And so, it appears quite likely that the air-trapping on pouring mechanism suggested by @baristapierre is a good explanation of the bubble distribution seen. But why do the bubbles form at all? The question of how bubbles form in air entrapment caused by turbulence is one that we may ask at the beach while watching (and listening) to the waves crashing in towards the seashore. Each wave generates thousands, millions of bubbles (hence the white caps and froth on the waves as they come in). These bubbles are not only responsible for the sounds you hear as the waves come in, but as they burst they release aerosols of salt and organic matter into the atmosphere that in turn affect cloud formation and can even influence hurricane dynamics.
And yet astonishingly, it was not until 2002 that a theory was developed (and experiments performed) to measure the bubble formation in water waves. Using high speed video, the study photographed simulated waves in a laboratory and found that the waves formed in two phases. A first involved the collapse of the air cavity formed as the wave folded in on itself. These bubbles are larger and responsible for the low frequency “crash” of the wave that you can hear. The second, concomitant, phase, involved the impact of the water with itself, much like the bubbles in the Aeropress. These bubbles were much smaller (< 1mm radius) and so the sound associated with them was a higher hiss. Together these bubbles create the crash-hiss sound that is so familiar with the breaking of the waves.
By carefully analysing 225 images over 14 wave breaking events, the study found that the number of bubbles per unit area decreased with bubble radius but with a different dependence depending on whether the bubbles were smaller, or larger, than approximately 1mm.
These results were checked against the Aeropress brew with the highest number of bubbles (1 May 2020). On the positives, it was clear that the bubble size observed was similar to the ocean waves study of 2002. The bubble density also decreased with increasing bubble radius (see the graph below). However the rate of decrease with radius was not as observed in the ocean study. There could be many reasons for this, including the fact that counting from a steamy photograph taken 30 seconds after the pour was not the most accurate method of analysis! Nonetheless, it does emphasise, that, though there are many connections between the physics of a coffee and the physics of the world, and though there are even more connections if we use the coffee as a prompt to let our minds wander into the wonders of the universe, the Aeropress is not an ocean and we can stretch analogy too far.
And so, while we may not learn much about ocean dynamics while brewing Aeropress coffee, it turns out we can learn a fair bit about experimental technique and how science is actually done, including what Polanyi meant about noticing unusual distributions. This will be the subject of the next post. In the meantime, what have you seen while brewing coffee? Do let me know in the comments, on Twitter or on Facebook.
Five items make up 2/3 of all lightweight identifiable waste collected from the Thames each year. These items make their way either through being dropped, sometimes deliberately littered, or through another path, into the river where, without litter picks, they are eventually washed out to sea. Part of the estimated annual ~10m tonnes of plastic waste entering into the oceans, they end in one of the gyres of the oceans, vast expanses of sea covered by floating rubbish.
Only much of this waste doesn’t. Or at least not as much as we think should do and we don’t know why. Despite the fact that there is an estimated 250 000 tonnes of waste floating in places such as the North Pacific Gyre, this is not as much as is expected. In fact, the visible waste makes up only a few percent of the waste that is expected to be there. Where is the rest of the waste, and what does it have to do with physics, or indeed coffee?
One of the ‘top 5’ items found in the Thames (coming in at number 4) is take away cups. This is followed closely by take-away containers. This means that our behaviour on leaving cafes, restaurants (and pubs) is affecting the litter that ends up in the river. And this is without counting the fact that food wrappers and drinks bottles (including water bottles) are two of the other worst offenders. It is not necessarily that people are deliberately throwing the items onto the pavement as they walk (though there is that too of course). The charity Thames21 that organises river-side clear ups and litter picks also thinks that some of the waste is coming as a result of people trying to put items into over-filled bins or so-called “tidy litterers“. But the truth is, they don’t really understand the route that many of these items take before entering the river system.
It is a significant problem for us now as many of us are trying to support local restaurants or cafes by ordering take away and even when a place has drink-in space, often it is single-use disposable cups that are used. Part of this is understandable. There is a hygiene concern, even if there are counter-arguments that re-usables are safe to use in these times of Covid-19. But I don’t want to trivialise this concern, partly because people are making very hard decisions about how to keep their businesses going or earn enough to pay the next set of bills. If there is any doubt about the safety, it needs to be considered holistically by those running and working in the businesses and not those like me able to work from home and able to get delivery or pop-in and pop-out (and, in fairness, it is easy to see from a barista’s point of view that handling an untouched single-use cup and giving it in a contactless way to a customer is safer than receiving their re-usable container in whatever state of cleanliness it is presented in).
This part seems a question of balance. Balancing the need for economic support with the concerns of the single-use plastic problem. Do the places that you frequent use recycled (and recyclable) plastics or compostable ones? If the latter, is there a compost bin within the cafe to help with the disposal of these? Ultimately, is your take-away coffee going to help the business or are there other items that you can purchase that don’t require the same amount of packaging.
These are considerations with no easy answers which leads to the second approach that you could take. In non-Covid times, charities such as Thames21 are always looking for volunteers to help with clean ups and to get involved in counting the types of litter that find their way to the rivers. Becoming a ‘citizen scientist’ in this way helps to quantify the amount of waste entering our rivers but it also helps Thames21 and the river authorities to understand how the waste gets there in the first place. Why are our river banks so filthy?
But then the last question. If we know that so much waste is getting into our river, and we know that this is being replicated around the world, why is so little of it making its way to the gyres? What is happening to it?
This affects, to some extent, what we do about our plastic behaviour – the decisions we ultimately make about whether to have a take-away coffee or whether to buy a disposable or re-usable face mask (or even make one). One of the explanations is that the majority of the plastic is becoming micro plastic (<5mm size pieces) or even nano plastic and so sinking into the seas rather than floating on the surface. These micro plastics are the result of the break-up of larger items by UV and micro organisms at sea and also the direct pollution of micro plastics into the sea by clothes being washed or from cleaning products etc. Indeed, the Thames21 citizen scientists discovered micro plastic pollution at 20 out of 21 sites along the river bank in a recent litter survey. A different explanation is that the plastics that are entering our seas today take years, even decades to reach the gyres which are made up of plastics from the 1970s and similar aged pieces. Both explanations mean that we need to stop the pollution at source, but if it is the former, there is not so much point in cleaning up the gyres by pulling the large litter out – the majority of the plastic that is in the oceans is actually underneath what is visible.
How can we determine what plastic waste goes where? Well, we can increase the modelling of ocean currents to improve our ideas about how waste is transported from source to gyre, but we can also try to have a look from space, from the satellites that are monitoring other aspects of our behaviour on Earth. Now it turns out that it is not easy to see plastic from space because with many of the techniques we would use, such as radar, plastic and water ‘look’ very similar. But one thing that that the satellite data has shown is the fact that there are peculiarly calm regions of sea near the gyres. Calm sea looks different from choppy seas in the same way that the light reflected off your coffee looks different if you are sitting with it calmly or if you are running with it and it is sloshing around the cup. But the connections go a bit further than this. The reason for the calm is because of surfactants on the surface of the seas. These surfactants (like soap) ‘calm’ the waves in much the same way as oil calms the waves. It doesn’t take much surfactant to cover the surface of a large area of water as a consideration of how much oil covers the surface of your coffee can tell you.
The surfactants are produced by microbial activity, the result of small bits of plastic (micro plastics) having been colonised by microbes before it sinks. The calm regions of the sea may therefore be indicating areas of hidden micro plastics and demonstrating the depth of the problem of single use plastic waste.
Where, in your kitchen, would you find a link between the physics of the everyday and the physics of black holes? It’s a question with many answers, and maybe you could think of a few. But one involves a process you may see while brewing your coffee, though you may have to slow down to see it.
The connection is in the way a gentle stream of water breaks up into droplets as it falls. Brewing coffee using a swan necked kettle in a V60, it is something that I see as I slow the rate of pour. Is this a good way of preparing a coffee? Possibly not, but it does allow me to experiment with the physics. You could also see the effect from a slowly dripping tap or in a few other places around the home. It occurs when the cylinder of flow is much longer than the radius of the flowing water.
The question is really, why would a cylinder of flowing water seemingly spontaneously break up into a broken stream of raining droplets? The answer is in a phenomenon now known as the Plateau-Rayleigh instability.
To see why it may occur, we can think about how water flows out of a kettle or a tap. In any cylinder of fluid there will be regions of the flow that are a bit fatter and regions that are a bit thinner. These can be imagined as a series of waves on the surface of the cylinder (you can see a schematic of this effect here). At small wavelengths, the water cylinder remains stable, so for very rapid (but small) fluctuations in the diameter of the flow, you will not notice any difference to the way you pour. But as the wavelengths become larger, and beyond a critical wavelength, the amplitude of these oscillations increase rapidly with time (the maths describing the ‘why’ is here).
As the amplitude of the oscillations grows, there will come a point at which the bulges are so large and the necks of the stream so thin (relative to the stream’s diameter) that surface tension effects will cause the necks of the cylinder to break resulting in the stream of droplets that you see. When Plateau first observed this in 1873, he thought that the continuous stream became a flow of droplets when the length of flow was just over 3 (around π) x the radius of the flow. In fact, the break up seems a little more complex, and from my V60 kettle I’d estimate that the length at which it occurs is greater than 3x the radius of the pour, but the experiments of Plateau and the theory of Rayleigh did rather explain what was going on with the stream.
How is this related to black holes? Black holes are massive objects that exist within a very small region of space. Many black holes are thought to be the result of the collapse of a massive star at the end of its life, although there are examples of smaller and more massive black holes. The sort that result from a collapsed star can have a mass around 20x that of the Sun but fit into a space with a diameter of just 10 miles, which is about the distance from Heathrow to Hammersmith (still not central London!). Every planet, moon, star or black hole has an “escape velocity” associated with it that is a function of the object’s mass. The escape velocity is the speed at which you would need to move away from the object in order to avoid being pulled back to the object’s surface. For the earth you need to travel at more than about 11 km per second in order to escape the earth and enter into orbit around it (or move beyond that). For the moon, because it has much less mass, the escape velocity is far lower. For a black hole, the escape velocity is much higher and actually exceeds the speed of light.
The “event horizon” of a black hole is the point at which the escape velocity from the black hole is so high that it exceeds the speed of light. We cannot see into the black hole, because the light cannot escape from within the event horizon.
It turns out that for certain mathematical reasons, it can be useful to consider the event horizon as a stretched fluid membrane with elastic like properties much the same as the surface tension causes to water. At this point it gets a little complicated because not all black holes are spherical*, some indeed can be cylindrical. So we have a cylindrical object with an event horizon with properties that cause it to behave in a manner similar to a fluid with surface tension.
You may well have seen where this is going already. Because yes, it turns out that such cylindrical “black branes” are susceptible to breaking up into many smaller objects exactly analogously to the Plateau-Rayleigh instability in a stream of water. Exactly how they broke up (eg. did they break into spherical objects) was left to further investigation, but the maths was developed in a 2006 study to explore this phenomenon further, you can read more about it here.
It is a bit of a bizarre connection to realise in your kitchen. But the world is often weirder, more beautiful, and more connected than we are sometimes tempted to think. Do let me know of other astronomical connections to your kitchen that you can see. I can think about one or two more related to black holes, but I’m sure you can think of many more. Please just leave a comment below, on Twitter or on Facebook.
*This is certainly true in the maths of black holes, it’s too far outside my subject field to know if such objects have been observed or thought to have been observed in reality.
Have you been making more coffee at home through the Covid-Lockdown times? Each morning, I have taken time to brew a coffee (or several depending on the way I feel that day) and then sit down and notice what is going on in the mug. The way the steam swirls upwards in turbulent patterns, the white mists on the surface of the coffee and the peculiar effects they have on reflected (and refracted) light from the coffee’s surface. And, the oils that appear on the surface of black coffee.
The appearance of these oils is very dependent on the way that you make your coffee. A cafetiere/French press is an immersion method of brewing coffee with no subsequent fine filtration of the grounds. It is therefore quite likely that the oils present in the roasted coffee bean will make their way to the surface of your coffee. If you brew by a pour over method on the other hand, it is thought that the paper filter should take out the oils as you brew. However, even when using a paper filter on a V60, a thin layer of oil can sometimes be seen on the surface of my coffee, visible in the sunlight on those mornings. How much oil is making it through the filter?
How can we know that it is just one molecular layer thick? In one of those experiments that it is probably better to know about rather than to rush out to repeat, a clue came in the 1760s when Benjamin Franklin put a teaspoon of oleic acid (found in olive oil) on the surface of Mount Pond on Clapham Common. As he watched, the surface of the pond, which had been active with many capillary waves blowing over it, was calmed as the oil dispersed across the surface. First the oil remained in a small patch but it then grew, and grew until it reached the other side of the pond.
Franklin had been expecting the calming effect of the oil on the water waves, in fact he had been looking for it. On his journey to the UK from the USA he had been watching the wakes behind the ships in the fleet that were accompanying his ship on the journey. Two of the ships showed remarkably calm wakes, a fact that he had remarked upon to the ship’s captain. The captain had responded quite flippantly that it was probable that the cooks had emptied their greasy water over the sides of the ship. Mariners knew that oil and greasy cooking water, calmed the waves around the ships. We can learn a lot by talking to each other and listening to their experience.
The mariners knew that oil calmed the water but why? How? If we think about the oil as a surface layer over the water, it becomes possible to imagine an answer to this. Without the oil, when the wind blows over the water it will act to exaggerate the small perturbations on the surface of the water (caused by water flow, falling raindrops etc) which can then grow into waves. With a layer of oil on the surface, when the wind blows, if the oil is thick, it will act to blow the oil into a thinner layer covering the water surface. If the oil is thin already, it would take a lot of energy to stretch the oil surface to accommodate a growing wave. Either way, rather than exaggerate an existing perturbation on the surface of the water, the wind over an oily surface will tend to drag out the oil film, which will have the effect of calming any perturbations rather than encouraging them.
But how realistic was it that Franklin’s teaspoon of oil could have covered Clapham Common pond? About one hundred years after Franklin, Agnes Pockels and Lord Rayleigh were studying the effect of oil on the surface tension of water. As they did so, they calculated the thickness of thinnest oil layer that they could disperse over the surface of the water bath they were studying. Pockels calculated this thickness as 1.3 nm, Rayleigh at 1.6 nm, either way, a layer that is 10 000 times thinner than a grain in the smallest espresso grind coffee.
And one molecular layer thick.
So to return to Clapham Common pond. 1 teaspoon is 5 cubic cm. If the oil formed a layer 1.5 nm thick over the surface of the pond, it would disperse over an area just slightly over 3000 square meters. It is perfectly possible for one teaspoon of oil to disperse over the surface of Mount Pond in Clapham Common. But what is possible is not necessarily advisable so let’s reverse the question and ask how much oil is on the surface of the coffee? Assuming that what is on our coffee is genuinely one molecular layer thick, or about 1.5 nm*. My cup has a radius of 4cm, meaning that the volume of oil on the surface is 0.0075 cubic millimetres. One metric teaspoon of olive oil is 5 cubic centimetres or 4.55 g. If we use the ratio of the volumes to calculate the ratio of the mass, we find that the oil we can see on the surface has a mass of about 7 micro grammes. A tiny amount, but a value consistent with studies suggesting that a small amount of cafestol (associated with the lipids in the coffee) gets through to the brew even in pour overs.
There is plenty to notice in a coffee, what do you see in yours?
*It is of course possible that the oils are actually thicker than this, but the paper filter does result in an oil film that is far from continuous across the coffee surface, suggesting that the oil is already stretched as far as it could be.
We have probably all come across the Leidenfrost effect, the splash of water into a hot frying pan causing drops of water to skirt across the hot surface before evaporating. We may even be familiar with it in frying pans and cooking surfaces. But what would happen if you swapped the frying pan surface for a (very hot) liquid surface. What happens to the Leidenfrost effect then?
One of the first differences between a frying pan and a bath of hot liquid (we’re not quite yet to the coffee bit) is that the frying pan based Leidenfrost effect requires a lot of heat: the frying pan has to be many degrees hotter than the boiling point of the liquid being levitated. But for the Leidenfrost effect to happen on liquid surfaces requires nowhere near so much heat. In some cases levitation can even occur if the liquid bath is just one degree higher than the boiling point of the levitating liquid. What makes a hot liquid so much different from a hot solid?
A second explanation is that a liquid surface is able to deform a bit to support the weight of the drop above it, this means that the drop has more of a chance of remaining levitating above the liquid surface. And yet, it turns out that there is more than that happening in liquids as a recent study in a prominent physics journal showed.
A toroidal vortex formed in the silicone oil under both the ethanol and HFE-7100 drops. We can see similar toroidal vortices in our V60 or by dripping milk into a glass of water; they are doughnut shaped regions of moving fluid, like smoke rings, they could be considered ‘milk rings’. But in this case, there was no drop entering into the bath of liquid as with the milk rings. The drop and the bath were not mixing at all. And, perhaps more puzzling, the direction of the rotation of the vortex was different for the two types of drop. For the alcohol drops, the liquid directly underneath the drop plummeted into the silicone oil before moving under and then back up to the surface to be pulled down at the centre again. Under the HFE-7100 it was different. There, the liquid at the centre of the doughnut surged up, dragged along the surface before going under and returning back once more to be pulled up at the centre of the torus.
Why would the two liquid drops show such different behaviour in the silicone oil substrate? It comes down to a competition of three forces. The first thing that you will notice is that if the levitating drop is slowly evaporating and will eventually disappear (as is the case with the frying pan), this means that it is absorbing heat from its local atmosphere in order to gain the energy needed for evaporation to occur (think about your hand getting cold after sanitising it with an alcohol liquid as the alcohol evaporates off). This means that the silicone oil immediately under the drop gets colder. Cold liquids are generally more dense than warm liquids and so the cold liquid sinks pulling the surrounding liquid down with it.
Linked with this effect is that the surface tension of a liquid decreases as the temperature of the liquid increases. This results in a flow of liquid from regions of low surface tension to regions of higher surface tension called a “Marangoni flow”. This is again something that we may have seen during the Covid-19 lockdown restrictions as videos were circulated showing the effect of soap on a layer of pepper scattered on the surface of water. The pepper retreats away from the soap because of these Marangoni flows which can in fact be very fast.
These two effects draw the liquid down at the centre of the torus and push the liquid up at the edges, this is what dominates when ethanol is levitating above the silicone oil. In contrast, a third effect dominates for the levitating drops of HFE-7100. Both ethanol and HFE-7100 drops are evaporating above the hot silicone oil surface and as they do so, the gas that evaporates out of them under the drop flows out from the centre of the levitating drop to the edge. Just as with a gentle breeze on a pond, this vapour flow leads to a shear force on the liquid underneath that pulls the liquid out from the centre of the torus towards the edges, down and then, to complete the circle, back up through the middle.
Remarkably, despite their different rotation directions, both types of vortex contributed to keeping the drop levitating. You can read more about the study in the summary here or in the journal here.
Given that water boils at 100C and that alcohol boils at 78C, it is feasible that by dripping vodka or another strong alcohol based drink onto our freshly prepared coffee we may see a similar effect. It may certainly be worth a try. I’ll leave this as an experiment that you can tell me about on Twitter, Facebook or in the comments section below, but it is an experiment with a positive result either way. Perhaps you will see levitating alcohol drops above your coffee. But even if you don’t, you can at least keep trying until you have made an interesting coffee based cocktail.
How many vortices do you see in your coffee? We finally arrive at the last in this series about the contributions of Helmholtz to the physics of a cup of coffee and the one that was to be the link with the (postponed) Coffee & Science evening at Amoret Coffee: vortices. But, beyond those that form behind a spoon, where do you see vortices in coffee and how can we connect them to dolphins?
Each morning as I prepare a pour over, I wait as each drop of coffee falls into the coffee bath below it. Some bounce up, some stay on the surface for some moments, many more pass straight through and get absorbed into the brew. I will admit that on most mornings, I am not thinking about the fact that I am watching one of the most beautiful pieces of physics unfold in front of my eyes and yet, this is how the processes occurring in the V60 were described by Lord Kelvin:
“[Helmholtz’s] admirable theory of vortex rings is one of the most beautiful of all beautiful pieces of mathematical work hitherto done in the dynamics of incompressible fluids.”
One of the most beautiful of all beautiful pieces of mathematical work? In my morning V60? How can we see these vortices as they fall? Sadly, it is perhaps easier to swap the coffee for plain water and drop food colouring into into it if we actually want to see these vortex rings form. As each coloured drop hits and goes through the surface, it forms a ring that curls up on itself and, if you are lucky, splits into many smaller rings, cascading to the bottom of the pot. You can see a film of the effect here or try it for yourself.
Each drop of coffee dripping from the filter into your coffee pot in the morning does this even if you can’t usually see it.
And though these rings must have been seen before Helmholtz’s paper in 1858, and even dolphins play with them in the sea, no one had attempted a mathematical model until Helmholtz. Helmholtz founded his mathematics on several theorems including the fact that a vortex cannot terminate within the fluid. It either has to terminate at the boundary of the fluid (like the vortex formed behind a spoon being dragged through coffee) or it has to close on itself (it forms a vortex ring) (more info here, opens as pdf).
Helmholtz seems to have come to vortices via an interest in organ pipes. He noticed that vortex sheets form at the inner surface of the pipe that can contribute significantly to the internal friction of the air flow through the pipe*. This means that, at the boundary between the moving air and the stationary air at the pipe edge there is a region of turbulent flow which leads to the formation of vortices. For Helmholtz, this had immediate consequences for measuring the speed of sound using pipes. Because where as previously the length of the organ pipe had been taken to be the distance between the maximum vibration (anti-node) and minimum vibration (node) of the sound wave, Helmholtz noticed that the presence of vortex sheets at the surface of the pipe would lead to an apparent lengthening of the resonator. If you used the length of the pipe to calculate the speed of sound, you would be very slightly wrong*.
As he investigated further, he found that these same surface-vortex effects explained a feature of organ design that had been known empirically but never explained. Why is it that in order for the character of the sound to be similar for each note, notes played through short, fat pipes must be accompanied by notes played through tall thin ones? Again it is to do with the air flow past the surfaces of the organ pipe.
In fact, these vortex sheets that appear at the boundaries between fluids appear so often, you can start to see them everywhere! They are in a cup of coffee if you put it on a record player (as with the picture of ink in a takeaway cup here) and they are in clouds that show a Kelvin-Helmholtz instability. Appearing like a series of waves on a cloud in the sky, Kelvin-Helmholtz instabilities occur when a layer of cold dry air flows fast past a layer of hot and humid air. At the boundary of the two layers, a vortex structure forms and because the hot humid air encounters the cold dry air within that vortex, clouds can form at the boundary which reveal the vortices driving them. Although the conditions to create them must occur quite frequently, they last only a very short amount of time (less than a minute is typical) and so are considered quite rare. Look out for them next time you can see that the weather is changing and the clouds are fairly high in the sky.
Of course, it is not just on Earth and in coffee that we see these vortex structures. We see them in the weather patterns of other planets, in the solar wind and in jets leaving supernovae. And it is not just in fluids that Helmholtz’s mathematics of vortices proved useful. In Helmholtz’s equations the fluid velocity associated with a vorticity described (exactly analogously) the magnetic force produced by an electric current distribution*.
Far more could be said about Helmholtz’s work on vortices and its links to both coffee and the weather on Saturn, but that will have to wait until the next Coffee & Science evening at Amoret. Until then, enjoy watching these astonishing structures in your coffee and let me know if you observe anything interesting with them.
Search online and you can find videos of machines that lift cogs or turn wheels that are powered by the steam rising off a coffee. You can see an example here and find instructions for how to build your own here (a “stay at home” hobby project perhaps?).
Although such machines are very much for the hobbyist, the principle of the steam engine drove the industrial revolution. And, even now, much of our power network relies on somehow heating water which then drives a turbine that generates electricity. Underlying this is the principle that energy can be transformed from one type to another but is, ultimately, always conserved.
The concept is easiest to visualise with a pendulum or a swing. At its height, the pendulum has a maximum of potential energy but is not moving (so its kinetic energy is zero). As it passes through its minimum height point, the speed of the swing (or pendulum) is maximum and the potential energy at a minimum. Indeed, the amount of potential energy lost by the pendulum is equal* to the amount of kinetic energy gained. The same can be extended to “work” which, in the language of physics is always energy. If a certain amount of energy is put in, a certain amount of work can be produced. In a closed system and without loss, the amount of energy you put in is the amount of energy you get out. In any real system, some of that energy is lost to heat or other methods of loss.
To use a more coffee related example, in an espresso machine, work is done to put the water under high pressure (and separately to heat it). This pressurised water is then allowed to escape through the coffee puck where the work originally done pressurising it gets transformed into the kinetic energy (speed) of the water going through the group head. Changing the pressure changes the speed at which the water goes through the puck in an analogous way to how changing the height of the pendulum drop affects the speed as it goes through its central point. Of course you won’t always see this because changing things like the grind size in the espresso puck will also affect the route that the water takes as it travels through the puck and so the actual speed at which you see the coffee-infused water leaving the espresso basket will be affected by that too. The real world is never quite so easy as the ideal.
A pour over works in a different way. Here, the energy is stored in the water ‘bath’ in the filter as gravitational potential energy. As the water falls, it gains kinetic energy at the expense of this gravitational energy (or height). As the espresso machine also works with gravity, the conclusion would be that the water will move much faster through the espresso puck than the pour over bed. That this often doesn’t seem to be so is again because of the effects of the resistance of the coffee bed or espresso puck, on the espresso and the pour over.
This concept of the conservation of energy has been engrained into us from an early age. And so it may be surprising that it is a fairly recent principle in physics. For although versions of this principle had been considered for many years, it had not been recognised until the 1840s (by James Joule and Robert Mayer in 1843 and 1842 respectively) that work and heat were interchangeable. And it wasn’t until 1847 that Helmholtz recognised that all energy was conserved. Although at that time he was using the word ‘force’ for what we now call ‘energy’, and what we now call kinetic energy was thought of as a ‘living’ energy. He wrote:
“… the loss in the quantity of potential force is always equal to the gain in living force, and the gain of the first is the loss of the second. Thus, the sum of the existing living and potential forces is always constant.”**
So, among the many contributions to physics that he made, Helmholtz also has a claim to being among those who developed the field of thermodynamics which remains crucial both for physics and for our industrial and technological progress.
There is perhaps a cautionary note here for any who are tempted to think that science and religion are always somehow in opposition. For the British scientists who contributed to the development of the idea of conservation of energy (such as Joule and William Thomson (Lord Kelvin)), the concept was founded on the idea of a Creator God: as only God could create or destroy, so it followed that energy of itself, could never be either created nor destroyed, it could only be transformed from one form to another. The idea of a God was, for them, implicit in the idea of the conservation of energy**.
Helmholtz had a philosophical disagreement here. For him, the principle was founded on a Kantian understanding of philosophy***. Certainly certain things had to be assumed at the beginning (such as the principle of causality and the existence of matter outside of our perception of it). But once these assumptions had been made, the principle of conservation of energy followed in a deterministic manner.
Does this matter? In our everyday experience of engines and the way things work, conservation of energy certainly seems to be crucial. We no longer question the principle but assume that one form of energy is transformed into another and is continuously conserved even as it is dissipated into the universe as heat as our coffee cools. But nonetheless, Helmholtz’s understanding was founded on certain assumptions, beliefs, just as Joule and Kelvin’s. It helps to be aware of the philosophical underpinning of our science so as to ensure we don’t have over confidence in what we can, and cannot, know.
So Helmholtz can teach us something else as we gaze into our coffee. Our world is multifaceted, and what we believe about what the world is, influences and informs our understanding of how the world works. Our challenge is to look into ourselves as we sip our coffee and to start to see what we believe we know and what we can actually know. And if we were to really do that, what conflicts would we find?
*With the usual caveats of no energy being lost to friction etc.
**”Helmholtz and the British Scientific Elite: from force conservation to energy conservation”, David Cahan, Notes Rec. R. Soc (2012), 66, 55-68
***”Helmholtz: from enlightenment to neuroscience”, M Meulders, MIT press, 2010