vortices

With this ring…

vortices in coffee
Vortices behind a spoon dragged through coffee.

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.

Vortex ring cascade, food colouring into plain water, V60 vortex
Dripping food colouring into a V60 of plain water: visualising the vortex rings that form every morning as you brew your coffee.

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.

vortices, turbulence, coffee cup physics, coffee cup science
Another cool consequence of boundary layers: Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player).

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*.

Kelvin Helmholtz instability in clouds over the M3 in January 2020
A Kelvin-Helmholtz instability in clouds over the M3 in January 2020.

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.

This is the last in a series of articles on the contributions of Helmholtz to our understanding of coffee. You can read an introduction here, his work on vision and colour here, the sounds of coffee here and the energy of coffee here. Next time, we’ll be back to experimenting with coffee, please do let me know (on Twitter, FB or in the comments) of any experiments you have been doing at this time, what have you seen in your brew?

*”Worlds of Flow”, Olivier Darrigol, Oxford University Press, 2005

Connectivity

Shades of light and dark. How do we see shadow, colour, depth? How is it linked to the physics of coffee?
Superscript and subscript

The other morning, grinding coffee in order to prepare a V60 (the last of a fantastically complex Natural El Salvador from Amoret coffee), I was hit by the intense aroma of rich, freshly ground beans. It seems at the moment that we are surrounded by more vivid impressions of things that have, in reality, always been there, but that have previously been obscured by other features of our lives. Such things have been revealed by the changes to our lives that have come about as the result of the “lock-downs” needed to reduce the transmission of Covid-19. The birdsong that seems more dramatic and intense than before the traffic subsided. The colours of the trees as the spring light bounces off and filters through the leaves no longer surrounded by a misty haze of pollution (now suggested through its absence). And of course the smell of the coffee hitting our olfactory senses.

Superscript and subscript

Before this period of social distancing and self-isolation, I had been preparing for another in the series of Coffee & Science evenings at Amoret coffee in Notting Hill. The title of the evening had been “Space Coffee” and we were going to explore the connections between what happened in your coffee cup with features that you can see in the atmospheres of planets such as Saturn and Jupiter. Actually the connections are a lot wider than that and can be seen on the Earth too, but the atmospheres of Jupiter and Saturn have some very peculiar structures that you may not immediately think could possibly be linked to your coffee cup. One of the key people who worked on the science behind this was Hermann von Helmholtz (known as H2 to his friendsa). For the Coffee & Science evening, the important work of Helmholtz was on vortices and fluid rotations, but it turns out that he has more links with a coffee cup than that, connections that can even give us some food (drink?) for thought in this time of separation.

which will win, gravity or light
The world has not really been turned upside down, but certainly the way that we view it could be. An opportunity to re-assess our view points?
Superscript and subscript

Helmholtz made many contributions to the understanding of our world including how we see it. In addition to inventing the ophthalmoscope (in ~1850), Helmholtz was interested in the way in which we perceive colour and how we manage to see in 3D. Thinking about the way in which we see things like light and colour and developing on the idea that how we perceive our world is, ultimately, received in each of our own minds via our sense organs, Helmholtz compared the sensations of light and colour to symbols of language: ways in which we interpret the world around us. As Michel Meulders writes in his fascinating biography of Helmholtz (told from the view point of a medical doctor rather than a physicist)b, Helmholtz had

“…stated lyrically that we should thank our senses, which miraculously gave us light and colour as responses to particular vibrations and odour and taste from chemical stimuli. We should thank the symbols by which our senses informed us of the outside world for the spell-binding richness and the living freshness of the sensory world.”

Superscript and subscript

What does it mean that I should thank my senses for the way in which I smell, see and hear the coffee beans as they are ground?

Superscript and subscript

The connections between Hermann von Helmholtz and coffee are more than just the vortices that form, and more than the fact that Michael Faraday once served him cups of it while he was preparing lectures for the Royal Institutionc. We’ll be exploring those links over the next few weeks, from how we see coffee, through how we hear it and eventually to what ties it all together. Please keep checking back but also, do let me know what new sensory symbols you have perceived in this time of opportunity to attention.

Superscript and subscript

a “Worlds of Flow”, Olivier Darrigol, Oxford University Press (2005)

Superscript and subscript

b “Helmholtz: from Englightenment to Neuroscience”, Michel Meulders, MIT press (2010)

Superscript and subscript

c “Helmholtz and the British Scientific Elite: from force conservation to energy conservation”, David Cahan, Notes & Records of the Royal Society, 66, 55-68 (2012) doi:10.1098/rsnr.2011.0044

Which direction? At Jacob the Angel, Neal’s Yard

Jacob the Angel, coffee Covent Garden
It is easy to miss Jacob the Angel as you enter Neal’s Yard, but an angel above the hoarding gives it away.

Jacob the Angel is tucked into Neal’s Yard in London’s Covent Garden. Named after Thomas Neale (1641-1699), Neal’s Yard is part of his development which is now known as Seven Dials. And rather like the larger 17th century development, this cafe-physics review of Jacob the Angel has a similar dilemma: so many avenues to explore, each wrestling for attention, which one to pursue?

But first the coffee. Roasted by Square Mile, coffee is available as the usual espresso based drinks or on V60 pour over. I had a Rwandan V60 that was full bodied and full of treacle like flavours. Owing to the geometry of the cafe, I didn’t get to check my ‘flavour notes’ against what the tasting notes thought I should perceive. The cafe space itself is fairly small but with a surprising amount of seating. Given this, it can feel a bit close as you squeeze past some of the people sitting down in order to place your order, (hence not double checking the tasting notes) however that is quickly set aside as you can gaze at the large selection of cakes (all with allergens clearly marked) arrayed on the counter.

On the walls of the cafe were paragraphs about the history of coffee and how a man named Jacob opened Britain’s first Coffee House in 1651 at the Angel Inn (in Oxford). The coffee itself came presented in a manner that was reminiscent of solar eclipses, while the sink next to our table was strikingly similar to those in my A-level chemistry lab. Unable to dissociate my memories of the sink with the reality of the environment at Jacob the Angel, it was a bit shocking when someone came to fill their glass of tap water there – don’t they realise what could have been in that sink?! Each thought train surfacing as a potential direction for the review, but then, above me, something moved. Looking up it was clear that a plant that was hooked to the ceiling was moving in a draught, but where was the breeze coming from? A small air-conditioning/heater unit was on the other side of the coffee house, circulating the air that was moving the plants.

plants, Jacob the Angel, Coffee Covent Garden
Plants above the tables at Jacob the Angel. How do they move in the breeze?

The moving plant had appeared to my peripheral vision as if it was floating in the breeze or perhaps flying. Now clearly there cannot be a flying plant, but in some ways the swaying leaves do illustrate the fluidity of air, which is a necessity for flight. The moving air demonstrates how the air imparts a force to the leaves (and the pot) causing them to sway. For things that genuinely fly this would be experienced as ‘drag’ – something that we have probably all experienced, even when not flying. Drag is increased if the object moving through the fluid (air) has a larger surface area perpendicular to the direction of movement: all being equal, bigger objects experience more drag. Imagine moving a spoon through coffee, it is easier to move a stirring stick rather than a tablespoon. But then, drag also depends in a non-trivial way on the shape of the object and how that changes the vortex wake behind it (look again at the spoon and how the vortices form behind it as it is dragged through coffee, you do not see those so easily with a stirring stick).

It is partly this sort of shape effect that seems to be behind Orsted’s recent restatement of the calculation of the amount of energy that their off shore wind farms can generate. By actually going out and measuring the air flow around the off shore wind farms, Orsted discovered that the air flow (which would be used to generate power) is affected not just by the individual windmill (as had been known and calculated), but its neighbours and the way these combine into the shape of the wind farm. There is still a lot we don’t understand about exactly how spoons move through coffee.

vortices in coffee
Vortices behind a spoon dragged through coffee.

But there is also a connection to a different type of “flying machine” if only through the name of the coffee house. For it was from the Angel Inn in (what is now) Aldwych that, more than 250 years ago, that an unusual ‘flight’ took place*. It was described in an advertisement in the paper:

“On Monday, the 5th of April 1762, will set out from the Angel Inn behind St Clements Church in the Strand…. a neat flying machine, carrying four passengers, on steel springs and sets out at four o’clock in the morning, and goes to Salisbury the same evening, and returns from Salisbury the next morning at the same hour… Each passenger to pay 23 shillings for their fare, and to be allowed 14lb weight baggage”.

How many more avenues could be followed while enjoying a slow coffee at this small but fascinating little cafe? Do let me know what you ‘see’ next time you visit.

Jacob the Angel is in Neal’s Yard, Seven Dials, London.

*”London Coffee Houses” by Bryant Lillywhite, pub. 1963

Time standing still at VCR, Kuala Lumpur

VCR chalkboard

A trip down memory lane via a new cafe. VCR in Bangsar, KL

One of the first science-based talks I gave was about how VCR tapes worked. Depending on how you viewed it (and whether you had to listen), this was either an achievement given that I was at school and didn’t really understand magnetism nor magnetoresistive devices, or a thing to be suffered through (for much the same reasons). So when I learned that a new café called VCR had opened in Bangsar in Kuala Lumpur, it prompted a series of fond (and a few embarrassing) memories.

Moving on, it is clear that this second branch of VCR (the first is in Pudu, in the main part of KL), aims to provoke such memories of times past. From the name of the wifi to the pulleys behind the counter and the wooden screen at the back of the café, various details around the café pull your memory in different directions. However the coffee is very much in the present. With three types of coffee available to try as a pour over as well as the standard espresso based drinks, this café has a lot to offer. The coffee is roasted by VCR themselves in their Pudu branch. There is also an extensive food menu with an interesting Chawan mushi as well as an intricate avocado toast (topped with pomegranate seeds, toasted quinoa and feta).

coffee at VCR Bangsar

Coffee and pour over jug. But is the number 68 or 89?

The friendly baristas were happy to advise on which coffee to match with which brewing device (though there seemed a marked preference for V60s on the days I visited). In total I tried 4 pour-overs, one with the Kalita Wave and the others by V60. These coffees were all excellent but very different. A couple were fruity, one was sweet and full bodied, one reminded me a bit of the local fruit durian, not I hasten to add because of its taste, but because the aroma from the cup was so different from the flavour of the drink. It was a great privilege to be able to try these different coffees consecutively and to really experience the variety of flavours in coffee. Great care was taken while making the pour over before it was brought over to the table, together with a jug of water, it also seemed to me that the baristas kept a discreet eye on me afterwards to ensure I enjoyed the coffee. So it was a good experience to have had the opportunity both to enjoy one of those pour overs and to observe the people and the surroundings of VCR when I had to wait for 1 hour for someone with no phone and no book. If you get the opportunity to do this I would very much recommend it. Find a comfortable café, order a coffee and then sit, without distractions, and watch what your mind notices and where it wanders for an hour.

An obvious place for a mind to wander would be to the mechanism of tape recording (and why mini-disks are the superior recording medium for the elegance of the physics involved). However, in an hour a mind wanders far further than the name. Supporting the cakes (and a display case for the 2nd place award of the brewers cup), was a table with a concertina type decoration around its edge. Was this a nod to the Kalita Wave brewing device? This is a significant difference between the V60 and the Kalita Wave: the ridges (or wave pattern) on the filter of the latter. How does coffee flow past these ridges? Does this difference in flow dynamics make a difference to the taste of the coffee?

variables grind size, pour rate, pour vorticity

It seems that there would be a lot of physics to observe in the fluid flow in a Kalita Wave filter.

A few weeks previously a friend had made a (lovely) coffee with her Kalita Wave. It was interesting to note the different dose of coffee she used and the way the grinds built up in the ridges (compared with my ‘normal’ V60). Why do the grinds end up in the ridges? Why is there a layer of dust on the blades of a fan? Why do some corners of a building collect more dust or leaves than others? Are these questions related and does it change the flavour of the coffee in the Kalita?

In fact, there are many subtleties in understanding how fluids move around solid objects. One of these is that at the interface of the fluid with the solid, the fluid does not flow at all, there is a stationary layer. Known as a boundary layer or Prandtl boundary layer (after the person who first suggested their existence, Ludwig Prandtl), realising these layers existed revolutionised the field of aerodynamics. The problem had been how to model the drag experienced by a solid object in a fluid flow. Although perhaps only of academic interest in terms of the flow of coffee around a Kalita filter or a spoon, by the end of the nineteenth century and particularly, with the invention of airplanes, how to calculate fluid (i.e air) flow around a solid (i.e. wing) object became very important for practical reasons.

vortices, turbulence, coffee cup physics, coffee cup science

Another cool consequence of boundary layers:
Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player).

Prandtl introduced the concept of a boundary layer in 1904. The idea allowed physicists to treat the main body of the moving fluid separately to the layer, very close to the solid, that was dominated by friction with the solid. This meant that the Navier-Stokes equations (that are used to describe fluid flow and ordinarily do not have an analytical solution) are simplified for this boundary layer and can be quantitatively solved. Although simple, by the 1920s Prandtl’s layer (and consequently the solvable equations) were being used to quantitatively predict the skin friction drag produced by airplanes and airships.

The boundary layer allows us to understand how vortices form behind cylinders or around the corners of buildings. I suspect a mix of the boundary layer, turbulence caused by the coffee going over many of the ridges and the brick like stacking/jamming of the coffee grains would combine to explain the difference in the grind shape around the Kalita Wave and the V60 filters. What this does to the flavour of the coffee and whether better brewing would involve more agitation, I will leave to Kalita Wave coffee lovers to investigate. And when you do, I would love to hear of your results, either here on Facebook or Twitter.

 

On rings, knots, myths and coffee

vortices in coffee

Vortices behind a spoon dragged through coffee.

Dragging a spoon through coffee (or tea) has got to remain one of the easiest ways to see, and play with, vortices. Changing the way that you pull the spoon through the coffee, you can make the vortices travel at different speeds and watch as they bounce off the sides of the cup. This type of vortex can be seen whenever one object (such as the spoon) pulls through a fluid (such as the coffee). Examples could be the whirlwinds behind buses (and trains), the whirlpools around the pillars of bridges in rivers and the high winds around chimneys that has led some chimneys to collapse.

Yet there is another type of vortex that you can make, and play with, in coffee. A type of vortex that has been associated with the legends of sailors, supernovae and atomic theory. If you add milk to your coffee, you may have been making these vortices each time you prepare your brew and yet, perhaps you’ve never noticed them. They are the vortex rings. Unlike the vortices behind a spoon, to see these vortex rings we do not pull one object through another one. Instead we push one fluid (such as milk) through another fluid (the coffee).

It is said that there used to be a sailor’s legend: If it was slightly choppy out at sea, the waves could be calmed by a rain shower. One person who heard this legend and decided to investigate whether there was any substance to it was Osborne Reynolds (1842-1912). Loading a tank with water and then floating a layer of dyed water on top of that, he dripped water into the tank and watched as the coloured fluid curled up in on itself forming doughnut shapes that then sank through the tank. The dripping water was creating vortex rings as it entered the tank. You can replicate his experiment in your cup of coffee, though it is easier to see it in a glass of water, (see the video below for a how-to).

Reynolds reasoned that the vortices took energy out of the waves on the surface of the water and so in that way calmed the choppy waves. As with Benjamin Franklin’s oil on water experiment, it’s another instance where a sailor’s myth led to an experimental discovery.

chimney, coffeecupscience, everydayphysics, coffee cup science, vortex

In high winds, vortices around chimneys can cause them to collapse. The spiral around the chimney helps to reduce these problem vortices.

Another physicist was interested in these vortex rings for an entirely different reason. William Thomson, better known as Lord Kelvin, proposed an early model of atoms that explained certain aspects of the developing field of atomic spectroscopy. Different elements were known to absorb (or emit) light at different frequencies (or equivalently energies). These energies acted as a ‘fingerprint’ that could be used to identify the elements. Indeed, helium, which was until that point unknown on Earth, was discovered by measuring the light emission from the Sun (Helios) and noting an unusual set of emission frequencies. Kelvin proposed that the elements behaved this way as each element was formed of atoms which were actually vortex rings in the ether. Different elements were made by different arrangements of vortex ring, perhaps two tied together or even three interlocking rings. The simplest atom may be merely a ring, a different element may have atoms made of figure of eights or of linked vortex rings. For more about Kelvin’s vortex atom theory click here.

Kelvin’s atomic theory fell by the way side but not before it contributed to ideas on the mathematics (and physics) of knots. And lest it be thought that this is just an interesting bit of physics history, the idea has had a bit of a resurgence recently. It has been proposed that peculiar magnetic structures that can be found in some materials (and which show potential as data storage devices), may work through being knotted in the same sort of vortex rings that Kelvin proposed and that Reynolds saw.

And that you can find in a cup of coffee, if you just add milk.

 

Reading tea leaves with Einstein and my great-grandmother

tea pot science

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

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

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

Thames, NASA image

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

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

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

adaptation from Einsteins paper

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

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

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

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

 

 

 

Stirring up some climate science

Everything is connected. At least, that is part of the premise of Bean Thinking, where the physics of a coffee cup is used to explore the physics of the wider world. So it was great to stumble upon a new connection that I had not previously appreciated¹.

vortices in coffee

Like the vortices behind a spoon dragged through coffee….

The connection is between climate science and that wonderful pastime of pulling a spoon through coffee and watching the vortices form behind it. Yet the research that revealed this connection was not looking for links between coffee and the atmosphere. Instead the researchers were interested in something seemingly (and hopefully) very far from a coffee cup: rogue waves.

Rogue waves are rare and extremely large waves that have been the subject of mariners tales for many years. Nonetheless, it is only relatively recently that they have become the subject of scientific research, partly because they are so rare and so outside our usual experience that they were thought to be the stuff of myth rather than of science. So it is only now that we are developing an understanding of how it can be that, in amongst a number of smaller waves, a massive wave of 20m height can suddenly appear, apparently out of nowhere. One of the groups looking at this problem investigated the effect of a particular sort of (known) instability on a series of waves in water. However, unlike other research groups, this particular study included the effect of the air above the water as well as the waves themselves.

Small waves seen from Lindisfarne

Rogue waves seem to come out of nowhere. A rogue wave can be 2 or 3 times the height of the other waves in the water at the time. How and why do they form?

Although this sounds a simple idea, modelling water waves in air is actually extremely complex. To do so, the authors of the study had to use a computer simulation of the air-water interface. It is not the sort of problem that can be solved analytically, instead the computer has to crunch through the numerical solutions. In order to start to see what was going on with the rogue waves, the authors had to simulate multiple waves of different amplitudes. Each simulation took weeks to perform. Given that this was only a few years ago (the study was published in 2013), you can start to see why people had previously been approximating water waves as waves in water (without worrying too much about the air interface).

Now here is where the link with coffee comes in. The group modelled waves as a function of steepness and found that, above a critical steepness, the wave breaking caused significant interaction between the air and the water layers. In addition to the bubbles that form when waves break, the movement of the air over the breaking wave formed into a vortex which, when it interacted with the back of the wave created an opposite vortex: a vortex dipole “much like the vortices that form behind a spoon dragged through a cup of coffee“.

Rayleigh Benard cells in clouds

The water droplets that form clouds are often ‘seeded’ by particles of salt or dust, such as the aerosols distributed by the vortices in this wave study. Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Just as with the vortices in the coffee cup, vortices were forming in the air behind the wave crest (which acted as the spoon) and travelled upwards through the atmosphere and away from the waves. As each wave broke, a train of vortex dipoles were produced that twirled off into the sky. Imagine a coffee bath and multiple spoons rather than a coffee cup. The authors suggested that these vortices could carry aerosols from the sea (salt, water droplets etc) into the atmosphere. Travelling within the vortices, these tiny particles could travel far further and far higher than we may have expected otherwise. Such aerosols can be critical for cloud formation and so the effect of these breaking waves could be important for climate modelling.

While an undergraduate, I had an opportunity to study a course in atmospheric physics. I remember the lecturer lamenting that while we (as a community, but not really as the students sitting in the lecture theatre at that time) understood atmospheric modelling quite well and that we understood how to model the oceans fairly well, we got problems when we tried to put the two sets of models together. It was clear that something wasn’t quite right. Years later, it seems that at least past of the reason for that is linked to those vortices that you see as you pull your spoon through your coffee cup.

Everything is connected indeed.

A summary of the study can be found here. The abstract (and link to the pdf) of the published paper can be found here. If you do not have access to the journal through a library, an early, but free, version of the paper is here – note though that this version may not include the amendments included after peer review.

 

¹A quote attributed to Jean-Baptiste Biot (1774-1862), is perhaps relevant here “Nothing is so easy to see than what has been found yesterday, and nothing more difficult than what will be found tomorrow.”

Reflections on physics and coffee

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

reflections, surface tension

Reflections on a coffee.

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

 

 

 

layering of coffee long black

Layers of coffee

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

 

interference patterns on coffee

Bubbles in coffee

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

 

 

Coffee, Van Gogh

Art in a coffee cup

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

 

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

 

Coffee Damping

vortices in coffee

Vortices behind a tea spoon

How often do you allow yourself to get bored? Or to sit in a cafe and take your time to enjoy your coffee properly, noticing its appearance, the smell ‘landscape’ of the cafe, pausing while you absorb the sounds of the cafe and playing with the feel of the coffee while you create vortices with your tea spoon?

If you regularly drink black coffee, you may have noticed how these vortices form more easily in the coffee once the crema has dispersed. Intuitively this may seem obvious to you, perhaps you wouldn’t even bother trying to form these vortices in a cappuccino, you’d know that they wouldn’t appear. The bubbles of the crema (or the milk in the cappuccino) quickly kill any vortex that forms behind the tea spoon (we’d technically call it ‘damping’ them). But even when we are aware of this, it is still surprising just how quickly the crema stops those vortices. Try forming a couple of vortices in a region of black coffee close to a region of crema. Indeed I thoroughly recommend ordering a good black coffee in a great cafe somewhere and just sitting playing with these vortices all the while noticing how their behaviour changes as the crema disperses.

latte art, flat white art

Latte art at The Corner One. Lovely to look at but not good for the vortices.

The damping caused by bubbles on the surface of a coffee is responsible for another phenomenon that you may have encountered in a cafe but, to be fair, are more likely to have noticed in a pub. Have you ever noticed that you are less likely to spill your cappuccino between the bar and your seat than you are your lovingly prepared filter coffee? Or perhaps, in the pub, you can get your pint of Guinness back to the table more easily than your cup of tea? (At least for the first pint of Guinness)

Back in 2014, a team investigated the damping properties of foam by controlling the size and number of bubbles on top of a liquid as it was vibrated (sloshed) about. They found that just five layers of bubbles on top of the liquid was enough to significantly damp the liquid movement as it vibrated from side to side. That is, five layers of bubbles suppressed the sloshing (try saying that after a couple of pints of Guinness). Much as I dislike emphasising the utility of a piece of science, this work has obvious implications for any application that requires the transportation of liquids such as the transport of oil containers. There is an obvious need to suppress the effect of liquid oil sloshing from side to side as it is transported by boat for example.

The foam on our latte or crema on our long black should indeed give us pause for thought as we sit in a cafe enjoying our coffee.

 

 

Seeing the trees for the wood at OJO Coffee, Bangsar, KL

coffees on display at OJO

OJO Coffee, Bangsar, Kuala Lumpur

It is very easy to sit for a long time watching the people and the surroundings at OJO Coffee in Bangsar, Kuala Lumpur. Initially I had thought that this medium-sized café with an impressive number of power points dotted around it was an independent. However similarities with CoffeaCoffee around the corner and a couple of other clues (CoffeaCoffee t-shirts) suggest that it is actually part of the CoffeaCoffee chain, something that was confirmed when I asked the barista. However, the standard of coffee in this chain should prompt some of the smaller independents to up their game a bit (and certainly all of the UK based chains). Not content with just serving the typical coffees of ‘latte’, ‘cappuccino’ etc. (which are made using their own blend), OJO’s additionally serves about 15 types of single origin coffee made with your choice of method (Hario V60, Aeropress or French press). For a while this summer I became a bit of a regular at OJO and so I would particularly recommend the Indonesian Sumatran prepared by V60, but with so many coffees to choose from (from the relatively local Indonesians to South American coffees from much further afield) there is plenty to try at this café.

wooden mosaic

The wall made of wood at OJO

The interior of OJOs is decorated with many types of wood. Different cuts of wood are made into a sort of wood mosaic on the wall while the tables are made using several types of wood so as to give a symbolism about the Sun that is a type of motif of the café. Much of the floor is wood too and so this got me thinking about the rainforests in this country. Malaysia has a rich variety of wildlife and forest, it is home to the Orangutan as well as many other species. Teak trees that can be used for more expensive furniture grow along the roadside. Much of this timber can be obtained sustainably and in a way that respects the rainforest and I am certainly not suggesting that the wood in OJOs was anything but sustainable. However, perhaps inevitably, there are many pressures on these invaluable forests. Some of these pressures have, in the recent past, resulted in significant deforestation. One such pressure is that of palm oil.

Palm oil is a massively useful commodity. It is now used in food products from margarine to biscuits to raisins (surprising but true, check the ingredients list of a packet of raisins) and non-food products such as soaps. It is literally everywhere. Both Malaysia and its neighbour, Indonesia, have profited enormously from growing and exporting palm oil. Unfortunately, at times the rainforest is cleared to make way for the palm oil plantations. As it is easier to burn felled trees to clear the land rather than to painstakingly pull the roots up by hand, the cleared forest is burned. But the ground is not any ordinary soil, the ground is often peat based which means that the fires on the surface penetrate deep below the ground and produce phenomenal amounts of smoke.

If at this point you were wondering where the ‘physics’ bit of this café-physics review is, I assure you it is coming. It is indeed linked to this environmental story and to OJOs, please keep with me.

Each year, parts of Malaysia, Singapore and Indonesia are enveloped by a haze produced by this burning peat land (It made the BBC in 2013 when it was particularly bad, but some haze is present for a few weeks every year). Haze has the appearance of thick fog but smells of smoke. At times, visibility can be reduced such that the tops of nearby tall buildings are obscured. Each time land needs clearing for new palm oil plantations, this smoke is produced. The haze can be reduced by local weather patterns but on many days, the haze is cleared by the torrential rains that can occur in this part of the world.

the haze is coming in

L-R: The haze comes in over part of KL in 2013 (series of 3 pictures)

It is commonly said that ‘rain clears the air’ but this is not completely true. It is not the raindrops themselves that somehow wash the air free of the dust of the haze, it is the vortices that form behind them*. Just as a spoon dragged through coffee produces vortices behind it, so a raindrop falling through the air forms vortices in its wake. The size of these vortices will depend on the size of the drop and the speed at which it falls through the air; a tea spoon and a dessert spoon pulled at different speeds through the coffee similarly produce different forms of vortex. So the amount of dust that is ‘sucked in’ and falls to the ground will depend on the type of rain that falls. Perhaps if you are in Malaysia, Singapore or Indonesia when this haze is present, you could make a study of which sort of rain clears the air most effectively. I have an idea but not the evidence to see if the idea is correct, it would be interesting to know what you think.

As I left OJO one afternoon, the rain had started to come down. The rain, or at least the vortices behind the raindrops, cleared some of the haze that had been around earlier. It is a temporary solution to a longstanding problem. A more long lasting solution may be to start (or continue) asking manufacturers of those biscuits you are eating: just how sustainable is the palm oil they are using?

OJO is at No 23, Jalan Telawi 3, KL

* JR Saylor and BK Jones, Physics of Fluids, 17, 031706 (2005)