Tag: experiments on your kitchen work top

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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

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Latte Art

Latte art scutoid tulip
The physics of bubbles. What links latte art to the shape of cells as an embryo develops?

An odd one out competition: which of the following is not a type of latte art? Tulip, heart, swan or scutoid? You may well ask, “what on earth is a scutoid?” and so identify this as the odd one out and, to some extent you would be right. Scutoids are not a type of latte art. But I would wager that you can still occasionally see them in your coffee.

Twitter can be a great thing and I was recently alerted there to a New York Times article about Karen Uhlenbeck by @Bob_Mat_Phys. Uhlenbeck is a mathematician at the University of Texas who has just won the Abel Prize in mathematics for her work on the maths of bubbles. The article was fascinating in itself but also mentioned in the article was the fact that there may be, on occasion, a connection between a cup of coffee and the cell structures seen in foetal development. And while I’m very well aware of the extraordinary number of connections that can be made between coffee and the science of the everyday world, I’ll admit, that one surprised me.

Metal jug and transparent glass
More bubbles in your coffee. But what determines their shape? And what shape are they?

By this point you may be unsurprised to hear that the connection is made via the scutoids, but what are they? A new type of shape, they were first described in a Nature Communications article about the development of cells as organisms such as fruit flies grew. Scutoids formed as the embryonic cells grew to form tubes or egg shapes. On one surface of the tube the cell was contacting a different number of cells to that which it contacted on the other surface (so perhaps the cell looked like a pentagon on the top and a hexagon on the bottom). In order for the cell to do this, it formed a further triangular face along one side of the cell and it is this cellular shape that is the scutoid.

Where is the connection with a coffee? Well, the amazing thing is that this shape can be the result of the physics that determines the shape of bubbles, in this case when they are confined between two curved surfaces, such as two cylinders. The shape of a bubble is the result of the minimisation of the surface energy of the bubble. So, in free space, the bubble will be spherical but somehow squash bubbles into a box and you can form a cube shaped bubble in the middle of the box. The shapes that form are the result of the minimum surface energy of the bubble surface. Now, if we return to the curved surfaces and the scutoids. The idea is that if there is a single layer of bubbles between two curved surfaces and that these surfaces are then moved away from each other, the bubbles will first resemble prisms and then, as the surfaces are stretched further, some bubbles will form a prism shape but with a triangular surface at one of the bounding walls: a scutoid.

latte art by Mace, Eiffel Tower and hot air balloon
It is astonishing what you can see in a coffee when you look closely enough.

The paper that showed this (published in Philosophical Transactions but you can read the full version here) combined mathematical modelling of the minimisation of surface energy with experiments involving two cylinders and some soap suds. They then photographed the resultant bubble structures. The results suggest that the minimisation of energy (ie. the physics of the bubble shape) could be a first approximation for explaining the cell structures that form in foetal development. But can you see them in your coffee?

You would need a coffee mug or French press and a smaller cylinder that fits neatly inside it. You would then need to form a foam somehow. Soap suds are obvious, some form of milk texturing would be more interesting. You can then look closely and see, can you in fact see scutoids in your latte art?

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General Home experiments Observations Science history slow Tea

A tense moment for a coffee…

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

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

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

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

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

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

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

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

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

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

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

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

 

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

²Reference to the kitchen is here.

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General Observations slow

The impact of water on coffee

lilies on water, rain on a pond, droplets
What is the crater shape produced by falling droplets of water on freshly ground coffee?

Recently there has been considerable discussion about the impact of water on the taste of your coffee. Although this is interesting not only from a chemistry perspective, but also an experimental design and an environmental one, Bean Thinking is probably not the best place to explore such effects of chemistry on coffee taste. If you are interested, there is a recent article about it in Caffeine Magazine, click here. Instead, on Bean Thinking, the idea would be to go a little more fundamental and ask instead what is the impact of water on coffee? What effect does dripping water have on the craters produced in freshly roasted coffee grinds?

You may have noticed craters produced by rain drops on sand or paused while preparing your drip brew to think about the different ways that water percolates through a filter compared to an espresso puck. But have you stopped to consider what determines the shape of the crater that is produced as a falling droplet impacts a loose bed of granular material (such as coffee). Perhaps you have looked at images of the Chicxulub crater on the Yucatan peninsula and wondered about asteroid impacts on the Earth or craters on the Moon but what about something closer to home? What if the impacting object were liquid and the impact surface more sand like? It’s a problem that affects how rain is absorbed by soil as well as the manufacture of many drugs in the pharmaceutical industry. But it is also something that we could experiment with in coffee. Is there a difference between craters formed in espresso pucks compared to those in the coffee in the filter paper of a V60?

bloom on a v60
Bubbles in a V60 filter – but what is the impact of individual drops of water on the dry grains of coffee? The ultimate in slow coffee.

Recently, a study appeared in Physical Review E that investigated the crater shapes produced by water droplets on a bed of dry glass beads (imitating sand). The effect of the impact speed of the water droplet as well as the packing density of the granular bed (sand/coffee) was studied. A high speed camera (10 000fps) was used in combination with a laser to reveal how the shape of the craters changed with time, from the initial impact right through until the crater was stable. The authors came up with a mathematical model to consider how the energy of the falling droplet was distributed between the impacting drop and the sand bed. Does the droplet of water deform first or does the energy of the impact go into displacing the sand and so forming the crater?

Perhaps unsurprisingly, when drops of water fell onto dense beds of sand (think espresso pucks but not quite so packed), the craters produced were quite shallow. It would take a lot of energy to displace the densely packed sand but not quite so much to deform the droplet. But when the drops fell onto looser sand beds (think drip brew coffee) the crater produced formed in two stages and depended on the velocity of impact. A deep crater was formed as the drop first impacted the sand. Then as the camera rolled, the sides of the crater started to avalanche producing much wider craters that had different shapes in profile (from doughnut to pancake type structures). For looser beds of sand, the faster the impacting drop, the wider the final crater. You can read a summary of the study here.

So what would happen for craters produced during making an espresso compared to those produced making a drip brew? A first approximation would be that the espresso coffee is more densely packed, so the craters should be shallower and less wide than those produced in the loose packed filter coffee. However then we need to think that the water used in making espresso is forced through the puck with high energy. In contrast, in drip brewing techniques, the water used has a lower impact energy, (it could be said that the clue is in the name). So the energy of the impact would form larger craters in the espresso pucks and smaller craters in the drip brewers, an opposite expectation from that of the packing densities, which effect wins?

coffee ground in a candle holder
Early experiments with coffee grind craters: There are advantages to working with glass beads and high speed cameras.

But is there anything else? Grind size! Espressos are made using finely ground coffee beans, with a typical “grain size” being about 10μm (0.01mm). Drip brewed coffee is somewhat coarser, a typical medium grind being compared to grains of sand (which vary between 0.05-2mm, 50 – 2000μm but we’d expect ‘medium’ ground coffee to be at the lower end of that). This is fairly similar to the ‘sand’ used in the study in Phys Rev E which used grains of size 70-110 μm. A slightly earlier study had shown how the crater shape depended on grain size for ‘sand’ ranging from 98 to 257 μm. That study had revealed that how the water interacted with the different grain sizes depended in turn on whether those grains were hydrophilic (wettable) or hydrophobic (water proof). It is probably safe to assume that the coffee used in an espresso grind has the same hydrophilic properties as the coffee used in drip brew but even so, we still have those three variables to contend with, packing density, impact energy and grind size. So, happy experimenting! Let’s find out how the impact craters left in coffee change with preparation method. And whatever else, it’s a perfect excuse (if one were really needed) to drink more coffee while slowing down and properly appreciating it.

With thanks to Dr Rianne de Jong for pointing me in some interesting directions (not all of which fitted in this piece) towards the interaction of water with coffee, more coming soon I hope.

 

 

Categories
Home experiments Observations slow

Something brewing in my V60

kettle, V60, spout, pourover, v60 preparation
The new V60 “power kettle”

It was my birthday a short while ago and someone who knows me well got me a perfect present: a kettle specially adapted for making pour-over V60 style coffees. Until this point I had been struggling with a normal kettle with it’s large spout but now, I can dream that I pour like a barista. Of course, it is important to try out your birthday present as soon as you receive it. And then try it again, and again, just to make sure that it does really make a difference to your coffee. So it is fair to say, that recently I have been enjoying some very good coffees prepared with a variety of lovely beans from Roasting House and my new V60/V60 kettle combination.

Spending the time to prepare a good coffee seems to make it even more enjoyable (though it turns out that whether you agree with this partly depends on why you are drinking coffee). Grinding the beans, rinsing the filter, warming the pot, the whole process taken slowly adds to the experience. But then, while watching the coffee drip through the filter one day, I saw a coffee drop dance over the surface of the coffee. Then another one, and another, a whole load of dancing droplets (video below). Perhaps some readers of Bean Thinking may remember a few months back a similar story of bouncing droplets on soapy water. In that case, fairly large drops of water (up to about 1cm wide) were made to ‘float’ on the surface of a dish of water that had been placed on a loudspeaker.

Sadly, for that initial experiment the coffee had been made undrinkable by adding soap to it. The soap had the effect of increasing the surface viscosity of the droplets which meant that the drop could bounce back from the vibrating water surface before it recombined with the liquid. Adding soap to the coffee meant that these liquid drops could ‘float’ (they actually bounce) on the water for many minutes or even longer (for more of the physics behind this click here).

science in a V60
A still from the video above showing three drops of coffee on the surface.

On the face of it, there are some similarities between the drops dancing on the coffee in my V60 and these bouncing droplets. As each drop falls from the filter, it creates a vibration on the surface of the coffee. The vibration wave is then reflected back at the edges of the V60 and when the next drop falls from the filter it is ‘bounced’ back up by the vibration of the coffee.

But there are also significant differences. Firstly, as mentioned, there was no soap added to this coffee (I was brewing it to drink it!). This means that the viscosity of the drops should be similar to that of ordinary water. Although water drops can be made to bounce, the reduced viscosity means that this is less likely. Secondly, the water is hot. This acts to reduce the viscosity still further (think of honey on hot toast). Perhaps other effects (such as an evaporation flux or similar) could be having an effect, but it is noticeable that although the drops “live” long enough to be caught on camera, they are not very stable. Could it be that the vibrations caused by the droplets hitting the coffee are indeed enough to bounce the incoming droplets back up but that, unlike the soapy-water, these “anti-bubbles” do not survive for very long? Or is something deeper at play? I admit that I do not know. So, over to you out there. If you are taking time to make coffee in a V60, why not keep an eye out for these bouncing droplets and then do some experiments with them. Do you think that the bounce vibration is enough to sustain the bouncing droplet – does the speed of pour make a difference? Is it associated with the heat of the coffee? I’d be interested to hear what you think.

(The original soapy-coffee bouncing droplet video).

If you see anything interesting or odd in your coffee, why not let me know, either here in the comments section below, e-mail, or over on Twitter or on Facebook.