wave particle duality

(Im)perfect reflections on coffee

science in a V60

Have you noticed droplets like these dancing on your drip-brewed coffee?

With the recent coffees from Hundred House and Quarter Horse, there have been many opportunities to observe the coffee brewing in the V60 in the mornings. The steam rising from the filter paper, the different ways different coffees bloom and out-gas, the droplets that skim the surface of the coffee and bounce off the walls of the jug and then, of course, the many different effects with light. Watching the dancing droplets (an explanation of why they may dance is here), it is perhaps not immediately obvious that you could form a connection between these, the light reflections and an insight into something you may have noticed while passing through customs. And yet the connection is definitely there.

The connection is formed through a technique called Raman spectroscopy. Named after Chandrasekhara Venkata Raman (1888-1970) who discovered the Raman effect in 1928. As the ‘spectroscopy’ part of the name suggests, it is a technique that offers a way to identify different chemicals, or components, in a substance. For coffee it has been used both as a non-destructive technique to determine the kahweol content of coffee beans and hence help as a test for identifying rogue robusta in arabica beans and as a way of analysing the brewed coffee. But what is it, how does watching a brewing V60 help to understand it and why would you want to know about Raman spectroscopy while travelling through an airport?

beauty in a coffee, coffee beauty

A collection of bubbles on the side of the coffee. What happens when one of the dancing droplets collides with a group of bubbles?

Generally, it helps to begin with coffee and the link is the way in which the droplets bounce off the side of the jug. Brew a coffee and watch them (if you are a non-coffee drinker, you could try dripping hot water through a filter paper into a jug). When one of these droplets hits the wall of the V60 container, it generally bounces back with a trajectory expected for an elastic collision. Given the relative masses of the droplet and the jug, the speed of the reflected droplet is essentially unchanged (even if its direction is reversed). This is similar to what we would normally expect for light. We are used to considering light as waves but because of the wave-particle duality of quantum mechanics it is equally valid to consider light as a stream of particles called photons. As the photons hit a surface and are reflected off, they recoil with the same energy that they initially had, just like the droplets in the coffee. But now look more closely at the dancing droplets. Normally they hit the walls and not each other but just occasionally, they can hit either another droplet or a group of bubbles that have formed on the coffee surface. In these cases, rather than get reflected as before, the droplets transfer some of their energy to the collection of bubbles causing them to move and to wobble. And when the droplet is reflected back, it has a noticeably slower speed (and so we could say a lower kinetic energy) than when it initially danced into its collision. Where is the analogue with light?

When we think about a coffee bean, we probably think about something that is about 1cm oval, brown and quite solid. But if we zoom in, we find that it is made up of a collection of atoms bound together in molecules or, if we are thinking about a solid like salt, in a crystal structure. These atoms act as if they are balls connected by springs and so they wobble as would any structure of masses connected by springs. This is true whether the crystal is diamond or the molecule is caffeine, kahweol, cocaine or semtex (do you see where the customs part is going to come in yet?). Different crystal structures have different atomic arrangements meaning that they are effectively connected by springs of differing strength. If you build a mental model of masses connected with springs, you can see that changing the spring strength will change the vibration energy of the structure. So if now we think about the photons hitting such a structure, while most will bounce off as we saw with the droplet hitting the V60 wall, some photons will trigger a wobble in the crystal structure and bounce off with lower energy. It is a process analogous to the droplet hitting and bouncing off the collection of bubbles on the coffee surface.

Sun-dog, Sun dog

Sun dogs are caused by a different interaction between light and crystals. Rather than the inelastic scattering of Raman spectroscopy, Sun dogs are caused by the refraction of light by hexagonal platelets of ice crystals.

When a photon of light loses energy, it is equivalent to saying that the frequency of the light has changed (which is very closely related to what Albert Einstein got his Nobel prize for in 1921). So a photon that creates a crystal vibration and is scattered off with lower energy has a lower frequency (or longer wavelength) than it had when it first hit the crystal. Importantly, the energy lost by the photon is identical to the energy gained by the vibrating crystal and so by measuring the frequency change of the scattered light we have a way of determining the energy of the crystal (or molecule) vibration. As this energy depends on the way that the atoms are arranged in the crystal or molecule, measuring the frequency shift offers us a way of identifying the chemical under the laser light: kahweol or cocaine.

It is not an easy technique as you can guess from the V60 analogy. Only around one in a million photons incident on a solid will be Raman scattered. You need some pretty decent optics to detect it. Nonetheless, it is a powerful technique because no two chemical structures are the same and so it can be used to identify tiny amounts of smuggled material completely non-destructively. It becomes easier to understand how this elegant technique has become useful for many areas of our lives from customs, through to pharmaceutical development and even into understanding how fuel cells work.

Although it is stretching the analogy too far to say that you can see Raman scattering by watching the droplets on your V60, it is certainly fair to say that watching them allows you the space to think about what is happening on a more microscopic level as your bag is hand-scanned at customs. What do you see when you look closely at your brewing coffee?

 

Coffee and cream baubles – not just for Christmas

floating, bouncing drops

Drops of water can be stable on the water’s surface for many minutes if you put the water on a loudspeaker, more info on how to create these at home here.

You may have noticed them before: balls of liquid dancing on the surface of your coffee (or tea) that seem to last for ages before being absorbed into the drink? Perhaps you have added milk to your coffee and noticed that it took some time before the milk entered into the brew?

It turns out, there’s some very interesting physics that is happening whenever you add milk to your tea or when you are preparing a pour-over. It can link coffee to wine and to quantum mechanics. It is worth taking a closer look at these drops.

You may remember that you could use a loud speaker to make droplets of coffee bounce on a cup of the same. The vibrations in the cup meant that the air between the droplet and the drink never got squeezed out of the space between them. So, rather than coalesce, the drop jumped up and down on the coffee surface before finally disappearing under. This type of bouncing bauble has been shown to behave in similar ways to quantum particles in wave-particle duality. An analogue of quantum physics in the macroscopic droplets on the surface of your drink.

But that type of bauble required the use of a loud speaker (or some similar way of generating vibrations on the surface of the coffee). What if you could ‘bounce’ a drop of coffee on a cup of coffee without any external props like speakers? Well, it turns out that you can. In November 2017 a group of researchers showed how a temperature difference between a drop falling into a drink and the drink itself could result in the drop appearing to float on the surface of the drink for many seconds. The obvious example was cold milk into a cup of coffee (or tea). But I think that it may also happen in a V60 when you prepare a pour over, more on that below.

science in a V60

Bubbles of liquid dancing on the surface of a brewing coffee.

The idea is quite simple. If there is a temperature difference between the drop and the coffee, when the drop approaches the coffee, there will be thermal gradients across the drop/cup system. Surface tension is temperature dependent: the higher the temperature, the weaker the surface tension. Differences in surface tension across the surface of a liquid result in compensating liquid flows (one of the best places to see this is in a glass of wine, but there’s also a great party-trick experiment you can do to demonstrate it which is here). So, because there is a temperature difference across the surface area of the droplet (owing to the difference between the droplet and the cup), there will be liquid flows set up within the drop. These flows are like circulating vortices which draw the surrounding air into the gap between the drop and the cup and so prevent the existing air between the drop and the cup from escaping. If the air has nowhere to escape to, the drop can’t merge with the drink, in fact it ‘levitates’ for a number of seconds.

The authors suggest that this is a reason that you can often see rain drops staying on the top of puddles or ponds before being subsumed into the water, or why you can see the cream (or milk) stay as globules on the surface of your coffee (or tea). And so I wonder, could this also be the explanation for an odd phenomenon that I sometimes notice while brewing coffee in my V60. Perhaps you have seen this too? After some time, the new drops of filtered coffee impacting on the surface skit along to the edge of the jug. They stay as balls of coffee on the coffee’s surface for quite some time before becoming part of the brew. You can see a photo of some of these droplets above. Initially I thought that this was because the surface of the coffee had started to vibrate with the impacting droplets. But it is also possible that it could be this temperature effect. As the (brewed) coffee in the jug would be cooler than the water dripping into it from the filter, there would be a temperature difference between the droplet and the coffee but the reverse of the milk-coffee situation. The drop would be warmer than the coffee it’s dripping into. The authors of the study suggested that it was the magnitude of the temperature difference that was the key, not the sign of the temperature difference. So that would fit with the V60 observations seen previously. However how would you show which effect (vibration or temperature difference) is responsible for the behaviour?

Enjoy playing with your tea, coffee and V60s. Do let me know the results of your experiments. Is it a vibration thing or does the temperature difference have to be there to begin with? Let me know what you think is going on.

I am also grateful to Amoret Coffee for alerting me to this story in the first place through Twitter. If you come across some interesting coffee-science, please let me know, either here in the comments section (moderated, please be patient), or on Twitter or Facebook.

 

 

 

Coffee, chaos and computing

Have you ever noticed drops of coffee skipping across the surface of your coffee as you have been preparing a V60? Or watched as globules of tea dance on the resonating surface of a take-away dragged across a table top? The dancing drops can be seen in this video of coffee being prepared in a V60:

These droplets are the result of some fascinating physics. Although we have encountered them on the Daily Grind before (here and here), the more physicists study them, the more surprises they throw up. While the droplets can be considered particles, they are guided around the coffee pot by the surface waves they create as they bounce. In a sense they are a macroscopic example of wave-particle coexistence. There is a significant temptation to explore whether they have relevance for the concept in quantum physics of wave-particle duality. But another aspect of this wave-particle coexistence has recently been shown to produce a different and unexpected connection. A connection between chaos and computing. And as you can create these droplets in coffee, perhaps we could say a connection between coffee, chaos and computing.

floating, bouncing drops

Drops of water can be stable on the water’s surface for much longer than 1 minute if you put the water on a loudspeaker, more info on how to create these at home here.

It is fairly simple to create these surface droplets in coffee at home. The secret to getting stable droplets on the surface is to create a vibration, a wave, on the surface of the coffee liquid. The droplets that then form on (or are introduced to) the surface ‘bounce’ on this wave. If you wanted to create surface droplets reliably at home, you would put your coffee on a loud speaker. I suspect that the reason that they appear in a V60 is that the first drops set up a standing wave on the surface of the coffee that acts to support later drops as they encounter the surface. If anyone has a different theory, please do let me know.

But how is it possible that these bouncing droplets connect chaos theory and computing? It is a consequence of the way that the globules of coffee on the surface interact with the waves that guide them around the coffee. Consider for one moment a particle bouncing around a confined space (the traditional example is of a ball on a billiards table). On an ordinary table, the billiard ball will behave quite predictably, start it off aimed roughly at the side of the table and it will bounce in an easily describable way. But if you make the ends curved or put circular objects in the middle of the table for the ball to bounce off, small differences in initial direction can result in large differences in the final path of the ball (for more details and an animation see here). The billiard ball behaves chaotically, and the initial path cannot be found from the final position, there is no way to re-trace the path of the ball, it is not “time-reversible”.

science in a V60

A still from the video above showing three drops of coffee on the surface.

The droplet bouncing on the liquid surface appears to move chaotically, just as the billiard ball on a circular table. However, unlike the billiard ball, the droplet is not a mere particle, but a particle linked to a self-generated surface wave. Each time the droplet bounces on the surface, it creates a small wave, like ripples on a pond. The path taken by the droplet is a complex interaction between this self-generated wave, the vibration keeping the droplet bouncing and the droplet itself. This means that if you are able to shift the phase of the bounce by 180º (meaning, that rather than bounce on an upward motion of the surface, the drop bounces on a downward motion or vice versa), the bouncing droplet not only reverses the direction it travels in, it retraces its path. Rather than behave as the chaotic billiard ball, the path taken by the seemingly chaotic globule of coffee can be exactly reversed.

Which is where the link with computing comes in. It is as if each “bounce” of the droplet “writes” information on the surface of the coffee in the form of a wave. The subsequent bounces “read” the information while the reversal of the direction of the bouncing droplet “erases” the stored information by creating a surface wave opposite to the initial one. The authors of the recent paper suggest that “in that sense [the walking droplet can] be termed as a wave Turing machine”, giving the final link to computing.

Whether or not this turns out to be useful for computing is, to me, almost irrelevant. What is interesting is that such a simple phenomenon, that anyone who makes pour-over coffee should have seen fairly often, is linked to such complex, and fundamental physics. If you would like to read more, there is a great summary article here while the actual paper is here.

 

Bouncing Coffee

floating, bouncing drops

Water droplets ‘floating’ on a bath of water (actually they bounce rather than float).

Perhaps you remember the video about how to ‘float’ coffee droplets on water posted on the Daily Grind a few weeks ago? The video featured an experiment that you could do at home in which droplets of water (or coffee, or even, if you were feeling adventurous, tea) could be made to stay as spherical droplets on the surface of a shallow dish of water for minutes at a time. Of course there were a few tricks: The water had soap added to it (10ml of soap to 100ml of water) and the shallow dish was on a loudspeaker which was playing music at the time. The whole experiment was very pretty. But hopefully as well as appreciating the aesthetics, you were asking ‘how’ and ‘why’? Why does the addition of soap mean that these globules of liquid appear to float on the liquid surface? And is the rumour you have heard about a connection with quantum physics true?

Well it turns out that people have known about these floating droplets for over a hundred years but why they behave as they do is still being investigated. It is another case of cutting-edge science appearing in your coffee cup*. So it’s worth taking a look at what is going on and why we needed to add soap and vibration for the droplets to remain stable on the water surface.

lilies on water, rain on a pond, droplets

When it rains, the rain drops don’t float on the pond

It seems to appeal to common sense and to everyday experience that if we drop a droplet onto a bath of water, the droplet will merge with the water and become part of the bath. After all, when we bring two drops that we have dripped on a table close to each other, at a certain distance between the two drops, they appear to touch and then rapidly merge into one big droplet (try it). And when it rains onto a pond, we don’t see lots of spherical droplets hovering over the surface of the pond! We know that it is the attractive van der Waals forces that bring the two drops together and then the effects of surface tension that minimise the surface area of the drops so that they become one big drop. So how is it that we can get a droplet to remain, as a droplet, on the surface of a bath of water?

How to bounce water droplets on a water surface

It could be said that the answer can be pulled out of thin air: Before the drops can merge, the air that separates them has to escape from the area between the droplet and the water bath. If the droplet can somehow be made to bounce back upwards before the air separating the droplet from the bath becomes thin enough for the two liquids to combine, the air could be made into a cushion to keep pushing the droplet upwards. This is why the experiment needs to be done with a vibrating dish of water, each time the surface vibrates upwards it is providing the drop with an acceleration upwards that overcomes gravity, like a miniature trampoline: The droplet is not floating, it is bouncing.

So why soap? We all know that the addition of soap decreases the surface tension of the water. But that is not why the addition of soap helps to stabilise the drops in this instance. No, soap has another effect and that is to increase the surface viscosity (and surface elasticity) of the water. Think about the air between the droplet and the dish. As the droplet bounces down (ie. the distance between droplet and water becomes a minimum), the air gets squeezed out of the layer between the droplet and the bath. On the other hand, as the droplet reaches its peak height, air will rush into the gap between the drop and the bath. If the liquid is not very viscous (eg. water), as the air rushes in (or gets squeezed out), it will combine with the liquid and form a turbulent layer on the surface of the droplet. If the viscosity is increased, the air cannot ‘entrain’ the liquid as the droplet bounces and so the drop keeps its shape more easily and is more stable. Soap increases the surface viscosity of the droplet and so helps with this effect. However soap also increases the surface elasticity and makes it harder for the air to flow out of the layer separating the drop from the bath. It is because soap does multiple things to the water (or coffee) that more recent studies have focussed on liquids with controllable viscosity but minimal surfactant effects, i.e. silicone oils. It is just that if you want it to work with coffee, it is easier to add the soap to get the experiment to work.

An “un-cut” video of coffee on water shows how tricky it can be to actually get these drops to be stable on the surface of the water.

Which leaves the quantum link. The experiment shown in the videos show single droplets (or droplet patterns) stabilised by vibrations caused by music. If instead of music you use fixed frequencies to excite resonances through the speakers, it is possible to get the droplet to resonate in a controlled way and, at a certain point, it will move. As the droplet moves, it appears to be guided by the vibrations of the liquid underneath the drop, it is a particle guided by a ‘pilot wave’. It turns out that such walking droplets show behaviour reminiscent of the ‘wave particle duality‘ found in quantum physics where particles (such as electrons and other sub-atomic particles) can be described both as particles and as waves. You can find a video describing the similarities between these bouncing droplets and quantum effects here.

 

* Ok, so you may not want to add soap to your coffee to see this effect but actually I first observed it in a milky tea. Adding milk to the coffee/tea would increase its viscosity which makes the observation of the bouncing droplets more likely. The ‘milk’ used in the video was actually soya milk which did not appear to increase the viscosity sufficiently to allow the droplets to bounce on the surface without soap.