The universe in a cup of coffee

black coffee, Vagabond, Highbury
The universe in a cup of coffee, but how much can we take this literally?

When people ask, what is Bean Thinking about, they often get the reply, it’s about “the universe in a cup of coffee”*. And it is perfectly true, much of the physics of the coffee cup is mirrored by the physics of the universe: you could think about the Black body radiation and the Cosmic Microwave Background, or the steam from the cup and cloud formation, but what about General Relativity? Could it really be that physics such as that of General Relativity mirrored in a coffee cup?

It could, perhaps, initially appear a ludicrous idea. Einstein’s theory of General Relativity explains the gravitational attractions of massive objects such as stars and planets through the curvature of space-time. And although what occurs on the planetary scale must also be valid on the scale of the coffee cup, we would surely expect classical, Newtonian physics to dominate here. But that would be to neglect the equally ludicrously named “Cheerios effect” and a paper that was published in Nature Communications earlier this month.

The cheerios effect is the phenomenon that you may have noticed on your tea or coffee whereby two floating objects on the surface are attracted to each other (and named after observations of the effect in a breakfast bowl). Two bits of a dropped biscuit come together or two bubbles bounce to form a pair. The effect occurs because both objects dent the surface of the drink by bending the surface of the liquid through surface tension effects. Consequently, the two objects don’t float on a flat coffee surface but a curved one and when they get close enough together, the surface tension effects bring the objects together into one big indentation rather than two smaller ones.

You can see surface tension effects from the curvature of the coffee around the edge of a cup. It is also visible around objects that float on top of the coffee.

On the face of it, this has similarities with the ‘cartoon version’ (or schematic) of the idea of gravity in general relativity. Each massive object (ie. any object with mass) bends the space-time around it, the more massive an object, the more the space-time is bent. This has the effect of seeming to bend light and leads to gravitational attraction. And yet there are very many differences. A liquid surface is 2D, planets clearly move in at least 4D, the way the surface bends owing to surface tension is surely not the same as the way that space time bends owing to its distortion through massive objects. It could go on only it turns out that some of the maths is quite similar: the surface is distorted proportional to the mass of the object in a cup of coffee, the attraction between the objects is a product of both masses (as it is with gravity). Indeed, it has even been proposed that studying the cheerios effect could be a way of gaining insight into some of the problems of general relativity. But there was always a catch: Friction.

On the surface of a coffee, although the floating object is bending the surface proportional to its mass, it is in some sense in contact with the fluid. When the object moves, there is a frictional resistance to the movement caused by the object’s interaction with the coffee. This makes it quite different from the situation in space. And so you would have been correct in your suspicion that general relativity would not be easily found in a coffee cup, but only for reasons of friction.

Which is where the recent Nature Communications paper comes in. Rather than float objects on coffee, the researchers floated silicone oil droplets on liquid nitrogen. Being a liquid, the nitrogen is subject to surface tension effects just like coffee, but being a very cold liquid (196 C below freezing point), it shows a second effect when the (room temperature, ie. warm) oil droplets are floated onto it: the inverse Leidenfrost effect.

Coffee, Van Gogh
What do you see in your coffee cup?

Again, you may have seen the Leidenfrost effect while frying eggs (or tofu if you’re vegan). When the frying pan is very hot, drops of water sprinkled into the pan will immediately vaporise in the layer between the pan and the droplet causing the drop to dance around the pan as if it is flying. The inverse Leidenfrost effect is, perhaps unsurprisingly, the inverse of this. When the liquid is very cold and a hot object is introduced to its surface it will instantaneously vaporise meaning that the hot object on the surface will skip over the cold liquid, without friction.

The reason that this is relevant to the idea of general relativity in a coffee cup is that this bending of the surface of the liquid nitrogen, coupled with the inverse Leidenfrost effect effectively levitating the drops means that you have a warped liquid surface, like the bending of space-time, but the floating object moves with absolutely no friction, because there is no contact between it and the liquid beneath. Clever.

And so what happens when you introduce two droplets to the nitrogen surface? How do they interact? Well, they attract each other and can even orbit each other like planets until, as the friction effects start to grow even in this system, the drops cease behaving as planets and can collide. It is a fascinating observation but one with relevance to biological self-organisation rather than an immediate extension to general relativity. That will be for another study, perhaps one with super-cold brew coffee.

So, the universe in a cup of coffee? Perhaps. But sometimes not strictly literally.

You can read the paper in Nature Communications here (it’s open access), or the summary in Physics.Org here.

*With suitable acknowledgement of the Feynman anecdote that you can see here.

Counting the caloric at Jaz & Jul’s Chocolate House, Chapel Market

Jaz Jules chocolate house

Jaz and Jul’s, The Chocolate House on Chapel Market

The London coffee houses of the seventeenth and eighteenth centuries have entered history as Penny Universities, places of debate and centres of news. Together with the (scientifically based) Grecian, there was Jonathan’s in Exchange Alley (origin of the stock exchange) and Lloyd’s on Tower Street (associated with insurance). But along side these coffee houses there were the chocolate houses, Whites and Ozinda’s on St James’ St and the Cocoa Tree in Pall Mall. White’s in particular developed such a reputation that it features in Hogarth’s The Rake’s Progress (which can be seen at Sir John Soane’s museum).

So it is an interesting bit of history repeating to find Jaz & Jul’s, a chocolate house on Chapel Market. The interior here is very far from Hogarth’s rendering of White’s. Here, light fittings hang from the ceiling like drops of chocolate about to melt into the café while photographs of cocoa plants and farms adorn the walls. Moreover the emphasis on social responsibility, including in sourcing, mean that this establishment is worlds away from the debauched shenanigans at White’s. Their coffee is roasted and supplied by Monmouth while the cakes are hand made and, needless to say, very chocolatey. The light and fluffy chocolate-Pimms cake arrived with my coffee presented on a plate and matching cup that reminded me of a mint-chocolate-chip ice cream.

Interior of Jaz and Jules Chapel Market

The chocolate counter at Jaz and Jul’s

The side of the counter was tiled to resemble a bar of chocolate, which immediately reminded me of the physics and chemistry of chocolate crystallisation. However, the physics connection of this cafe-physics review is a bit more lateral than that. Soon after I had enjoyed my incredibly chocolatey cake at Jaz & Jul’s, a study was released which showed that Britons were significantly under-reporting their daily calorie intake. Could it be that the obesity epidemic is a result of us eating too much rather than merely exercising too little? Apparently, rather than consume the (recommended) levels of 2500 kcal for men and 2000 kcal for women, many people were eating up to 3000 calories per day. Everything in moderation of course and there was plenty of room in my own calorie count for that great piece of cake (honestly). But the word ‘calorie’ turns out to have a connection with chocolate in a more unexpected way.

Calorie comes from the Latin, calor, meaning heat which in turn hints at how we used to think about heat itself. While we now think of heat as energy, which is why it doesn’t even strike us to equate the ‘energy’ in the chocolate cake with the number of kilo-calories in it, this is not how heat was always viewed. In fact, in the eighteenth century, about the time of the old chocolate houses, heat was thought of as a type of fluid, caloric. Caloric was thought to be able to flow in and out of all substances. When something got hot it was because the caloric flowed into it, when something got cold, it was because the caloric had leaked out. Caloric theory was in many ways very successful in understanding heat and heat processes. For example, the theory easily explained thermal expansion, if a fluid had to flow into something in order for that thing to warm up, then surely, the fluid has to occupy some space, the object must expand to hold it!

Mint choc chip cutlery

Coffee with the Chocolate-Pimms cake.

One area that was tricky for caloric theory though was the fact that friction could cause something to heat up. Such heat generation is crucial for our extraction of chocolate. Once harvested from the plant and cleaned, the cocoa bean is first roasted then shelled to leave the cocoa ‘nibs’. These nibs are then ground more finely. As they are being ground, the friction caused by grinding is enough to cause sufficient heat to melt the cocoa butter in the nibs which is then extracted and retained for later use*. How could you explain this heating if you thought of heat as a fluid? The traditional explanation was that as the two objects rubbed against each other (in this case, nib and stone grinder), the caloric fluid would be squeezed out, it would appear as if heat had been generated.

Benjamin Thompson, Count Rumford (1753-1814), disagreed with this explanation of heat. In the course of a colourful career he had been involved in manufacturing cannons in Bavaria. Rumford had noticed that a lot of heat was generated each time a cannon shaft was bored out. The heat produced continued as long as the grinding continued. If the heat were due to the cannon leaking caloric, surely there would be a point at which the cannon stopped getting any hotter. Yet this did not happen. Rumford suggested (correctly) that instead what was happening was that the energy generated by the boring was being transferred into the metal of the cannon, causing microscopic motion.

Although the heat as motion/energy idea eventually caught on, caloric in some ways still survives in the name that we give to our food energy intake. And so we can return to the cake, could it be that spending time thinking about the caloric in the cake can justify the calories consumed eating it? Sadly the jury is out on whether thinking counts as calorie counting exercise. It seems that the brain’s energy consumption is already so great (at 20% of our resting metabolic rate), that intense thinking does not add too much to the energy consumed by the brain. So we’ll need another excuse and I don’t think we have to look far. The coffee and chocolate at Jaz & Jul’s is delicious enough to justify a significant chunk of your daily calorie count, just based on considerations of taste. Everything in moderation!


Jaz and Jul’s is at 1 Chapel Market, N1 9EZ

*”Chocolate: A Global History”, by Sarah Moss and Alexander Badenoch, published by Reaktion Books, 2009


Grass or clay at Brickwood, Clapham

coffee Clapham common

Weather for Wimbledon? It was raining when we tried Brickwood in Clapham

It was raining heavily as we met friends for coffee at Brickwood, near Clapham Common, a few weeks back. Inside it was fairly crowded so we were shown to a cosy little area downstairs where we found a table. The staff were all friendly and with coffee roasted by Caravan, it was easy to sit and enjoy a great Americano while waiting for the others to arrive. Sadly, all of the cakes on the menu contained nuts (with the exception of scones). This was a shame because it was otherwise an interesting place to sit and observe the surroundings and it would have been nice to have been able to give it a ‘tick’ in the cafes with good nut knowledge box*. Still, the coffee was very good and there was plenty to observe, even in the basement.

Glancing around the room, the first thing that struck me was a white board on the wall. Taken together with the artificial lighting (necessitated by the area being in the basement), this was highly reminiscent of the maths ‘common room’ at work. A further mathematical connection comes from the fact that the grandfather of John Venn (of the Venn diagram) lived nearby. A prominent local clergyman, Venn St, just around the corner from Brickwood, is named after him. Still, that is quite a digression. There were also interesting bits of physics and science to notice in the café itself.

the 'carpet' of the floor at Brickwood

Grass or concrete? What factors control the bounce of a tennis ball.

Downstairs, the floor was covered in what appeared to be an artificial grass. This gave the whole experience of having a coffee here a bit of a surreal twist. Just as happens with real grass, a path was visible on the ‘grass’ where people had walked, something that can be used when rambling in the country to help you find your way around (when GPS or map temporarily fail you). The book “The Walker’s Guide to Outdoor Clues and Signs” gives many such details about how to navigate in the country without a map (including how to tell from trees which way is North).

However, as we are now in the second week of the Wimbledon Tennis tournament, this cafe-physics review is going to have a tennis slant instead. We could think about how different it would be were we to drop a tennis ball onto the ‘grass’ downstairs, or (what I remember to be) the wooden floor upstairs. Tennis started off as an indoor sport, played on courtyards in stately homes and monasteries. ‘Lawn tennis’, or what we now recognise as just ‘tennis’, developed in the nineteenth century and was played on grass. Thinking about how a tennis ball would  bounce on the floor in the basement or upstairs in Brickwood is therefore somehow reminiscent of the history of the sport.

whiteboard, Brickwood, Clapham

Like being in the maths common room but with better coffee and flowers

Tennis balls are designed to bounce 53-58 ” (134.6-147.3 cm) when dropped onto a concrete floor from a height of 100″ (254 cm). Other surfaces have different elasticity and/or friction. The behaviour of the ball will be quite different therefore when it bounces on different surfaces, affecting the speed (and therefore height) and even angle of the bounce (for more info on the physics click here). The different characteristics of the surfaces mean that different types of play are required to succeed on the court. To be successful across all courts (from the clay of Roland Garros to the Decoturf of the US Open and the grass of Wimbledon) requires a tennis player who can adopt many different playing styles. Would it help a tennis player to have a training in physics and an understanding of the details of aerodynamics, spin and friction that are involved as the ball whizzes through the air? Probably not. But for us mere observers who prefer eating the strawberries and cream and savouring great coffees while discussing the game, a bit of physics may perhaps add to our enjoyment.

Brickwood (Clapham) is at 16 Clapham Common South Side, SW4 7AB

*to be fair, Brickwood did have “good nut knowledge”, they knew all their cakes contained nuts. Perhaps the tag needs revising to be “nut-allergy-friendly”.