molecular reality

On mountains, molecules and coffee

A tea plantation in the mountains of the Cameron Highlands, Malaysia. But how high would you need to climb in order to boil water at the perfect temperature to prepare your brew?
A tea plantation in the mountains of the Cameron Highlands, Malaysia. But how high would you need to climb in order to boil water at the perfect temperature to prepare your brew?

Walking in the hills or, if you are lucky, the mountains, we can easily be reminded that atmospheric pressure decreases with height. We just have to look at the way that the plastic water bottles we may be carrying have been crushed, or open a yoghurt pot slightly too close to our face. We may remember that the boiling point of water decreases with decreasing atmospheric pressure and so that a kettle boils more quickly at the top of a mountain than at the bottom. But how high would we need to climb to make a perfect cup of coffee with just-boiled water? And what has this to do with the reality, or not, of molecules?

Although the effect appears obvious to us, it is not trivial to calculate exactly how the atmospheric pressure varies with height. To see why, we could think about what pressure is. The pressure exerted by a gas on an object is proportional to the number of gas molecules colliding with and recoiling from the object concerned. These collisions create a force on the object and pressure is just force ÷ area. So why would this change with height?

Small waves seen from Lindisfarne
Think about a layer of air with air pressure above and below it but further acted on by gravity pulling it down. What happens?

Think about a layer of air. Above it, the molecules in the gas are exerting a pressure, pushing down on the air. Below it, there are molecules pushing upwards and keeping it up. But there is one more force that we need to consider: gravity. In physics, we like to think of things in equilibrium, perfectly balanced. So when we think about our layer of air, the forces acting down on the layer of air (the pressure from above and the gravity of the earth) have to be perfectly compensated by the force acting up, i.e. the pressure from below. If this were not the case, the layer of air would sink. Perhaps it is starting to become clearer, why the density of the atmosphere decreases with height. The only thing that remains is to work out exactly how it does it.

And while we could do the calculation here, it has (fortunately) already been done for us by a remarkable physicist called Jean Perrin back in 1910. He was remarkable not just because of the detail of his experiments but also because of the connections he made.

“It appeared to me at first intuitively [that]…. Just as the air is more dense at sea-level than on a mountain top, so the granules of an emulsion, whatever may be their initial distribution, will attain a permanent state where the concentration will go on diminishing as a function of the height from the lower layers and the law of rarefaction will be the same as for the air.”

Jean Perrin, Brownian Movement and Molecular Reality, 1910
coffee at Watch House
In search of the perfect coffee. How far would you travel?

Perrin realised that to calculate the balance of forces acting on our imagined layer of air, one has to assume molecules exist, just as we have done above but something that was not obvious at the turn of the 20th century. But he also realised that this calculation would be the same for any fluid containing a suspension of particles whether that was the atmosphere or a drop of water colour paint. Assuming that the molecules exist allows us, and allowed Perrin, to make quantitative predictions for the variation of pressure with height or, in Perrin’s case, the variation of the number of granules in an emulsion with depth. Perrin considered a paint pigment suspended in water under the microscope, but his theory is also valid for the (non-soluble) matter in coffee. The fact that these quantitative predictions matched so extraordinarily well with the experimental observations of thousands of water droplets containing suspended paint pigment (the poor PhD students of Jean Perrin!) went a long way to proving the existence of molecules. Hence Perrin’s book “Molecular Reality” and the ceasefire in a philosophical disagreement about whether physics should seek to understand what was happening or merely describe phenomena such as pressure (but that’s another story).

Which takes us back to how to brew coffee properly. Calculating the variation of pressure with height is the first part of the problem. The second is calculating what that means for the boiling point of water, which actually is done by extrapolating from experimental data. But it does mean that we can calculate, for a small range of temperatures near 100C, the altitude at which you would need to boil a kettle for the boiling temperature to be identical with the optimum brewing temperature for your drink. Listed below are a few recommended mountains on which you can prepare your drink of choice. I will leave it to someone else to calculate the energy saving (and hence the saving in CO2 equivalent emissions) of boiling your kettle on top of a mountain rather than in your kitchen. We’ll assume that there’s electricity on top of Mont Blanc.

Drink – Recommended brew temperature – Equivalent Altitude – Suggested mountain

Coffee – 93.3 C* – 2000 m – Kebnekaise (Sweden),

Coffee – 96 C** – 1000 m – Any of the Scottish Munroes

Oolong tea – 87.8 – 93.3 C*** – upwards of 2000m – Mont Blanc (France) could be good

Pu’er tea – 93 – 100C| – why leave your living room?

*Coffee Detective

**The Kitchn/Blackbear coffee

***The Spruceeats

|The tea leaf journal

Time out

Perhaps an unusual post but there is so much opportunity to stop, think and notice at the moment. Whether it is relaxing in a café with a cold brew or sipping a take-away in a park. There is time to slow down and ponder. Here are three points that have been puzzling recently. What do you think? Perhaps you have other things that you ponder while sitting in a café? Let me know either in the comments section below, on twitter or on Facebook.

oat milk, kone, filtering

Oat milk filtering through the Kone filter – but what does oat milk tell us about Brownian motion, molecular ‘reality’ and the nature of a scientific theory?

Molecules, the atmosphere and oat milk.

On pouring home-made oat milk into a cup of black tea, it is noticeable that a large part of the oat milk is dense and falls to the bottom of the cup (before being stirred by the turbulence in the tea). A similar phenomenon is found in the rarefaction of gases through the height of the atmosphere and in the distribution of dye in water paint. This latter effect was used to establish the existence of molecules back in 1910. The idea that Brownian motion was caused by molecules had been problematic because there was no way to see molecules in a liquid producing the Brownian motion. The theory linking the two was only developed properly in the early twentieth century. What makes a scientific theory? Is it legitimate to postulate something that cannot currently be observed experimentally?

Packing value

Why does roasted coffee often come in plastic packaging that is unrecyclable and not very reusable? What could prompt a move to a more circular economy. Would it be possible to recycle plastic bottles into coffee ‘boxes’ with an air valve at the bottle top (see pictures). This would increase the recyclability without seeming to affect the taste of the coffee?

bottle, coffee bottle, coffee box, coffee packaging

An idea for a circular economy suitable coffee packaging? Recycled plastic bottles as airtight coffee containers.

Related to that, what are your coffee values? Do you favour taste and aroma, traceability, sustainability? Does the packaging that your coffee arrives in feature? Which of these is more important to you? Does the way you drink coffee reflect this?

Footfall past a café

How many people are walking past the café you are sitting in each minute? How many does that translate to per day (accounting for differences in day/night footfall)? Assuming the paving stones remain the same, how long would it be until the successive footprints of all these people caused erosion of the pavement surface? What are the implications of this for the geological features near you?

Whatever you think about in a café or while drinking a coffee, enjoy your time taken out to think. Perhaps you will notice something (or realise something) very interesting or noteworthy and if you have any thoughts on any of the above do let me know either in the comments, on Twitter or on Facebook.


Molecular reality at the Turkish Deli, Borough

Just as the air is more dense at sea-level than on a mountain top, so the granules of an emulsion, whatever may be their initial distribution, will attain a permanent state where the concentration will go on diminishing as a function of the height from the lower layers, and the law of rarefaction will be the same as for the air” (Jean Perrin)

Turkish Deli, Turkish Coffee

The Turkish Deli, Borough Market

I have long had a fascination for the history of coffee and the different styles of brew. So it should be no surprise that I went to try The Turkish Deli in Borough Market for the Daily Grind. Very close to Monmouth, the Turkish Deli serves Turkish-style coffee and a delicious looking array of Turkish delights. Although quite far from the brew bars and single estate coffee types of some cafés now in London, Turkish coffee nonetheless offers the opportunity to slow down and appreciate the moment. Perhaps even more so than an espresso, since you are forced to wait for the coffee to be ready. The coffee is presented to you, straight from the Ibrik, in a small cup with a fantastic looking crema on top of it. At this point you are told that you will have to let it settle for at least four minutes before even thinking about starting to drink it. Indeed, the person in front of me in the queue was advised that he could “sit down, watch the world go by” while waiting for the crema on the coffee to turn a very dark (black) colour, indicating that the coffee was finally ready.

before settling, Turkish coffee

Waiting for the coffee to be ready

If you take sugar in your coffee you have to add it right at the start, before the coffee is warmed to the point of boiling (though it is not boiled). The reason is fairly obvious if you think about it. Turkish coffee has a large amount of sediment, this is the reason that you need to leave it for four minutes for the sediment to ‘settle’. Adding sugar during this settling time would mean that you would need to stir the coffee which would disturb the sediment and prevent it from quickly settling. Instead, you either take your coffee sugar-less or you add your sugar before starting this settling process.

Jean Perrin, (author of the quote at the start of this week’s Daily Grind) used the gradient of sediment in a different liquid (gamboge – a bright yellow paint pigment) to confirm the existence of molecules, just over one hundred years ago. He was exploring Brownian motion, the seemingly random motion of bits of dust, sediment etc, on the top of the coffee cup which had been explained in terms of “molecules” in the coffee (or water, or paint), hitting the bits of dust on the surface. Jean Perrin (1870-1942), realised that if Brownian motion was being caused by molecules, they would not just be causing the movement of the dust (and sediment) on the surface, it would be a three dimensional effect. Measuring the gradient of sedimentation would be a way to prove the molecular theory of Brownian motion and, simultaneously, to prove the existence of molecules.

Turkish coffee

The surface of the coffee reminded me of a coastline, itself connected (mathematically) to Brownian motion

Imagine a bit of sediment in the middle of the liquid (it could be a Turkish coffee, for Perrin it was the paint). That piece of sediment is going to be pulled down by gravity but in addition, it is going to be pushed up by molecules from below and down by molecules in layers above it. This is the bit that is related to Brownian motion. We know that even after leaving it for a long time, much of the sediment is still suspended mid-way up in the cup. It follows that the total forces acting downwards on the sediment (from gravity and the molecules above it) must be the same as the total force acting upwards (from the molecules below).

This means that the mass of sediment held at any particular level in the coffee must decrease with height. If the size of each piece of sediment is identical (which was ensured by Jean Perrin in his paint but is not the case for the Turkish coffee), then the number of pieces of sediment held aloft in the coffee/paint would decrease with height from the bottom to the top. All Perrin had to do therefore was to count (with a microscope) the number of bits of sediment as a function of height in order to test whether the molecular theory for Brownian motion was correct.

Turkish coffee, Borough market, sedimentary, sedimentation

The sediment at the bottom of the cup, don’t drink this bit!

To obtain statistics, Perrin and his assistants would count 11000 particles in one emulsion and repeat this experiment 1000s of times, but his patience paid off. By 1910, (only a few years after starting his observations), Perrin could claim that “the molecular theory of the Brownian movement can be regarded as experimentally established, and, at the same time, it becomes very difficult to deny the objective reality of molecules”. In 1926 he received the Nobel prize in recognition of this work.

Returning to the coffee, it is a very good drink with which to slow down and watch the world go by, perhaps while pondering molecular reality. When you get towards the bottom, do not drink the sediment but do take time to appreciate the mouthfeel and flavour as you drink this beverage that, in many ways represents an early chapter in the coffee story and one that continues to be made very well at the Turkish Deli.

The Turkish Deli is in Borough Market, Stoney Street, London, SE1 9AA

Quotes taken from “Brownian Movement and Molecular Reality”, Jean Perrin, 1910