Air raising

Small waves seen from Lindisfarne

How do clouds form? How does temperature vary with altitude, and what does coffee have to do with any of it?

You put a drop of alcohol on your hand and feel your hand get cooler as the alcohol evaporates, but what has this to do with coffee, climate and physics?

Erasmus Darwin (1731-1802) was the grandfather of Charles of “Origin of the Species” fame. As a member of the Lunar Society (so-called because the members used to meet on evenings on which there was a full moon so that they could continue their discussions into the night and still see their way home) he would conduct all sorts of scientific experiments and propose various imaginative inventions. Other members of the Lunar Society included Matthew Boulton, Josiah Wedgwood and Joseph Priestley. The society was a great example of what can happen when a group of people who are interested in how things work get together and investigate things, partly just for the sake of it.

One of the things that Darwin had noticed was that when ether* evaporates from your hand, it cools it down, just as alcohol does. Darwin considered that in order to evaporate, the ether (or alcohol or even water) needed the heat that was provided by his hand, hence his hand started to feel cooler. But then he considered the corollary, if water (ether or alcohol) were to condense, would it not give off heat? He started to form an explanation of how clouds form: As moist air rises, it cools and expands until the moisture in the air starts to condense into droplets, clouds.

hole in water alcohol

There are several cool things you can notice with evaporating alcohol. Here a hole has been created in a thin layer of coffee by evaporating some gin. You can see the video of the effect here.

As with many such ideas, we can do a ‘back of the envelope’ calculation to see if Darwin could be correct, which is where we could also bring in coffee. The arabica growing regions are in the “bean belt” between 25 °N and 30 °S. In the sub-tropical region of that belt, between about 16-24°, the arabica is best grown at an altitude between 550-1100 m (1800-3600 ft). In the more equatorial regions (< 10º), the arabica is grown between 1100-1920m (3600-6300 ft). It makes sense that in the hotter, equatorial regions, the arabica needs to be grown at higher altitude so that the air is cooler, but can we calculate how much cooler it should be and then compare to how much cooler it is?

We do this by assuming that we can define a parcel of air that we will allow to rise (in our rough calculation of what is going on)¹. We assume that the parcel stays intact as it rises but that its temperature and pressure can vary as they would for an ideal gas. Assuming that the air parcel does not encounter friction as it rises (so we have a reversible process), what we are left with is that the rate of change of temperature with height (dT/dz) is given by the ratio of the gravitational acceleration (g) to the specific heat of the air at constant pressure (Cp) or, to express it mathematically:

dT/dz = -g/Cp = Γa

Γa is known as the adiabatic lapse rate and because it only depends on the gravitational acceleration and the specific heat of the gas at constant pressure (which we know/can measure), we can calculate it exactly. For dry air, the rate of change of temperature with height for an air parcel is -9.8 Kelvin/Km.

contrail, sunset

Contrails are caused by condensing water droplets behind aeroplanes.

So, a difference in mountain height of 1000 m would lead to a temperature drop of 9.8 ºC. Does this explain why coffee grows in the hills of Mexico at around 1000 m but the mountains of Columbia at around 1900 m? Not really. If you take the mountains of Columbia as an example, the average temperature at 1000 m is about 24ºC all year, but climb to 2000 m and the temperature only drops to 17-22ºC. How can we reconcile this with our calculation?

Firstly of course we have not considered microclimate and the heating effects of the sides or plateaus of the mountains together with the local weather patterns that will form in different regions of the world. But we have also missed something slightly more fundamental in our calculation, and something that will take us back to Erasmus Darwin: the air is not dry.

Specific heat is the amount of energy that is required to increase the temperature of a substance by one degree. Dry air has a different specific heat to that of air containing water vapour and so the adiabatic lapse rate (g/Cp) will be different. Additionally however we have Erasmus Darwin’s deduction from his ether: water vapour that condenses into water droplets will release heat. Condensing water vapour out of moist air will therefore affect the adiabatic lapse rate and, because there are now droplets of water in our air parcel, there will be clouds. When we calculate the temperature variation with height for water-saturated air, it is as low as 0.5 ºC/100 m (or 5 K/Km), more in keeping with the variations that we observe in the coffee growing regions†.

We have gone from having our head in the clouds and arrived back at our observations of evaporating liquids. It is fascinating what Erasmus Darwin was able to deduce about the way the world worked from what he noticed in his every-day life. Ideas that he could then either calculate, or experiment with to test. We have very varied lives and very varied approaches to coffee brewing. What will you notice? What will you deduce? How can you test it?


*ether could refer to a number of chemicals but given that Erasmus Darwin was a medical doctor, is it possible that the ether he refers to was the ether that is used as an anaesthetic?

†Though actually we still haven’t accounted for microclimate/weather patterns and so it is still very much a ‘rough’ calculation. The calculation would be far better tested by using weather balloons etc. as indeed it has been.

¹The calculation can be found in “Introduction to Atmospheric Physics”, David Andrews, Cambridge University Press



An easy way to get a halo

The other day I was talking to a primary school child about condensation, what it was, where to see it etc. So I asked,

“Do you drink coffee?”


“Do you drink tea?”


(I started to worry about the future generations). Nonetheless, I pulled out my cup of steaming coffee and pointed to the water droplets around the edge of the mug (which are very common if you haven’t warmed your cup before pouring your hot coffee into it) and noticed a sudden expression of recognition cross the child’s face.

“Like when you breathe on a mirror?”

Kettle drum at Amoret

Condensation on around the top of the jug on this V60

Yes, exactly so (and probably a much better example for a kid anyway, the problem of being an adult with a one track mind!). As the child had realised, the science in your coffee cup is connected to phenomena that occur elsewhere in the world. In the case of condensation, it occurs when the temperature of the surface onto which condensation happens is below what is called the “dew point”. Determined by the relative humidity in the environment, the dew point is the temperature below which water vapour in the air will condense into liquid water.

Of course the dew point gets its name from the dew that can form after a chilly night. Which brings us to another property of those water droplets that form around the rim of your coffee mug. Although it is not easy to see on the mug, each droplet is acting as a lens, focussing the light that falls onto it. As the surface of the mug is fairly flat, rather than form spherical droplets, the drops that form on the side of the mug are squashed hemispheres. This is not the case when dew forms on grass. Tiny hairs on the surface of the grass protrude from the leaf meaning that the water droplets form into spheres (which is, incidentally very similar to the reason that a duck is so waterproof). When the sun comes up, each sphere of water focusses the sunlight onto the grass behind it which reflects it back, right in the direction it came from.

heiligenschein, self portrait

Self-portrait with weak heiligenschein. Share your photos with me on FB or Twitter.

This means that if you stand with your back to the sun and look at your shadow on dew covered grass, you will very probably see a region of bright light surrounding your head, your heiligenschein. German for “Holy light”, heiligenschein is the effect of all of those spherical dew lenses reflecting the sunlight back towards you. You can only see the effect around your ‘anti-solar’ point (a position defined as being 180º from the Sun from the viewpoint of the observer, see here for what this means visually). This means that while you will see heilgenschein around your head, or around the shadow of the camera that you use to photograph it, you will never see the halo around someone else’s head even while they themselves can clearly see it.

I’m sure there’s some sort of metaphor there, perhaps one to contemplate next time you’re drinking a hot, steaming coffee.


Clouds in my coffee

clouds over Lindisfarne

How do clouds form?

Does your coffee appear to steam more next to a polluted road than in the countryside?

This is a question that has been bothering me for some time. Perhaps it seems an odd question and maybe it is, but it is all about how clouds form. Maybe as you read this you can glance out the window where you will see blue skies and fluffy white clouds. Each cloud consists of millions, billions, of water droplets. Indeed, according to the Met Office, just one cubic metre of a cloud contains 1 hundred million water droplets. We know something about the size of these droplets because the clouds appear white which is due to the way that particles, including water droplets, scatter sunlight. Clouds appear white because the water droplets scatter the sunlight in all directions. In contrast, the particles in a cloudless sky scatter blue light (from the Sun) more than they scatter red. Consequently, from our viewpoint, the scattered light from the clouds appears white while the sky appears blue. The sort of directionless light scattering that comes from the clouds happens when the scattering sites (ie. the water droplets) are of a size that is comparable to, or larger than, the wavelength of light. This means that the water droplets in a cloud have to be larger than about 700 nm in diameter (or approximately just less than a tenth of the size of the smallest particle in an espresso grind). The particles in the atmosphere on the other hand scatter blue light more than they scatter red light because they are smaller than the wavelength of the blue light. You can find out more about light scattering, blue skies and cloudy days, with a simple experiment involving a glass of milk, more details can be found here.

glass of milk, sky, Mie scattering

A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself

So each of the one hundred million water droplets in a cubic metre of cloud is at least about a micron in diameter. We can then estimate how many water molecules make up one droplet by dividing the mass of a droplet of this size by the mass of one water molecule. This turns out to be more than 1000 million water molecules that are needed to make up one droplet of cloud. So, 1000 million water molecules are needed for each of the 100 million drops that make up one, just one, cubic metre of cloud. These numbers are truly huge.

But can so many molecules just spontaneously form into so many water droplets? Unlike a snowball, the water droplet in a cloud cannot start very small and accumulate more water, getting larger and larger until it forms a droplet of about a micron in size. Water droplets that are much smaller than about a micron are unstable because the water molecules in the drop evaporate out of it before they get a chance to form into a cloud (precise details depend on the exact atmospheric conditions). Water droplets need to come ‘ready formed’ to make the clouds which seems unlikely. So how is it that clouds can form?

Condensation on mug in CGaF

Look carefully at the rim of the mug. Do you see the condensation?

It turns out that the water droplets form by the water condensing onto something in the atmosphere. That something could be dust, or salt or one of the many other sorts of aerosol that are floating around in our skies. Just as with a cold mug filled with hot coffee, the dust in the air gives the water molecules a cold surface onto which they can condense. This sort of water droplet can ‘snowball’ into the bigger droplets that form clouds because the water is now condensing onto something and so does not evaporate off again so easily. At the heart of each water droplet in a cloud is a bit of dust or a tiny crystal of salt. Which brings me back to my question. It is much more dusty along a polluted road  than it is in the clean air of the countryside. Is this going to be enough of an effect to affect the probability of cloud formation? Does your coffee steam more as you cross the road than when you walk through the park?

It is a question that demands an experiment (and associated video). Last year, the Met Office suggested this simple experiment for observing clouds in a bottle. Unfortunately however, I have yet to make this experiment work in a way that would allow me to test whether polluted air produces thicker clouds than cleaner air. If you have any suggestions as to a good experiment (that will work on camera!) please let me know either in the comments section, by emailing me, or on Facebook. In the meanwhile, I’d be interested to know what you think, so if you think this post is about you, please let me know.



In the Greenhouse at CoffeeGeek

Coffee Geek and Friends, Coffee Victoria

Coffee Geek and Friends

Earlier this year, a new café opened up in Victoria. Coffee Geek and Friends is located at the far end of Cardinal Place as you enter from Victoria Street. Cardinal Place is an odd sort of shopping centre, a small collection of shops with a glass roof. The building site near Coffee Geek as well as the constant stream of people rushing to and fro make Coffee Geek an ideal place to spend some time watching the world go by. Coffee is by Allpress espresso and is served in very individual mugs. Apparently there is a range of geek-ery in the cafe including a ‘centre piece’ water filter but I admit I missed that as I was too focussed on my coffee. Coffee Geek and Friends is definitely a cafe to keep in mind (along with Irish & June’s) if you need a good place to meet near Victoria Station.

It was a very humid day when I enjoyed my coffee at Coffee Geek and, because the mug had not been pre-warmed before my Americano/long black (my notes don’t specify which) was poured into it, condensation quickly formed around the rim of the mug. The condensation forms for the same reason that dew forms after a cool night: the vapour pressure of the water above the coffee (or the ground) has reached the dew point at the temperature of the mug. The lower the temperature, the lower the vapour pressure has to be for the water in the atmosphere to start condensing into liquid droplets. Hence you will often find that your coffee is more ‘steamy’ on a winter’s, rather than a summer’s day.

Condensation on mug in CGaF

Look carefully at the rim of the mug. Do you see the condensation?

Just over two hundred years ago, William Charles Wells made a study of dew. He observed the weather conditions under which dew formed. He observed on which surfaces dew collected. He noted whether the dew formed on space facing surfaces or ground facing surfaces. After several years of careful study he published his “Essay on Dew” in 1814. His work, showed that the earth radiated heat at night (when it was not being kept warm by the Sun) and therefore that space was cold. Cloud cover reduced the amount by which the ground cooled which implied that cloud cover was acting as a type of blanket for the Earth, keeping the heat trapped inside. Later calculations of the balance between the heat radiated by the Earth and the heat received by the Sun confirmed that, without some heat getting trapped by clouds and ‘greenhouse’ gases in the atmosphere, the earth would be a good 30 C cooler than it is observed to be. Although these calculations are just rough, “back of the envelope” figures, detailed calculations confirm that the Earth is in a delicate balance, heated by the Sun, cooled by radiation and kept warm (and live-able) by a layer of natural greenhouse gases. This “natural greenhouse effect” has been necessary for our development, the problem is that now we are adding yet more greenhouse gases to the atmosphere which threatens to tip the established delicate balance by a few degrees.

Cardinal Place roof, greenhouse

The roof of Cardinal Place shopping centre. A very appropriate place for a meditation on the greenhouse effect

What we now call the greenhouse effect are these extra gases, which are more efficient at trapping heat within our atmosphere. If you can imagine what has been happening over the past three hundred years or so as we have been pumping yet more of these gases into the atmosphere at an accelerated rate, we are in danger of tipping this delicate balance towards further heating of the earth. The 2015 Paris Climate Conference is being held with the aim of requiring all nations to agree to a legally binding commitment to reduce the amount of extra greenhouse gases that we emit to a level that will only result in a temperature increase of 2C. To achieve this requires all of us to work together to reduce our own ‘carbon footprint’. Each of us will have to find our own, individual ways to reduce our emissions but perhaps when we look at the condensation on the rim of our coffee cup, we could remember William Charles Wells and his essay on dew and just think, what can I do, at this moment, to reduce my carbon footprint? Maybe it could be something as simple as turning off that phone (to conserve the battery) and watching what is going on in a café instead. A small gesture but one that would be good for us as well as the earth.

Coffee Geek and Friends is at the northern end of Cardinal Place shopping centre (opposite Westminster Cathedral).

As a Coffee Geek note, I would like to just comment that my notes on Coffee Geek and Friends were written using a “linux-sure” ball point pen. Not particularly environmentally friendly but definitely quite geeky.

Levitating water

V60 from Leyas

Time to look more closely at the surface of your black coffee.

Have you ever sat watching the steam that forms above a hot Americano? Beneath the swirling steam clouds you can occasionally see patterns of a white mist that seem to hover just above the dark brew. Bean Thinking is about taking time to notice what occurs in a coffee cup and yet I admit, I had seen these mists and thought that it was something that was just associated with the evaporation of the water and that “someone”, “somewhere” had probably explained it. So it was entirely right that I was recently taken to task (collectively with others who have observed this phenomenon and taken the same attitude) for this assumption by the authors of this paper who wrote “The phenomenon that we studied here can be observed everyday and should have been noticed by many scientists, yet very few people appear to have imagined such fascinating phenomena happening in a teacup., espresso grind

The water particles in the white mist are a similar size to the smallest particles in an espresso grind. Photo courtesy of, (CC Attribution, No Derivs). The coin shown is a US nickel of diameter 21.21 mm

The authors of the study show that the white mists (these “fascinating phenomena”) are, in fact, layers of water drops that have a typical diameter of around 10 μm (which is roughly the size of the smallest particles in an espresso grind). Although the white mists exist above tea and even hot water as well as coffee, they are probably easiest to see against the black surface of the Americano.

More surprising than the fairly uniform distribution of water droplet size though is the fact that the authors of this study showed that the droplets were levitating above the coffee. Each water droplet was somehow literally hovering above the surface of the coffee at a height of between 10 – 100 μm (which is, coincidentally, roughly the particle size distribution in an espresso grind).

white mists, slow science

You can (just about) see the white mists over the surface of this cup of tea (which is a still from the video below)

One of the questions that the authors of the paper have not yet managed to answer is what is causing this levitation? Could it be the pressure of the hot coffee evaporating that keeps these particles held aloft? This would explain the observation that the mists form patterns similar to those caused by (heat) convection currents. Alternatively perhaps the droplets are charged and are kept away from the coffee by electrostatic repulsion, an explanation that is suggested by the behaviour of the droplets when near a statically charged object (eg. hair comb, balloon, try it). Perhaps the levitation is caused by the droplets spinning and inducing an air cushion under them? Why not design some experiments and try to find out. It would be great if we can drink hot black coffee in the name of science. Let me know the results of your observations in the comments section below. In the meanwhile, here is a video of the white mists in tea, enjoy your coffee:

You can read the study at: Umeki et al., Scientific Reports, 5, 8046, (2015)


Brunswick House

Brunswick House, coffee, cortado

Coffee at the Brunswick House cafe

Last Thursday, I had the opportunity to try the coffee at Brunswick House. The old building which houses this cafe/restaurant sits on the corner of a major junction two minutes walk from Vauxhall tube station and feels somewhat out of place with the buildings around it. Inside, the incongruity continues with quirky decor and bookcases stacked with all manner of titles. Coffee beans are supplied by the roasters Coleman Coffee. As it was a lunchtime, I had a very enjoyable cortado (an espresso “cut” with steamed milk in a ratio of 1:1 – 1:2) which was full of flavour but not too bitter. With friendly staff and a spacious interior, this is definitely a place to return to whenever I am next in the Vauxhall area.

However, The Daily Grind is not so much interested purely in the coffee as in the connections between what we can observe in the coffee cup and the physics of the wider world. At Brunswick House, this came in the form of the link between one way in which we know that space is cold and a seemingly mundane observation, the condensation of water onto cold surfaces. Lifting my glass to appreciate the cortado, I noticed a number of water droplets on the (cold) saucer underneath the (hot) cup. As I kept the cup on the saucer, the saucer became warmer and the water droplets evaporated. By the time I finished my coffee, the saucer was dry. We can observe a similar phenomenon on the inside rim of a cup of steaming hot coffee. As we watch, water droplets form around the cold rim of the cup before starting to evaporate off again as the cup gets warmer. How is this related to the coldness of space? For that, we have to digress to an essay written two hundred years ago about dew.

cortado, Brunswick House, everyday physics, coffee cup science

The cortado on the saucer. 

William Charles Wells published his “Essay on Dew” in 1814 after two years of patient observation of the circumstances under which dew formed in the mornings. By carefully noting the weather conditions of the night preceding the dew fall and the surfaces onto which the dew formed, Wells came to some important conclusions. Firstly, the surfaces onto which dew formed suggested that the earth must be radiating heat into space; space must be cold. Secondly, the earth lost more heat on some nights than on others, it appeared that certain clouds kept the surface of the earth warm. If Wells was right it suggests that there is a natural greenhouse effect which is helpful for life on earth. This in turn suggests that the surface temperature of the earth is the result of a delicate balance between heat transfer to and away from our planet. Upsetting this balance (by introducing more greenhouse gases for example), could have serious consequences. Was Wells right? Perhaps we should start noticing when and where dew forms. So, over the next few weeks, make a note of dew laden mornings. Where did the dew form and under what circumstances? Do you agree with Wells? Let me know in the comments section (below). In a few weeks we will revisit Wells and his essay, in the meanwhile, enjoy your coffee!