relative humidity – Bean Thinking

canali Curators Coffee — Clouds viewed from a London cafe. How do clouds form?

Clouds form because water droplets condense. But there is a hidden difficulty in this seemingly simple statement because, while true, it is not, at first sight, clear how they condense.

To see the problem imagine spilling coffee on two consecutive days, a really damp one and then a really dry one. We know from our experience that when the weather is dry the coffee will evaporate and dry more quickly (leaving a coffee-ring). On damp days the drop is more stable against evaporation, that is, it stays as a droplet. We can continue our thought experiment by thinking what happens when we have a large coffee spillage versus a drop. The drop will dry quickly whereas the large spill will take ages to dry out (unless we mop it up).

Where does this leave clouds? Consider two water molecules coming together and condensing into a very small drop. It is quite clear that, just like our small coffee drop spill, this droplet will be unstable against evaporation, meaning that it evaporates almost as soon as it has formed. Perhaps this seems an extreme example, we do not often consider a water droplet as being formed of two molecules (nor is it clear that the term ‘evaporation’ is strictly appropriate in this case). So how many water molecules would have to, spontaneously, come together to form a droplet that does not evaporate almost as soon as it is formed? Take a guess. What seems reasonable?

coffee bowl pour over — Frequently water droplets will condense onto something as opposed to merely forming on their own. Consequently it is useful that our planet is fairly dusty.

At a relative humidity of 101%, a stable droplet has to be larger than about 0.1 µm diameter* (larger than about 1/50000 of a coffee bean). Which means that to form a stable droplet, about 140 million water molecules would all have to combine in the same spot and condense together simultaneously. It seems not terribly likely and yet this is what our statement at the start of this post implied “clouds form because water droplets condense”.

Which aspect of our understanding is wrong, or incomplete?

It is in our assumption about how the water molecules are condensing. Rather than spontaneously combine, each molecule condenses onto something, just as a dew forms on the ground, so these droplets start to condense onto dust particles and other, smaller, aerosols in the atmosphere. This means that at the heart of most cloud droplets is a bit of dust and that dusty places may be expected to be, all else being equal, more cloudy. Or at least that last part was my understanding of the situation: would a take-away coffee taken away in a polluted London street appear to steam more than in the by-ways of a village?

Unable to determine how to design an experiment to test this idea (while keeping all other things equal), it was interesting to come across an almost flippantly made statement in a book while I was preparing for the next evening of Coffee & Science at Amoret.

“Urban emissions of sulphate aerosols from fossil fuel burning and dust production caused by industrial activity and human occupation result in poorer visibility and increased frequency of fogs [in dense urban areas such as cities]”.

Does our coffee steam more in the cities? The answer to this may well be ‘yes’!

And there was more, apparently the increasing use of clean air legislation has resulted in fewer foggy days and more days of sunshine in urban areas**. Is it possible therefore that you could start to use your take-away coffee cup as some form of pollution detector? Watching for the steam to appear as you wander from street to street.

Sadly for the coffee cup pollution detector, whether the water condenses onto the dust droplet or not is also a function of the temperature and humidity, parameters that will make it tricky to develop the pollution detecting re-usable coffee cup. But, the physics is sound and if you do one day come across such a device, please remember where you read it first!

*”Introduction to Atmospheric Physics”, DG Andrews, (2008)

**”The ice chronicles: the quest to understand global climate change”, PA Mayewski & F White, University Press of New England (2002)

Coffee & Contrails (I)

contrail, sunset — A set of criss-crossing contrails taken in the evening.

If you gaze up at the sky on a clear day, you will often see a few contrails tracing their way across the blue. Formed as a result of water in the atmosphere condensing onto exhaust particles from aeroplanes, contrails are a regular feature of the skies in our modern life. There are at least two ways that I can think of, in which the physics of the contrail is connected to the physics of the coffee cup, so, there will be two Daily Grind articles about them. This first one, about the physics of how we see them, and a second post (scheduled for 10th June) about interesting effects that we can see in them.

Perhaps now would be a good point to go and make a cup of coffee before coming back to this post. Make sure that you notice how the steam clouds form above the kettle spout as the water boils. Do you see the steam at the spout itself, or just a few centimetres above it? With the cup next to you, notice the steam rising above it. Does the steam seem more obvious on some days than others? For example, the coffee always seems to me to steam more on cold damp days in winter than on warm-ish days in late spring. Both of these observations (about where and when we see the steam clouds) are mirrored in the contrails, it’s time to take a closer look at the coffee.

V60 from Leyas — The clouds above a coffee cup are a rough indicator of the relative humidity.

The difference in the day to day visibility of the steam above the coffee cup is an indicator of the relative humidity of the atmosphere. If we prepare our cup of coffee on a day when the relative humidity is already high, adding that extra bit of water vapour from the cup leads to clouds of steam above the mug, as the water condenses into droplets of liquid water and forms clouds. If our coffee was instead prepared on a day with low relative humidity, the water vapour above the coffee cup is less likely to condense into clouds. Contrails are formed high in the atmosphere when the relative humidity is quite high. Exhaust particles from the engines of the plane offer a surface onto which the water in the surrounding (humid) atmosphere can condense to form clouds. We know that it is mostly the atmospheric moisture that is forming the contrails (rather than water from the exhaust itself) because of research done by NASA. In research flights, the amount of water vapour leaving the aeroplane engine was 1.7 grammes per metre of travel while the mass of water in the contrail was estimated to be between 20.7 and 41.2 kilograms per metre. This means that contrails can give a clue as to the weather: on dry days, contrails will not form because the water in the atmosphere is likely to remain a gas and therefore invisible to us, it is only when the air is already quite humid that contrails are likely to form and persist.

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

Then there is the question of why we see them at all. Contrails appear as white clouds trailing behind the plane. We see them as white because of an optical effect caused by the size of the condensed droplets of water (actually ice) in the contrail. Objects appear as having different colours either as a result of light absorption by chemicals in the object (leaves are green because of chlorophyll) or as a result of light scattering from the object. A water droplet is colourless and so the colour we see coming from the droplet must be purely a consequence of light scattering rather than a light absorption effect. Clouds appear white because the water droplets within the cloud are as large, or larger than, the wavelength of visible light (0.7 μm). Droplets this size will scatter all wavelengths of visible light and so appear white. If the droplets were much smaller than the wavelength of light they would scatter different wavelengths by different amounts. It is because the atmosphere is full of such tiny particles (and molecules) that blue light is scattered more than red light in the atmosphere and so the sky appears blue to us from our vantage point on the Earth’s surface. Milk is composed of large fat droplets (which will scatter a white light) and smaller molecules which will preferentially scatter blue light, just as the sky. This is why you can mimic the colours of the sky in a glass of milk. It is because the water droplets have formed a few cm above the kettle spout that you can see them scattering the light. For exactly the same reason, the contrails in the sky appear as white clouds.

Contrails can persist in the sky for anything from a few minutes to a few days. Just like clouds, contrails affect the way that light (and heat) is reflected from the Sun or back towards the Earth. However, unlike normal clouds they are entirely man-made, another factor that could have an unknown effect on our climate. A few years ago, a volcano eruption in Iceland caused the closure of UK airspace (as well as the airspace of much of Europe). I remember being in the queue to buy a cup of coffee in the physics department and hearing the excited conversation of two atmospheric physicists behind me. For the first time they were able to study some particular atmospheric effects without the influence of any contrails. In effect they could start to understand the influence of contrails by this unique opportunity of taking measurements during their absence. What was a major pain in the neck for so many travellers in 2010 meant a lot of extra (but presumably very interesting) work for them.

Coffee & Contrails (II) is about the structures you can sometimes see within the contrail. If you can think of any other connections between coffee and contrails (or coffee and clouds) why not let us know in the comments section below.