Clouds in my coffee

A little fog

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)

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.