coffee cup pollution detector

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 ┬Ám 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)