white mists

Corona gazing in cafes

interference patterns on coffee

There are many ways in which rainbows of colour are produced as light interacts with our coffee or in a cafe. Looking around yourself now, how many do you see? What physics underlies each?

As the nights grow longer and the days colder, we notice that windows steam up as the water vapour in the café condenses onto the cooler glass. Perhaps we see a similar thing on our glasses while we are drinking tea or on the windows of a bus. Initially we perhaps become frustrated at our inability to see what is going on outside but then we notice the colourful patterns around the lights of passing cars and of street lights. Haloes of coloured light around a central bright spot. What does this tell us and where else can we see it, either in a café or in life generally?

On a window pane, a large number of small droplets of water have condensed into what appears to us as a fog on the glass. As the light shines through from the car headlights, each droplet acts as an obstacle to the light and so bends it. You could see a similar effect with the waves on the sea going around stones or perhaps if you brew a large cup of coffee with the surface waves going around a spoon (let me know if you manage to see this bending in a coffee cup). The amount that the light bends is dependent on the wavelength of the light (look carefully at the waves going around obstacles in ponds to see this) and so different wavelengths (different colours) get bent by different amounts and interfere with each other at different points – a spectrum is produced. It is a phenomenon known as diffraction.

Not all beans are equal! How could you quickly distinguish between arabica and robusta beans?

This phenomenon means that we have a way of separating the frequencies (or wavelengths) of light. And so this means that we have a way of measuring the chemical composition of some substances as different chemicals absorb different frequencies and so have ‘fingerprints’ in the light they scatter. By passing the light scattered from a substance (such as arabica coffee beans compared to robusta) through a diffraction grating (which is an obstacle with a pattern of fixed size), we can separate the frequencies being scattered and see if any of them are ‘missing’ (ie. they have been absorbed by the material we’re studying). It would be  a bit like looking at that rainbow pattern in the café window and not seeing blue, its absence tells you something. This is one of the ways that robusta beans can be quickly found if they have been substituted for arabica beans in coffee trading.

Coffee Corona

Look carefully: Sometimes you can infer the existence of a thin (white) mist over your coffee by the corona pattern around reflected light fittings.

But it is not just its technological aspect that has interest for us surely? When gazing at the moon on a misty evening, the halo around the moon suggests the clouds between us and it. It is something that poets have remarked upon to evoke atmosphere, it is something that we can gaze at as we imagine the giant café window of our atmosphere. But the size, and distinctness of the lunar corona actually give us clues about the droplets making up the cloud. And then we look closer to home and to our own coffee and we see the same diffraction pattern again looking back at us from our coffee’s surface. Occasionally it is possible to see haloes on the coffee surface around the reflection of overhead lights in the café. A coffee corona! This reveals to us the fact that there are droplets of water above the surface of our coffee; an extra layer of hovering droplets. Something that we can sometimes see more directly in the dancing white mists.

Diffraction is a beautiful phenomenon that allows us to gaze and to contemplate how much we are able to deduce and how much we have yet to understand. How atmospheric our coffees and cafés are and the journey of understanding that we have taken to get to this point. Coffee gazing is a hobby that should be taken up by far more of us.

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Back of the envelope calculations with coffee

coffee at Watch House

Coffee is generally a great help for reading, but to properly see the clouds in your coffee, it may help if you prepared yourself a brew now.

To read this post it will help if you have a cup of lovely, hot, freshly prepared coffee or tea with you.

Got it? Ok, let’s begin.

A few weeks ago, there was a talk given by Prof. Paul Williams of the University of Reading about the Mathematics of turbulence and climate change. An entertaining talk about the importance of, and the effort of comprehension required to, use mathematics in order to understand climate change. There were several thought provoking comments through the talk that demanded further reflection. But one, almost throw-away comment has been bugging me since. Although I’ve forgotten the exact words, they went along the lines of

Of course mostly we think about the impact of climate change on the weather, after all, we live in the bottom few metres of the atmosphere and so that is what mostly affects us. What I would like to talk about is the effect of climate change on airplane turbulence…

The bottom few metres of the atmosphere? It’s true. The bit we’re most experienced with is just a tiny portion of it. It’s about perspective. To us, it seems the atmosphere is very big, we pump all sorts of exhaust fumes into it and they disappear. We have expressions such as “the sky is the limit” that suggests that the atmosphere is a huge volume of gas. We all know it is not really limitless, but day to day, on our human scale, it seems enormous.

Now the mathematics that Prof Williams uses to calculate the effect of changing temperature and carbon dioxide levels on the jet stream (and consequently the turbulence felt by planes) is way beyond the sort of back of the envelope calculation that we can do with a cup of tea (or coffee). Understandably, to even start to comprehend these mathematical models requires years of training in maths and physics. However, assuming that we are not ourselves atmospheric physicists, there are things that we can do to help us to see our atmosphere in a more realistic way. And this is where your coffee comes in.

Earth from space, South America, coffee

Clouds swirling above our common home. But if the atmosphere is represented by the white mists on the surface of a cup of coffee, what size coffee are we drinking?
The Blue Marble, Credit, NASA: Image created by Reto Stockli with the help of Alan Nelson, under the leadership of Fritz Hasler

Take a close look at that coffee. Assuming it is not cold brew, hopefully your coffee or tea is still fairly warm. Watch the surface of the coffee. You may start to see movement such as convection in the mug, perhaps you can see a film of oil on the surface. But do you see something else? In very hot tea or coffee, you should be able to see what appear as white mists hovering over the surface of the cup*. It is easy to miss them, but as you watch, cracks suddenly appear in the mists and then there is a re-organisation of them which allows you to start to see them dancing over the surface of your drink*.

These mists are the result of the levitation of many thousands of droplets of water just above the surface of the coffee. I have written about them elsewhere. No one knows quite how they levitate above the surface, but what is known is that they are at a distance of up to 100 μm (0.1mm) from the surface of the coffee.

Let’s construct a scale model of our coffee as the Earth and its atmosphere. These mists can then do a fairly good job of representing the atmosphere with its drifting clouds. So, assuming that the mists are the atmosphere and the coffee is the Earth (on the same scale), what size of coffee would you have to have? Would you be drinking:

a) an espresso

b) a long black

c) a venti

d) a ristretto

Think you know the answer? Let’s work it out with a “back of the envelope” calculation. The easy bit is deciding the radius of the Earth, it’s just under 6400 km, our first problem comes with the estimate of the thickness of the atmosphere. There are several layers in the atmosphere. The one that we are most familiar with, the one closest to us is the troposphere. This extends for the first 16 km above the surface of the Earth (though this varies with latitude, it is only 8 km at the poles). Most of our weather happens in this region and it is also the layer of the atmosphere that planes fly in. Above the troposphere is the stratosphere which extends until about 50 km. Beyond that, things get very rarified indeed though the boundary between our atmosphere and “space” does not happen for several hundred km (indeed, the orbit of the International Space Station is in this bit of our extended atmosphere).

Coffee Corona

Look carefully around the central (reflected) white light. Can you see a rainbow like spreading of the colours? Another manifestation of the white mists on the coffee surface.

As we are mostly concerned with the weather (and airplane flight etc) though, it seems sensible to define the atmosphere height to be the top of the troposphere. After all, most of us will tend to think that the Space Station is in, well, space. This definition is further justified by the fact that about 75% of the mass of the atmosphere is found within this region (the atmosphere gets thinner as you go higher).

What size coffee would we be drinking if the white mists (0.1 mm above the coffee surface) represent the 16 km of the Earth’s atmosphere? We’ll call the coffee height, hc. Our first step is quite easy, we can just use the ratios of the heights to calculate the coffee size:

(height of troposphere)/(radius of Earth) = (white mist height)/(height of coffee)

A bit of rearrangement:

height of coffee = (white mist height)*(radius of Earth)/(height of troposphere)

hc = (0.1) * (6400)/16

hc = 40 mm (4cm)

So for the mists to represent the atmosphere in your coffee, you would need to be drinking a 4cm tall coffee which is probably a smallish long black. I would leave it to you to calculate the coffee size for the atmosphere defined as outer space (beyond the orbit of the International Space Station). But perhaps this perspective gives us another way of looking at our atmosphere. Vast indeed, but fragile too.

*As I was writing this, I had a warm, very drinkable, cup of coffee but it wasn’t steaming and so showed no white mists over the surface. The mists are best seen in freshly made, very hot drinks.