Mie scattering – Bean Thinking

Seeing the light at Cable Co, Kensal Rise

coffee in Kensal Rise, Cable Co — Cable Co, coffee in Kensal Rise

It was fairly late on a February afternoon that we came upon Cable Co on Chamberlayne Road, (opposite Kensal Rise station). With a fairly ‘industrial’ type look, there are plenty of tables at the edge (and in the window) of the café at which to enjoy your coffee. There are also plenty of coffees on offer. Although I had an Americano, I noticed (too late) that pour-overs were available. Coffee is roasted by Climpson and Sons. As it was late in the day, the remaining cakes in the display case all looked to be nutty (or at least likely to be nutty) and so, sadly, I had to wait until I got home for my slice of cake. It was good coffee though, even without the cake, but in a bit of novelty the coffee came ‘deconstructed’, so I got to add the amount of water that I preferred, a nice touch.

Golden light from the setting sun streamed in through the windows (which is a navigation clue & tells you which side of the road this café is on). The effect of the Sun was to bathe the café in light and to silhouette our fellow coffee imbibers making the café take on a film-like atmosphere. The light had another effect though. The steam rising from both the jug of water and my espresso became far more visible than it would normally have been. I watched as the steam clouds formed vortices and turbulent patterns, one fluid (steam) moving through another (air). It was very difficult to catch this in a photograph, a fact that I took in support of my idea that it is impossible to catch the beautiful, beauty is necessarily transient (but my companion in these reviews took as evidence in favour of their idea that I really ought to use a “proper”, manual, camera and not my iPhone).

Steam, scattering, colour — Steam rising from hot water, seen at Cable Co, Kensal Rise

Still, those turbulent rising patterns of steam were visible and that implies that light was being scattered from the droplets of water in the steam. The size of the droplets influences the colour that we perceive when we view the steam clouds. If the clouds appear white, it is because the droplets that are scattering the sunlight have a diameter roughly equal to (or greater than) the wavelength of visible light. The wavelength of light varies between about 400 nm (violet) to 700 nm (red) which means that these water droplets have to be at least 700 nm across. To put this in perspective, the smallest particles of coffee in an espresso grind are about 10 μm diameter which is 14 x bigger than the droplets in the steam cloud.

Of course, how water droplets scatter light above a steaming coffee has implications for our understanding of why the clouds in the sky appear white (and why the sky is blue). Someone who did a lot of early work in understanding the way that light scattered off water droplets in air was John Tyndall (1820-1893). Tyndall was an experimentalist as well as a famous communicator of science. He regularly gave lectures at the Royal Institution that included demonstrations of the experiments that he himself was working on¹. One of these involved scattering light from water droplets (and therefore demonstrating why he thought the sky was blue).

Interior of Cable co — Light streaming into the cafe.

The idea is that sunlight scatters from water droplets differently depending on the diameter of the droplet. When the water droplets are approximately the diameter of the wavelength of red light, 700 nm, there is very little wavelength dependence to the light scattering. Practically this means that the droplets will appear white. If on the other hand, the droplets are much smaller than the wavelength of light, the light scattering starts to be wavelength dependent. So as the droplet gets smaller, blue light (short wavelength) gets scattered a lot by the droplets, while red light (long wavelength) is not scattered so much. This means that if you are looking at a cloud of steam formed by these small droplets at an angle between the sunlight and yourself (say, 90º), the cloud will appear to have a blue tinge. If on the other hand you look straight through the cloud at the sunlight coming in, it will have a red-hue because the blue light will have been scattered out of the cloud leaving only the red colours to come through.

The experiment can be easily demonstrated at home by using very dilute milk in water (see video here or further explanation here). If you put a few drops of milk in a glass of water and then look at the colour of the milky-water as a function of angle, you should see it change from red to blue as you move the glass relative to the light source. The connection with the blue sky seems clear, small particles (in-fact, they can be as small as molecules) scatter blue light preferentially and so, apart from at sunrise and sunset, the sky will appear blue. As Tyndall wrote:

“This experiment is representative, and it illustrates a general principle…. that particles of infinitesimal size, without any colour of their own, and irrespective of the optical properties exhibited by the substances in a massive state, are competent to produce the colour of the sky.”²

Cable Co is at 4 Bridge House, Chamberlayne Road, NW10 3NR

¹A Vision of Modern Science, John Tyndall and the role of the scientist in Victorian culture, U. DeYoung, Palgrage MacMillan, 2011

²Quoted in John Tyndall, Essays on a Natural Philosopher, Ed. WH. Brock, ND. McMillan, RC. Mollan, Royal Dublin Society, 1981

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html

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.