A short (lived) black

coffee at Story
A black coffee with bubbles on top. The colours on a bubble are the result of light interference. But sometimes the top of the bubble could appear black. What is happening there?

The long black can be distinguished from the Americano by the order in which the espresso and the water are added to the cup. This in turn will affect the type of bubbles on the surface of the coffee. As a guess, the long black (espresso last) will have many more but smaller bubbles than the Americano (water last) which will probably have larger, but fewer bubbles. Perhaps this guess is wrong, this could be an excuse to get out and drink more coffee.

We are used to the coffee being black and the bubbles on the surface reflecting a rainbow of shimmering colours that change with the light and with time before they finally burst. We know the physics of the colours on the bubbles: they are the result of the interference of reflections from the outer and inner surface of the bubble cancelling out certain colours and adding to others dependent on the bubble skin’s thickness. But what about black bubbles? Or, if not entirely black, perhaps the cap of the bubble can, for a short while, appear black just before the bubble bursts?

It is easier to take a short break from coffee and look for this effect in soap films. Like the bubbles on coffee, soap bubbles are caused by the surfactant in the soap solution having a hydrophilic (water loving) and hydrophobic (water hating) end. The hydrophilic end of the surfactant can point into the water (coffee) leaving the hydrophobic end to form a surface. When this is agitated with air, the hydrophilic ends remain contacted with water resulting in bubbles which are thin layers of water surrounded by these surfactant molecules. In coffee the surfactant is not soap but is formed by the lipids and fatty acids. These bubbles are therefore slightly weaker than the soap based bubbles and so while they will form on a coffee, it is not easy to make a film of a coffee bubble in the same way as you can dip a wire loop into a soap solution and come out with a soap film.

However, we can use the stability of the soap film to investigate the colours in the coffee bubbles and watch the colours evolve with time. At this point, I would strongly encourage anyone reading to grab a solution of soap and a wire loop and start playing with soap films.

Soap film in a wire loop held by a crocodile clip.
A soap film in a wire loop showing reflected horizontal coloured bands that are the result of light interference.

Holding the wire loop so that the soap film is vertical with a light source shining at it, we can watch as the film changes from being uniformly transparent to having bands of colour form and move down the film. We watch as there is a red/green band and another red/green band and then on top of the bands there appears a white, or at least pale blue, almost white, band and above that a layer that doesn’t reflect the light at all. If we view the soap film against a dark background looking only at the reflected light, this top portion of the film appears black. Rotating the loop we can see that the bands effectively stay in the same position because it is gravity pulling on this soap film that is causing the film to be thicker at the bottom than at the top. And we recognise that the coloured bands are revealing that thickness change to us by the fact that they are changing throughout the film. If we are careful as we rotate the wire, we could even see vortex like motions as the layers settle into their new position relative to the frame including at the very top where there are swirls and patches of fluid that mix the black layer with the coloured bands. What is going on there?

In fact, this black layer is one of the thinnest things that they human eye can see, and it occurs because of a subtle piece of physics. All waves have a number of properties defined by the position of the peaks and troughs on the wave. The wavelength is the distance between two equivalent points on the wave. The amplitude is the height of the peak (or trough). And the phase is the position of the wave relative to the peak (or trough). When light is reflected at a surface of a material that has a refractive index greater than that which the light is travelling through (eg. air into water, soap, or glass), the reflected wave has a 180 degree phase shift relative to the incident wave. Each peak becomes a trough, each trough becomes a peak. When light is already travelling through water, soap or glass and gets reflected at the surface of the material that is effectively air, there is no phase shift and the light is reflected back with the same phase as the incident wave (a peak remains a peak and a trough a trough).

At the top of the soap film, the layer is so thin that the light reflected from the first surface (180 degree shift) overlays that reflected from the back surface (no phase shift) so that peak and trough cancel each other out and we see no light reflected whatsoever for any visible wavelength; the surface looks black.

As bubbles ‘ripen’ or age, they will become thinner at the top of the bubble. It is at this point that you may be lucky enough to see a region of the bubble from which no light is reflected, this is the black film.

Which leads to some immediate questions. When we look carefully at the soap film, the boundary between the upper white band and the black film is quite sharp, it is not gradual as we may expect if the soap film were completely wedge shaped with gravity. It suggests that the top of the film is very thin and then suddenly gets thicker at the point where we start to see the colour bands. Moreover, the black film does not appear to mix with the thicker film just beneath it. As we watch, just before the soap film bursts, we get turbulence between the black layer and the thicker film, but the turbulent patterns appear like two fluids next to each other, not the same fluid in a continuum. And then, one final question. If we can’t measure the thickness of the black film with light (because it is all reflected as black) how can we know how thick this film is? If we rely on the light interference method, all we can say is how much thinner it is than the wavelength of light.

In fact, careful experiments have revealed two types of black film, which to us experimenting at the kitchen table would be indistinguishable. There is the common black film and the Newton black film. The Newton black film is effectively two layers of surfactant molecules only and is about 5nm thick (which is 5 millionths of a millimetre). The common black film is thicker, but is still much less than 100 nm thick. Investigating how these films behave is still an active area of research.

One last observation may prompt us to play for a bit longer with the soap films. Johann Gottlob Leidenfrost (1715-94) noted that if you put a sharp object such as a needle through the region of the soap film that showed the coloured bands, the film could self-heal and wouldn’t necessarily burst. If however you pierced the black region of the film, the film always burst entirely.

It seems that we could play endlessly with soap films, perhaps while watching the bubbles in our coffee. However you enjoy your coffee, have fun experimenting.

A couple more soap films showing reflected coloured interference bands. At the top, the film has become so thin that no light is reflected (clearly seen in the image on the right, where the lamp in the top left should be a circular reflection but is not reflected in the region above the coloured bands). In the image on the left, you can see what looks like turbulence or mixing just above the uppermost band.

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