Umeki – Bean Thinking

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

Clouds of steam hover just above your brew, dancing on the surface in sharp, almost violent, sudden movements. You can see it almost every time you drink a long black, cup of tea or even a glass of hot water. But what on earth is going on?

Back in 2015, a paper by Umeki and others showed that these dancing white mists were levitating water droplets, a common manifestation of something that had been noticed in lab experiments a few years earlier. Hundreds of water droplets, each about 10 μm diameter (the size of the smallest grains in an espresso grind) somehow just hover above the coffee surface. You can read more about that study here. Yet there remain questions. How do the water droplets levitate? What causes those violent movements in the cloud? Can contemplating your coffee help to understand these questions?

To explore what is happening with the white mists, we need to view them in an environment that we can control so as to change one or other of the parameters in the ‘coffee’ and see what happens to the mists. And this is what Alexander Fedorets and co-workers have been doing for a few years now (even before the work of Umeki). What Fedorets has noticed is that when you heat a small area (about 1mm²) of a thin layer of liquid, it is not just possible to create these white mists, you can see the droplets levitating and they form hexagonal patterns of droplets. This is quite astonishing because whereas we are used to solids forming crystals (think of water and snowflakes for example), a formation of liquid droplets in a “self-organised” pattern is an unusual phenomenon.

floating, bouncing drops — You can stabilise much larger droplets of water (up to a couple of mm diameter) by vibrating the water surface. This is a very different phenomenon but is also an interesting effect you can create in your coffee.

Then we can ask, what is it that causes these droplets of water to levitate above the surface? According to a recent paper of Fedorets, the answer is indeed as simple (in the first approximation) as the fact that these droplets are in a delicate balance between being pulled into the coffee by gravity and pushed upwards by a stream of evaporating water molecules. This balance suggests that we can do a ‘back of the envelope’ calculation to estimate the size of the droplets and also to understand what happens when the coffee cools down. We start by thinking about the gravitational pull on the droplet, the force on that is just F↓ = mg (where g is the gravitational acceleration and m is the mass of the droplet) so, if we write this in terms of the density of water, ρ, and the radius, r, of the droplet:

F↓ = ρ (4/3)πr³.g

Similarly, we know how to calculate the upwards force on a particle created by a flow of liquid (steam). It is the same expression as Jean Perrin used to understand the layering of water colour paint in a droplet of water (which is the same as the layering of coffee in a Turkish coffee) and so proved experimentally Einstein and Langevin’s theories of Brownian Motion (which you can read about here). If the steam has a velocity U and the dynamic viscosity of the steam is given by μ, the upwards force given by the steam is:

F↑ = 6πμUr

For the droplet to ‘balance’ (or levitate) above the surface, F↓ = F↑ so with a bit of re-arrangement we get the radius of the droplet as given by:

r = √[9μU/(2ρg)]

Plugging in sensible numbers for μ (2×10^-5 kg/ms) and U (0.1 m/s), and using the density of water (10³ kg/m³) and g = 9.8 m/s² gives a radius for the droplet of 17 μm which fits very well with what is observed.

Rayleigh Benard cells in clouds — The white mists often seem to vanish as if they were sustained by Rayleigh Benard cells in the coffee. Rayleigh Benard cells can also be found in the clouds in the sky, in fact, anywhere where there is convection.
Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

But does the expression tell us anything else? Well, the radius is proportional to U; the velocity of the steam. So if you increase the temperature, you should increase the radius of the levitating droplets. This is exactly what is seen. Also, as the temperature of your coffee drops and there is less steam coming off the surface, it will become harder to stabilise these white mists; the mists will disappear as the coffee cools. This is something you can test for yourself: what is the optimum temperature at which to see the white mists (and drink your coffee)?

But the study by Fedorets showed something else. Something quite intriguing and perhaps relevant to your experience. Fedorets had stabilised the droplets on the surface by using an infra red laser and held them into a fixed area by only heating a small region of the liquid. In that sense the study is quite far from our physical experience with a coffee. But what Fedorets noticed was that these stabilised droplets grew with time. As the droplets grew, the bottom of the droplet got closer and closer to the liquid surface until, suddenly, the droplet collapsed into the liquid. This collapse caused a capillary wave on the water surface which is a small wave regulated by the surface tension of the water. And this wave then caused the surrounding droplets to collapse into the liquid interior. Because this happened very quickly (the wave travels at about 1m/s which is equivalent to a slow stroll at 3.6km/h), to us, looking at our coffee, it would appear that a violent storm has momentarily erupted over the surface of the white mists.

As the wavelength of a capillary wave is determined by the surface tension of the liquid, this suggests that if you change the surface tension of the coffee you may change the speed or perhaps the appearance of the collapse of these white mists. You can change the surface tension of your coffee by adding either soap or alcohol to your long black. Umeki did add a surfactant (to reduce the surface tension) and didn’t notice a significant difference to the speed of the wave but maybe other factors (such as temperature) were dominant in that experiment. It certainly seems a good excuse to investigate. Let me know if you experiment with your coffee and if the white mists move faster or slower in your Irish coffee compared with a morning V60, you may want to film the results if you intend to drink the coffee afterwards.

The work of Fedorets and of Umeki were both published under ‘open-access’ meaning that anyone can read them (without paying). You can read Umeki’s study here and Fedoret’s study here.

V60 from Leyas — Time to look more closely at the surface of your black coffee.

Have you ever sat watching the steam that forms above a hot Americano? Beneath the swirling steam clouds you can occasionally see patterns of a white mist that seem to hover just above the dark brew. Bean Thinking is about taking time to notice what occurs in a coffee cup and yet I admit, I had seen these mists and thought that it was something that was just associated with the evaporation of the water and that “someone”, “somewhere” had probably explained it. So it was entirely right that I was recently taken to task (collectively with others who have observed this phenomenon and taken the same attitude) for this assumption by the authors of this paper who wrote “The phenomenon that we studied here can be observed everyday and should have been noticed by many scientists, yet very few people appear to have imagined such fascinating phenomena happening in a teacup.”

ineedcoffee.com, espresso grind — The water particles in the white mist are a similar size to the smallest particles in an espresso grind. Photo courtesy of ineedcoffee.com, (CC Attribution, No Derivs). The coin shown is a US nickel of diameter 21.21 mm

The authors of the study show that the white mists (these “fascinating phenomena”) are, in fact, layers of water drops that have a typical diameter of around 10 μm (which is roughly the size of the smallest particles in an espresso grind). Although the white mists exist above tea and even hot water as well as coffee, they are probably easiest to see against the black surface of the Americano.

More surprising than the fairly uniform distribution of water droplet size though is the fact that the authors of this study showed that the droplets were levitating above the coffee. Each water droplet was somehow literally hovering above the surface of the coffee at a height of between 10 – 100 μm (which is, coincidentally, roughly the particle size distribution in an espresso grind).

white mists, slow science — You can (just about) see the white mists over the surface of this cup of tea (which is a still from the video below)

One of the questions that the authors of the paper have not yet managed to answer is what is causing this levitation? Could it be the pressure of the hot coffee evaporating that keeps these particles held aloft? This would explain the observation that the mists form patterns similar to those caused by (heat) convection currents. Alternatively perhaps the droplets are charged and are kept away from the coffee by electrostatic repulsion, an explanation that is suggested by the behaviour of the droplets when near a statically charged object (eg. hair comb, balloon, try it). Perhaps the levitation is caused by the droplets spinning and inducing an air cushion under them? Why not design some experiments and try to find out. It would be great if we can drink hot black coffee in the name of science. Let me know the results of your observations in the comments section below. In the meanwhile, here is a video of the white mists in tea, enjoy your coffee:

You can read the study at: Umeki et al., Scientific Reports, 5, 8046, (2015)