levitation

From fried eggs to coffee boules via milk rings

Egg no pales, coffee, garden centre
We can often see the Leidenfrost effect when we cook a fried egg. But could we see it while simultaneously preparing a coffee cocktail?

We have probably all come across the Leidenfrost effect, the splash of water into a hot frying pan causing drops of water to skirt across the hot surface before evaporating. We may even be familiar with it in frying pans and cooking surfaces. But what would happen if you swapped the frying pan surface for a (very hot) liquid surface. What happens to the Leidenfrost effect then?

One of the first differences between a frying pan and a bath of hot liquid (we’re not quite yet to the coffee bit) is that the frying pan based Leidenfrost effect requires a lot of heat: the frying pan has to be many degrees hotter than the boiling point of the liquid being levitated. But for the Leidenfrost effect to happen on liquid surfaces requires nowhere near so much heat. In some cases levitation can even occur if the liquid bath is just one degree higher than the boiling point of the levitating liquid. What makes a hot liquid so much different from a hot solid?

The first explanation could be that a liquid surface is absolutely flat at the molecular level. Frying pans and other surfaces have scratches and dents and all sorts of bumps that mean that bubbles can form at the interface and disrupt the levitation of the drop. Could this be it? Probably not as a complete explanation because people can study the Leidenfrost effect over semiconductor wafers which are also atomically flat and even there, many more degrees are needed between the temperature of the surface and the boiling point of the drop than are observed in liquid substrates.

A second explanation is that a liquid surface is able to deform a bit to support the weight of the drop above it, this means that the drop has more of a chance of remaining levitating above the liquid surface. And yet, it turns out that there is more than that happening in liquids as a recent study in a prominent physics journal showed.

If you look carefully at the surface of the coffee in the V60 jar, you will see it is bent underneath the drop on top of it. While the drop on the coffee here is not ‘floating’ because of the Leidenfrost effect (it is stable due to other effects described here), the fact that liquids may be able to bend under drops has been thought to make the Leidenfrost effect more stable on some liquid surfaces.

That study used a bath of silicone oil as the heated surface. The drops that levitated were either of two different liquids: ethanol (ordinary alcohol) or HFE-7100 (an engineered fluid designed to replace ozone depleting chemicals in certain industrial applications). What made the study so interesting was that tiny fluorescent particles were mixed with the silicone oil that allowed the researchers to see how the liquid underneath the drop was moving.

A toroidal vortex formed in the silicone oil under both the ethanol and HFE-7100 drops. We can see similar toroidal vortices in our V60 or by dripping milk into a glass of water; they are doughnut shaped regions of moving fluid, like smoke rings, they could be considered ‘milk rings’. But in this case, there was no drop entering into the bath of liquid as with the milk rings. The drop and the bath were not mixing at all. And, perhaps more puzzling, the direction of the rotation of the vortex was different for the two types of drop. For the alcohol drops, the liquid directly underneath the drop plummeted into the silicone oil before moving under and then back up to the surface to be pulled down at the centre again. Under the HFE-7100 it was different. There, the liquid at the centre of the doughnut surged up, dragged along the surface before going under and returning back once more to be pulled up at the centre of the torus.

Why would the two liquid drops show such different behaviour in the silicone oil substrate? It comes down to a competition of three forces. The first thing that you will notice is that if the levitating drop is slowly evaporating and will eventually disappear (as is the case with the frying pan), this means that it is absorbing heat from its local atmosphere in order to gain the energy needed for evaporation to occur (think about your hand getting cold after sanitising it with an alcohol liquid as the alcohol evaporates off). This means that the silicone oil immediately under the drop gets colder. Cold liquids are generally more dense than warm liquids and so the cold liquid sinks pulling the surrounding liquid down with it.

Linked with this effect is that the surface tension of a liquid decreases as the temperature of the liquid increases. This results in a flow of liquid from regions of low surface tension to regions of higher surface tension called a “Marangoni flow”. This is again something that we may have seen during the Covid-19 lockdown restrictions as videos were circulated showing the effect of soap on a layer of pepper scattered on the surface of water. The pepper retreats away from the soap because of these Marangoni flows which can in fact be very fast.

Milk rings can be formed by dripping milk into a glass of water. But similar fluid rings can also form in liquids hot enough to support cold Leidenfrost drops levitating above them.

These two effects draw the liquid down at the centre of the torus and push the liquid up at the edges, this is what dominates when ethanol is levitating above the silicone oil. In contrast, a third effect dominates for the levitating drops of HFE-7100. Both ethanol and HFE-7100 drops are evaporating above the hot silicone oil surface and as they do so, the gas that evaporates out of them under the drop flows out from the centre of the levitating drop to the edge. Just as with a gentle breeze on a pond, this vapour flow leads to a shear force on the liquid underneath that pulls the liquid out from the centre of the torus towards the edges, down and then, to complete the circle, back up through the middle.

Remarkably, despite their different rotation directions, both types of vortex contributed to keeping the drop levitating. You can read more about the study in the summary here or in the journal here.

Given that water boils at 100C and that alcohol boils at 78C, it is feasible that by dripping vodka or another strong alcohol based drink onto our freshly prepared coffee we may see a similar effect. It may certainly be worth a try. I’ll leave this as an experiment that you can tell me about on Twitter, Facebook or in the comments section below, but it is an experiment with a positive result either way. Perhaps you will see levitating alcohol drops above your coffee. But even if you don’t, you can at least keep trying until you have made an interesting coffee based cocktail.

A coffee balancing act

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.

What haloes and crowns reveal about your coffee

Coffee Corona

Look carefully around the reflected white light. Do you see the rainbow like pattern?

Several weeks ago I had been enjoying some very good black coffee at OJO in Bangsar, KL. As is fairly typical for me, I had been trying to observe the white mists that form just above the coffee. White mists are fascinating, tissue-like clouds that you can often see hovering above the coffee. They form, tear suddenly and then reform into a slightly different pattern. As I was photographing my coffee, I noticed what seemed to be interference patterns on the mists (see picture), just like oil on water, a rainbow-like shimmering over the coffee surface. Yet that explanation did not make sense; interference patterns form because the layer of oil on water has approximately the same thickness as the wavelength of visible light (see more info here). The water droplets that make up the white mists are a good 15 times thicker than the wavelength of light. It is not possible that these mists are producing interference effects, it has to be something else.

Then, last week and back in London, I was walking towards the setting Sun one evening when I saw what looked like a rainbow in a cloud. What caused this and how was it related to what I had seen earlier in my coffee? A short trip to the library later and it was confirmed. What I had seen in the clouds was most likely a Sun-dog. Formed by the refraction of sunlight by ice crystals in the atmosphere, Sun-dogs manifest as bright regions of rainbow. The Sun-dog appeared in cirrus clouds because these are made from the sort of ice crystals that produce brilliant Sun-dogs. These ice crystals are flat and hexagonal so they refract sunlight exactly as does a prism. Just like a prism, red light and blue light will be refracted by differing amounts and so they will appear at different places in the sky. The minimum angle of refraction produces the most intense colouration and, for hexagonal platelets of ice, this occurs at 22º away from the light source.

Sun-dog, Sun dog

A Sun-dog in the clouds to the right of the setting Sun

I do not find degrees a particularly helpful way of thinking about distance but what helped me is that, in terms of the sky, if you hold your outstretched hand out at arms length, the distance from your thumb to the tip of your finger is, approximately, 22º. Hence, if you see a halo around the Sun at about that distance, it is most likely a refraction effect due to ice crystals in the sky and if you see an intense rainbow roughly parallel to the elevation of the Sun, it is very likely to be a Sun-dog.

What does this tell us about the colours in the mists above the coffee? Well, clearly the mists are not made of ice crystals but neither is the ‘rainbow’ colouring as far as 22º from the light source (a light bulb reflected in the coffee). Also, the rainbow is less vivid and, if you look closely, inverted from the rainbow in the clouds. In the cloud, the inner edge of the arc was red and the outer edge blue, in the coffee, the outer edge is more reddish, while the inner is more blue-ish. This is another clue. On the same evening as I had seen the Sun-dog, there was a full moon and around the Moon was a glowing ring, tinged slightly reddish on the outside. The ring was far closer to the Moon than the Sun-dog had been to the Sun. This Moon-ring, and the coffee colouring are the same effect, they are examples of ‘corona’ (literally crown) and they are caused by diffraction of light rather than refraction.

straw, water, glass

It is refraction that makes the straw appear broken in this glass of water.

Refraction we are all quite familiar with, it is the bending of a straw in a glass of water as you look through the glass. Diffraction is a little more tricky, but it is a consequence of how the light moves past an object. It can be understood by thinking about how water waves pass objects in a stream (or by playing with the simulation here). The amount that the wave is diffracted depends on both the size of the object and the wavelength of the wave. As blue light has a much shorter wavelength than red light, the blue will be diffracted by a different amount to the red. If the objects diffracting the light are of a similar size (as water droplets in white mists are going to be) a spectrum, or a rainbow of colour will appear around the light source. The more uniform the droplet size, the more vivid the spectrum in the corona. The thin cloud around the Moon that evening was made up of many different sized droplets and so the rainbow effect was very subtle. In contrast, around the reflection of the light bulb in the coffee, the water droplets in the white mist are a fairly similar size and so the spectrum is more vividly seen.

Seeing rainbow effects in the sky (or in the coffee) therefore gives us many clues as to what is in the sky or indeed, levitating above the coffee. Please do send me any pictures you have of coronae around light source reflections in your coffee, or indeed sun dogs if you are fortunate enough to see them*.

* Sun dogs are in fact apparently fairly common, it is more that we have to be attentive to see them.