June 2020 – Bean Thinking

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.

With this ring…

vortices in coffee — Vortices behind a spoon dragged through coffee.

How many vortices do you see in your coffee? We finally arrive at the last in this series about the contributions of Helmholtz to the physics of a cup of coffee and the one that was to be the link with the (postponed) Coffee & Science evening at Amoret Coffee: vortices. But, beyond those that form behind a spoon, where do you see vortices in coffee and how can we connect them to dolphins?

Each morning as I prepare a pour over, I wait as each drop of coffee falls into the coffee bath below it. Some bounce up, some stay on the surface for some moments, many more pass straight through and get absorbed into the brew. I will admit that on most mornings, I am not thinking about the fact that I am watching one of the most beautiful pieces of physics unfold in front of my eyes and yet, this is how the processes occurring in the V60 were described by Lord Kelvin:

“[Helmholtz’s] admirable theory of vortex rings is one of the most beautiful of all beautiful pieces of mathematical work hitherto done in the dynamics of incompressible fluids.”

One of the most beautiful of all beautiful pieces of mathematical work? In my morning V60? How can we see these vortices as they fall? Sadly, it is perhaps easier to swap the coffee for plain water and drop food colouring into into it if we actually want to see these vortex rings form. As each coloured drop hits and goes through the surface, it forms a ring that curls up on itself and, if you are lucky, splits into many smaller rings, cascading to the bottom of the pot. You can see a film of the effect here or try it for yourself.

Vortex ring cascade, food colouring into plain water, V60 vortex — Dripping food colouring into a V60 of plain water: visualising the vortex rings that form every morning as you brew your coffee.

Each drop of coffee dripping from the filter into your coffee pot in the morning does this even if you can’t usually see it.

And though these rings must have been seen before Helmholtz’s paper in 1858, and even dolphins play with them in the sea, no one had attempted a mathematical model until Helmholtz. Helmholtz founded his mathematics on several theorems including the fact that a vortex cannot terminate within the fluid. It either has to terminate at the boundary of the fluid (like the vortex formed behind a spoon being dragged through coffee) or it has to close on itself (it forms a vortex ring) (more info here, opens as pdf).

Helmholtz seems to have come to vortices via an interest in organ pipes. He noticed that vortex sheets form at the inner surface of the pipe that can contribute significantly to the internal friction of the air flow through the pipe*. This means that, at the boundary between the moving air and the stationary air at the pipe edge there is a region of turbulent flow which leads to the formation of vortices. For Helmholtz, this had immediate consequences for measuring the speed of sound using pipes. Because where as previously the length of the organ pipe had been taken to be the distance between the maximum vibration (anti-node) and minimum vibration (node) of the sound wave, Helmholtz noticed that the presence of vortex sheets at the surface of the pipe would lead to an apparent lengthening of the resonator. If you used the length of the pipe to calculate the speed of sound, you would be very slightly wrong*.

As he investigated further, he found that these same surface-vortex effects explained a feature of organ design that had been known empirically but never explained. Why is it that in order for the character of the sound to be similar for each note, notes played through short, fat pipes must be accompanied by notes played through tall thin ones? Again it is to do with the air flow past the surfaces of the organ pipe.

vortices, turbulence, coffee cup physics, coffee cup science — Another cool consequence of boundary layers: Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player).

In fact, these vortex sheets that appear at the boundaries between fluids appear so often, you can start to see them everywhere! They are in a cup of coffee if you put it on a record player (as with the picture of ink in a takeaway cup here) and they are in clouds that show a Kelvin-Helmholtz instability. Appearing like a series of waves on a cloud in the sky, Kelvin-Helmholtz instabilities occur when a layer of cold dry air flows fast past a layer of hot and humid air. At the boundary of the two layers, a vortex structure forms and because the hot humid air encounters the cold dry air within that vortex, clouds can form at the boundary which reveal the vortices driving them. Although the conditions to create them must occur quite frequently, they last only a very short amount of time (less than a minute is typical) and so are considered quite rare. Look out for them next time you can see that the weather is changing and the clouds are fairly high in the sky.

Of course, it is not just on Earth and in coffee that we see these vortex structures. We see them in the weather patterns of other planets, in the solar wind and in jets leaving supernovae. And it is not just in fluids that Helmholtz’s mathematics of vortices proved useful. In Helmholtz’s equations the fluid velocity associated with a vorticity described (exactly analogously) the magnetic force produced by an electric current distribution*.

Kelvin Helmholtz instability in clouds over the M3 in January 2020 — A Kelvin-Helmholtz instability in clouds over the M3 in January 2020.

Far more could be said about Helmholtz’s work on vortices and its links to both coffee and the weather on Saturn, but that will have to wait until the next Coffee & Science evening at Amoret. Until then, enjoy watching these astonishing structures in your coffee and let me know if you observe anything interesting with them.

This is the last in a series of articles on the contributions of Helmholtz to our understanding of coffee. You can read an introduction here, his work on vision and colour here, the sounds of coffee here and the energy of coffee here. Next time, we’ll be back to experimenting with coffee, please do let me know (on Twitter, FB or in the comments) of any experiments you have been doing at this time, what have you seen in your brew?

*”Worlds of Flow”, Olivier Darrigol, Oxford University Press, 2005