scutoid

Latte Art

Latte art scutoid tulip
The physics of bubbles. What links latte art to the shape of cells as an embryo develops?

An odd one out competition: which of the following is not a type of latte art? Tulip, heart, swan or scutoid? You may well ask, “what on earth is a scutoid?” and so identify this as the odd one out and, to some extent you would be right. Scutoids are not a type of latte art. But I would wager that you can still occasionally see them in your coffee.

Twitter can be a great thing and I was recently alerted there to a New York Times article about Karen Uhlenbeck by @Bob_Mat_Phys. Uhlenbeck is a mathematician at the University of Texas who has just won the Abel Prize in mathematics for her work on the maths of bubbles. The article was fascinating in itself but also mentioned in the article was the fact that there may be, on occasion, a connection between a cup of coffee and the cell structures seen in foetal development. And while I’m very well aware of the extraordinary number of connections that can be made between coffee and the science of the everyday world, I’ll admit, that one surprised me.

Metal jug and transparent glass
More bubbles in your coffee. But what determines their shape? And what shape are they?

By this point you may be unsurprised to hear that the connection is made via the scutoids, but what are they? A new type of shape, they were first described in a Nature Communications article about the development of cells as organisms such as fruit flies grew. Scutoids formed as the embryonic cells grew to form tubes or egg shapes. On one surface of the tube the cell was contacting a different number of cells to that which it contacted on the other surface (so perhaps the cell looked like a pentagon on the top and a hexagon on the bottom). In order for the cell to do this, it formed a further triangular face along one side of the cell and it is this cellular shape that is the scutoid.

Where is the connection with a coffee? Well, the amazing thing is that this shape can be the result of the physics that determines the shape of bubbles, in this case when they are confined between two curved surfaces, such as two cylinders. The shape of a bubble is the result of the minimisation of the surface energy of the bubble. So, in free space, the bubble will be spherical but somehow squash bubbles into a box and you can form a cube shaped bubble in the middle of the box. The shapes that form are the result of the minimum surface energy of the bubble surface. Now, if we return to the curved surfaces and the scutoids. The idea is that if there is a single layer of bubbles between two curved surfaces and that these surfaces are then moved away from each other, the bubbles will first resemble prisms and then, as the surfaces are stretched further, some bubbles will form a prism shape but with a triangular surface at one of the bounding walls: a scutoid.

latte art by Mace, Eiffel Tower and hot air balloon
It is astonishing what you can see in a coffee when you look closely enough.

The paper that showed this (published in Philosophical Transactions but you can read the full version here) combined mathematical modelling of the minimisation of surface energy with experiments involving two cylinders and some soap suds. They then photographed the resultant bubble structures. The results suggest that the minimisation of energy (ie. the physics of the bubble shape) could be a first approximation for explaining the cell structures that form in foetal development. But can you see them in your coffee?

You would need a coffee mug or French press and a smaller cylinder that fits neatly inside it. You would then need to form a foam somehow. Soap suds are obvious, some form of milk texturing would be more interesting. You can then look closely and see, can you in fact see scutoids in your latte art?