Coffee ring bacteria

coffee ring, ink jet printing, organic electronics

Why does it form a ring?

We have all seen them: Dried patches of coffee where you have spilled some of your precious brew. The edge of the dried drop is characteristically darker than the middle. It is as if the coffee in the drop has migrated to the edge and deposited into a ‘ring’. It turns out though that these coffee rings are not just an indication that you really ought to be cleaning up a bit more often. Coffee rings have huge consequences for the world we live in, particularly for consumer electronics. Various medical and diagnostic tests too need to account for coffee ring effects in order to be accurate. Indeed, coffee rings turn up everywhere and not just in coffee. Moreover, the physics behind coffee rings provides a surprising connection between coffee and the mathematics of bacteria growth. To find out why, we need to quickly recap how coffee rings form the way they do.

When you spill some coffee on a table it forms into droplets. Small bits of dust or dirt or even microscopic cracks on the table surface then hold the drop in the position. We’d say that the drop is pinned in position.

artemisdraws, evaporating droplet

As the water molecules leave the droplet, they are more likely to escape if they are at the edge than if they are at the top. Illustration by artemisdraws.com

As the drop dries, the water evaporates from the droplet. The shape of the drop means that the water evaporates faster from the edges of the drop than from the top (for the reasons for this click here). But the drop is stuck (pinned) in position and so cannot shrink but instead has to get flatter as it dries. As the drop gets squashed, water flows from the centre of the drop to the edges. The water flow takes the coffee particles with it and so carries them to the edge of the drop where they deposit and form into a ring; the coffee ring. You can see more of how coffee rings form in the sequence of cartoons below and also here.

However in this quick explanation, we implicitly assumed that the coffee particles are more or less spherical, which turns out to be a good assumption for coffee. The link with the bacteria comes with a slightly different type of ‘coffee’ ring. What would happen if we replaced the spherical drops of coffee particles with elliptical or egg shaped particles? Would this make any difference to the shape of the coffee rings?

Artemisdraws

As water evaporates from A, the drop gets flatter. Consequently, the coffee flows from A to B forming a ring. Illustration by artemisdraws.com

In fact the difference is crucial. If the “coffee” particles were not spherical but were more elliptical, the coffee ring does not form. Instead, the elliptical particles produce a fairly uniform stain (you can see a video of drying drops here, yes someone really did video it). The reason this happens is in part due to a pretty cool trick of surface tension. Have you ever noticed how something floating on your coffee deforms the water surface around it? The elliptical particles do the same thing to the droplet as they flow towards the edge. (Indeed, the effect is related to what is known as the Cheerios effect). This deformation means that, rather than form a ring, the elliptical particles get stuck before reaching the edge and so produce a far more uniform ‘coffee’ stain when the water dries.

E Coli on a petri dish

A growing E. Coli culture. Image courtesy of @laurencebu

By videoing many drying droplets (containing either spherical or elliptical particles), a team in the US found that they could describe drying drops containing elliptical particles with a mathematical equation called the Kardar-Parisi-Zhang equation (or KPZ for short). The KPZ equation is used to describe growth process such as how a cigarette paper burns or a liquid crystal grows. It also describes the growth of bacterial colonies. Varying the shape of the elliptical particles in the drying drop allows scientists to test the KPZ equation in a controllable way. Until the team in the US started to ask questions about how the coffee ring formed, it was very difficult to test the KPZ equation by varying parameters in it controllably. Changing the shape of the particles in a drying drop gives us a guide to understanding the mathematics that helps to describe how bacterial colonies grow. And that is a connection between coffee and bacteria that I do not mind.

As ever, please leave any comments in the comments section below. If you have an idea for a connection between coffee and an area of science that you think should be included on the Daily Grind, or if you have a cafe that you think deserves a cafe-physics review, please let me know here.

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