shape – Bean Thinking

lilies on water, rain on a pond, droplets — What is the crater shape produced by falling droplets of water on freshly ground coffee?

Recently there has been considerable discussion about the impact of water on the taste of your coffee. Although this is interesting not only from a chemistry perspective, but also an experimental design and an environmental one, Bean Thinking is probably not the best place to explore such effects of chemistry on coffee taste. If you are interested, there is a recent article about it in Caffeine Magazine, click here. Instead, on Bean Thinking, the idea would be to go a little more fundamental and ask instead what is the impact of water on coffee? What effect does dripping water have on the craters produced in freshly roasted coffee grinds?

You may have noticed craters produced by rain drops on sand or paused while preparing your drip brew to think about the different ways that water percolates through a filter compared to an espresso puck. But have you stopped to consider what determines the shape of the crater that is produced as a falling droplet impacts a loose bed of granular material (such as coffee). Perhaps you have looked at images of the Chicxulub crater on the Yucatan peninsula and wondered about asteroid impacts on the Earth or craters on the Moon but what about something closer to home? What if the impacting object were liquid and the impact surface more sand like? It’s a problem that affects how rain is absorbed by soil as well as the manufacture of many drugs in the pharmaceutical industry. But it is also something that we could experiment with in coffee. Is there a difference between craters formed in espresso pucks compared to those in the coffee in the filter paper of a V60?

bloom on a v60 — Bubbles in a V60 filter – but what is the impact of individual drops of water on the dry grains of coffee? The ultimate in slow coffee.

Recently, a study appeared in Physical Review E that investigated the crater shapes produced by water droplets on a bed of dry glass beads (imitating sand). The effect of the impact speed of the water droplet as well as the packing density of the granular bed (sand/coffee) was studied. A high speed camera (10 000fps) was used in combination with a laser to reveal how the shape of the craters changed with time, from the initial impact right through until the crater was stable. The authors came up with a mathematical model to consider how the energy of the falling droplet was distributed between the impacting drop and the sand bed. Does the droplet of water deform first or does the energy of the impact go into displacing the sand and so forming the crater?

Perhaps unsurprisingly, when drops of water fell onto dense beds of sand (think espresso pucks but not quite so packed), the craters produced were quite shallow. It would take a lot of energy to displace the densely packed sand but not quite so much to deform the droplet. But when the drops fell onto looser sand beds (think drip brew coffee) the crater produced formed in two stages and depended on the velocity of impact. A deep crater was formed as the drop first impacted the sand. Then as the camera rolled, the sides of the crater started to avalanche producing much wider craters that had different shapes in profile (from doughnut to pancake type structures). For looser beds of sand, the faster the impacting drop, the wider the final crater. You can read a summary of the study here.

So what would happen for craters produced during making an espresso compared to those produced making a drip brew? A first approximation would be that the espresso coffee is more densely packed, so the craters should be shallower and less wide than those produced in the loose packed filter coffee. However then we need to think that the water used in making espresso is forced through the puck with high energy. In contrast, in drip brewing techniques, the water used has a lower impact energy, (it could be said that the clue is in the name). So the energy of the impact would form larger craters in the espresso pucks and smaller craters in the drip brewers, an opposite expectation from that of the packing densities, which effect wins?

coffee ground in a candle holder — Early experiments with coffee grind craters: There are advantages to working with glass beads and high speed cameras.

But is there anything else? Grind size! Espressos are made using finely ground coffee beans, with a typical “grain size” being about 10μm (0.01mm). Drip brewed coffee is somewhat coarser, a typical medium grind being compared to grains of sand (which vary between 0.05-2mm, 50 – 2000μm but we’d expect ‘medium’ ground coffee to be at the lower end of that). This is fairly similar to the ‘sand’ used in the study in Phys Rev E which used grains of size 70-110 μm. A slightly earlier study had shown how the crater shape depended on grain size for ‘sand’ ranging from 98 to 257 μm. That study had revealed that how the water interacted with the different grain sizes depended in turn on whether those grains were hydrophilic (wettable) or hydrophobic (water proof). It is probably safe to assume that the coffee used in an espresso grind has the same hydrophilic properties as the coffee used in drip brew but even so, we still have those three variables to contend with, packing density, impact energy and grind size. So, happy experimenting! Let’s find out how the impact craters left in coffee change with preparation method. And whatever else, it’s a perfect excuse (if one were really needed) to drink more coffee while slowing down and properly appreciating it.

With thanks to Dr Rianne de Jong for pointing me in some interesting directions (not all of which fitted in this piece) towards the interaction of water with coffee, more coming soon I hope.

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.