On the 23rd October, 1997, a paper was published in the journal Nature titled “Capillary flow as the cause of ring stains from dried liquid drops.” The title is in the dry style that scientific papers can be written. An alternative title could have been “How coffee stains form”*. Perhaps you would think, surely someone had known how coffee stains formed before 1997? And maybe you would go on to think: certainly 21 years later in 2018, we’d know all there was to know about the coffee stain? I hope that readers of Bean Thinking would not think “who cares about coffee stains?”, but I wonder whether it was the combination of disinterest and assuming that someone somewhere surely knew how they formed that meant it took until 1997 for anyone to ask the question: well how do they form?
Coffee is a very popular drink among scientists, though even this does not explain how popular this paper has become. A paper’s popularity can be measured in ‘number of citations’ which tells you how many times other authors have found this piece of work important enough to reference it in their own published paper. As of early November 2018, this paper has been cited nearly 3300 times. Why? Well, there seem to be at least two reasons. Firstly, it turns out that the coffee stain effect is of enormous technological relevance; it may even have been used in the manufacture of the device you are using to read this website. But secondly even now, 21 years later, we still don’t understand what is going on, there is still much to learn and some of it is some very subtle and very beautiful physics.
Very recently for example, a new paper was published in Physical Review Letters. This one was titled “Density-driven flows in evaporating binary liquid droplets“. Another exciting title, another time we’ll retitle it for the purposes of this post: “what happens when you mix alcohol with a coffee type suspension, dry it at different angles and film it drying.” Arguably this time the given title is more succinct. Why does it make a difference if you add alcohol to your coffee rather than just drink it straight (the coffee, not the alcohol)? And what happens to the resulting coffee stain?
Maybe of an evening you’ve been relaxing with a glass of wine, or something stronger, and noticed the “legs” rising up the glass. Their formation and appearance is due to the differing surface tensions between alcohol and water and the fact that alcohol evaporates more easily than water, you can read more about that effect here. The point is that because of the difference in surface tension between alcohol and water, you get a flow of liquid from areas of low surface tension (higher alcohol content) to high surface tension (high water content). And it was this that had been thought to drive coffee stain formation in droplets which were a mix of liquids, water and alcohol for example. But how do you isolate this effect from the other effect in which alcohol evaporates more quickly than water and so there are changes in density and buoyancy of the droplet?
To answer this you could add n-butanol to the water (or coffee) rather than alcohol. Just like ethanol based alcohol (the sort you may get in gin), n-butanol has a much lower surface tension and lower density than water but unlike alcohol, it evaporates much less readily than water. So, in a water-butanol mix it will be the water that goes first, while exactly the opposite will happen for an alcohol-water mix. In a drying droplet, the liquid evaporates most quickly from the edge of the drop. Therefore, after an initial, chaotic stage (imaginatively called stage I), you will end up with a droplet that is water rich around its rim in the alcohol-water mix but n-butanol rich around the droplet edge in an n-butanol-water mix (stage II). This suggests a way that you can distinguish the flows in the drop due to surface tension effects from those due to the differences in density between water and alcohol/n-butanol.
How would you test it? One way would be to compare the droplets evaporating as if you had spilled them on the table top with droplets evaporating ‘upside-down’, as if you had tipped the table by 180° after spilling your coffee. You can then watch the flow by taking many photographs with a camera. In this way you would be able to test whether it was surface tension flow (which should be in the same direction within the drop whether the droplet is upright or suspended) with gravity driven flow which should be opposite (the drop is upside down after all).
The authors of the study did this and found that the flow in upright drops of alcohol-water was opposite to that in n-butanol-water drops. This is what is expected both in surface tension dominated flow and in gravity dominated flow. But, when the drops were inverted, the flow within the droplet did not change absolute direction, instead it changed direction relative to the substrate (it may be helpful to see the cartoon), in both droplet types. Expected for a gravity driven flow (dense liquids move downwards), this is exactly the opposite to what would be expected with surface tension driven flow. It is sensible to conclude that the flow in drying droplets containing two liquid types is dominated by gravity, or as the authors phrased it “density-driven flows in evaporating binary liquid droplets”.
While the authors did a lovely job of watching the flows within the droplet, what happened to the the actual coffee stain? It could prompt us to do an experiment at home. How does adding alcohol affect the appearance of a coffee stain if the drop is upright compared to if you turned the drops all upside down? What happens if the droplet is not held upside down but instead at an angle to the vertical? There are many ways you could play with this result, see what happens, have a glass of wine and see if that gives you any insight into what you see with your coffee. As ever, have fun and if you do get any interesting results, please do let me know here, on twitter or over on FB.
*The dry scientific author in me wants to point out that although catchier, the title “how coffee stains form” does not actually capture the extent of the physics nor what the paper was about (the fact that this happens more often than just in coffee) and the given title was much better. The coffee drinker in me thinks yes, but, surely we could make it all about coffee anyway…
