What the article doesn't emphasize enough:
Pinning of the contact line is crucial (e.g. due to surface roughness), otherwise the ring would not be as pronounced. Due to higher curvature, evaporation is faster at the edges, causing the non-evaporating solids to flow to the edge leading to more of them there in the end when everything has dried up. But on a smooth surface, droplets just shrink. When they don't, you get the ring stain.
It is a bit annoying that the article does not link any relevant research. There is a wikipedia page on the topic (https://en.wikipedia.org/wiki/Coffee_ring_effect), but afaik it is an interesting problem in many different contexts, for example in inkjet printing (one can find plenty of articles there as well).
This is the original seminal work on coffee drop evaporation out of Sid Nagel’s lab, with theoretical support from Tom Witten and Todd Dupont and their students.
Like everything out of the Nagel lab, at least from that era, it combines a keen curiosity about things we take for granted with rigorous physical experiments and insight.
The Nagel/Witten collaboration was one of the many lovely things at the University of Chicago in that era, and it was always tremendous fun to see them present and get a glimpse at how they approached problems.
It was like looking over the shoulder of giants: often humbling and always educational.
I think this was explained in a documentary by Discovery Channel some 20 years ago. I remember it vividly. One application of this was to use this process to manufacture very thin wires by deposition of atoms.
Evaporation is more at the edge. More of the water makes its way to the edge. The water carries more color to the edge. So that is why the ring of coffee color is formed.
But why is the water making its way to the edge all the time?
Gravity / water pressure. Consider an overly simplified case[0]: A molecule "disappears" from the edge, leaving a cavity (blue circle). Waiting to flow into the cavity are two molecules, one on the inner side (red) and another on the outer side (purple) of the cavity. Molecule on the inner side is being "pushed" into the cavity by a much larger "body" of water (pink) than is the molecule on the outer side (light purple). So even though both molecules will move into the cavity, the inner molecule will move farther. Repeat a few quintillion times, and you've got directional flow from the middle to the edge.
Because the drop/puddle is trying to keep its shape. I think that's what the current top comment is saying about the contact line being fixed. On rough surfaces the edge can't just retreat as it evaporates, and if I understand correctly it also wants to keep the rounded shape at the edge due to surface tension, so water gets pulled in from the rest of the puddle to fill it out.
It's because as the coffee dries, the liquid gets pulled to the rim, leaving all the coffee gunk behind in a ring. Turns out, this same trick helps make better inks and paints too!
I once noticed on a neighbor's garbage can, which had their house number spray painted on it, that the paint had mostly flaked off except around the edge of the numbers which was adhered better. The paint would have been thinner from the spray application.
Is this completely correct? Coffee isn’t homogeneous. There are particulates and oils that will separate out. Anything pushed to the top will also move towards the edge given the shape of the droplet. There is also capillary action to consider. Seems like there should be more than one effect that leads to the edges of the stain being darker.
This is not the same phenomenon though? Chromatography is based on different adsorption affinity of the different molecules of the liquid to the stationary phase.
Many kinds of stains are darker at the edges. It's because the capillary action slows down there. The area of the stain increases in proportion to r^2, and there is evaporation also. Thus the stain only spreads to a certain size. As the solvent thins out, it's not able to carry the pigment quickly, and so the pigment particles pack closer together. Pigment is still arriving from the center of the stain, but not moving farther out any more, so it has to accumulate.
This is the same reason suburban sprawl continues to grow despite the reduced density at the edge. There’s a premium for a perception of being mostly surrounded by open space, out past all the other housing developments and strip malls that are a back towards the city. It creates a bump of economic gradient at the frontier.
I'm disappointed the article and all the comments here ignored Mach banding...
On top of all the mechanism that would distribute the solids in a bit of a ring, we also have a perceptual distortion that would enhance the contrast a bit, making it look like a stronger gradient than it actually is.
What the article doesn't emphasize enough: Pinning of the contact line is crucial (e.g. due to surface roughness), otherwise the ring would not be as pronounced. Due to higher curvature, evaporation is faster at the edges, causing the non-evaporating solids to flow to the edge leading to more of them there in the end when everything has dried up. But on a smooth surface, droplets just shrink. When they don't, you get the ring stain.
Relevant: https://www.nature.com/articles/nature10344
It is a bit annoying that the article does not link any relevant research. There is a wikipedia page on the topic (https://en.wikipedia.org/wiki/Coffee_ring_effect), but afaik it is an interesting problem in many different contexts, for example in inkjet printing (one can find plenty of articles there as well).
Indeed, article appears to be old encyclopedia style, no citations, oversimplified.
A better ref imo:
https://www.nature.com/articles/39827 (1997)
This is the original seminal work on coffee drop evaporation out of Sid Nagel’s lab, with theoretical support from Tom Witten and Todd Dupont and their students.
Like everything out of the Nagel lab, at least from that era, it combines a keen curiosity about things we take for granted with rigorous physical experiments and insight.
The Nagel/Witten collaboration was one of the many lovely things at the University of Chicago in that era, and it was always tremendous fun to see them present and get a glimpse at how they approached problems.
It was like looking over the shoulder of giants: often humbling and always educational.
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I think this was explained in a documentary by Discovery Channel some 20 years ago. I remember it vividly. One application of this was to use this process to manufacture very thin wires by deposition of atoms.
Evaporation is more at the edge. More of the water makes its way to the edge. The water carries more color to the edge. So that is why the ring of coffee color is formed.
But why is the water making its way to the edge all the time?
Diffusion, more specifically capillary flow I think. Water will flow from the saturated to the unsaturated areas.
Gravity / water pressure. Consider an overly simplified case[0]: A molecule "disappears" from the edge, leaving a cavity (blue circle). Waiting to flow into the cavity are two molecules, one on the inner side (red) and another on the outer side (purple) of the cavity. Molecule on the inner side is being "pushed" into the cavity by a much larger "body" of water (pink) than is the molecule on the outer side (light purple). So even though both molecules will move into the cavity, the inner molecule will move farther. Repeat a few quintillion times, and you've got directional flow from the middle to the edge.
[0]https://i.imgur.com/mVOiwxH.png
Because it evaporates [mostly] from the edge, so new water flows there to make up for it.
Because the drop/puddle is trying to keep its shape. I think that's what the current top comment is saying about the contact line being fixed. On rough surfaces the edge can't just retreat as it evaporates, and if I understand correctly it also wants to keep the rounded shape at the edge due to surface tension, so water gets pulled in from the rest of the puddle to fill it out.
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My guess would be: because there is more space in the outer ring than the inner ring.
It's because as the coffee dries, the liquid gets pulled to the rim, leaving all the coffee gunk behind in a ring. Turns out, this same trick helps make better inks and paints too!
I once noticed on a neighbor's garbage can, which had their house number spray painted on it, that the paint had mostly flaked off except around the edge of the numbers which was adhered better. The paint would have been thinner from the spray application.
Is this completely correct? Coffee isn’t homogeneous. There are particulates and oils that will separate out. Anything pushed to the top will also move towards the edge given the shape of the droplet. There is also capillary action to consider. Seems like there should be more than one effect that leads to the edges of the stain being darker.
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Radial chromatography: https://en.wikipedia.org/wiki/Radial_chromatography
when liquid phase is applied to impermeable solid, i.e. glass sheet.
you have solid phase "radial" chromatography.
This is not the same phenomenon though? Chromatography is based on different adsorption affinity of the different molecules of the liquid to the stationary phase.
oh it very much is!
At first I thought this website would be pages with title "Why is..." but the .is is Iceland's TLD ;)
It's too bad they don't use more user-friendly URLs like why.is/coffee-stains-darker-at-edges
This is exactly what I've done with my blog. See e.g. https://andri.yngvason.is/repairing-the-washing-machine.html
This is WHY I read HN daily. Omg.this.is.funny.org
I am pretty sure they used this domain hack on purpose :)
Many kinds of stains are darker at the edges. It's because the capillary action slows down there. The area of the stain increases in proportion to r^2, and there is evaporation also. Thus the stain only spreads to a certain size. As the solvent thins out, it's not able to carry the pigment quickly, and so the pigment particles pack closer together. Pigment is still arriving from the center of the stain, but not moving farther out any more, so it has to accumulate.
Serendipitously enough, I just started skimming this book of factoids I got from Five Below, and three questions in this phenomenon is addressed:
https://www.google.com/books/edition/Do_Geese_Get_Goose_Bump...
Hmm not just coffee stains too. If you've ever had a water leak on gypsum board, the edges of the water ring are darker.
I think that's a similar but different effect, as the water travels outwards from the centre due to capillary action it pulls particles with it.
Also blood.
Side bit from some recent news about dried blood and its crackle pattern... https://phys.org/news/2025-04-blood-droplets-inclined-surfac... (saw it https://news.ycombinator.com/item?id=43852446 though it didn't get too much attention)
Also all particulates.
It isn't about the chemistry of the suspended/dissolved solids.
Same for watercolor painting:
https://grail.cs.washington.edu/projects/watercolor/paper_sm...
This has been a little mystery for me when I don't immediately dispose of my pour over coffee filters. Similarly they end up quite dark at the edge.
But as per the article, that's where most of the evaporation happens, and more of the color is left behind there.
And of course, if you use LaTeX, and need coffee stains on your paper there is a package for it:
https://ctan.math.illinois.edu/graphics/pgf/contrib/coffeest...
This is the same reason suburban sprawl continues to grow despite the reduced density at the edge. There’s a premium for a perception of being mostly surrounded by open space, out past all the other housing developments and strip malls that are a back towards the city. It creates a bump of economic gradient at the frontier.
People buy at the frontier because they can afford the housing there, even at the severe loss of amenities.
Especially if the next 20+ years of their life is going to be driving their kids to sports games anyway.
I feel like that's completely unrelated.
Exhibits the same behaviour.
Coincidentally, ergo unrelatedly.
Basically the same curve. Reminded me of it. That’s all.
> There’s a premium for a perception of being mostly surrounded by open space
Maybe? In urban areas the opposite is true - rent goes up the closer you are to a major subway station
https://www.renthop.com/research/nyc-mta-subway-rent-map-202...
Glancing at the domain name, I got a burst of nostalgia for whytheluckystiff.net.
Hah! What a great domain name!
I'm disappointed the article and all the comments here ignored Mach banding...
On top of all the mechanism that would distribute the solids in a bit of a ring, we also have a perceptual distortion that would enhance the contrast a bit, making it look like a stronger gradient than it actually is.
fluid pressure pushes particles outwards
Because of neurodivergence causing their perception
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