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

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?

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!

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.

[supplementary]

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.

At first I thought this website would be pages with title "Why is..." but the .is is Iceland's TLD ;)

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.

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.

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