The dark ring at the edge of a dried coffee stain forms because the drop's contact line stays pinned to the surface as it evaporates, so the surface area cannot shrink. To replace the liquid lost to evaporation, an outward flow develops from the center to the edge, carrying suspended particles (coffee grounds, ink pigment) with it, so by the time the liquid fully evaporates, most of the solid material has concentrated at the rim. This mechanism, called capillary flow, was described in a Nature paper on ring stains from dried liquid drops.
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A follow-up paper in Physical Review E about three years later developed a more detailed 'flow and deposit' theory, showing how pinning, particle interactions, and internal flow can be tuned to change the stain pattern.
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The researchers demonstrated that engineering the shape of suspended particles can create jamming inside the flow, keeping pigment particles in place even as the surrounding liquid still moves outward.
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This control matters practically for functional printing inks, where a uniform deposit is needed instead of pigment collecting only at the edges.
835 words · auto-generated from the episode video
1:46:04stains and they dry out, the edges of the coffee stains are always much darker than the interior. I've actually always wondered this but not actually thought about it. >> Yeah. I've like noticed it. >> Yeah. Yeah. Yeah. And then and then now because of the golden goose I'm like diving deep and I'm like oh this is quite interesting. Um so they came out with a paper in nature that was had another amazing title capillary flow as the cause of ring stains from dried liquid drops. Here is the idea. So let's imagine a liquid drop with a bunch of coffee stains with with with like coffee liquid drop with coffee.
1:46:45What is going to happen as it evaporates? That's the question we're trying to answer. Okay. So, if we look at a coffee stain on the upper left, that's a liquid drop. Let's say >> on the bottom left, what they've done is introduce micrflu microsphheres into the coffee and they image it to track how the microsphheres are moving around in the coffee. And what they notice is all of the microsphheres are moving out to the edge. There is movement that is happening towards the edge of this coffee stain. Now why is that? Here is the idea.
1:47:26Picture the drop as a low dome like you know the experiment that we were talking about with the penny and then you drop like water on it. Similarly coffee just on a piece of paper or something like that. The boundary is going to be established based on how much coffee you spilled, but as it evaporates, the the coffee stain doesn't shrink. The area stays exactly the same. So, what's going to happen now? If the area stays exactly the same, the the liquid is leaving and by conservation of mass, you need to replace the liquid at the edges,
1:48:08right? And so if we go back to photo number 58, I just want to show you the model that they have. Yep. And there the liquid is leaving, right? It's evaporating. On the right hand side, they've got this figure that shows the liquid is evaporating. But because the liquid is evaporating, >> you need a flow from the interior to the exterior >> that is going to replace that liquid >> because the surface area of the drop has to remain the same. >> Oh man. Right? And because of that, you see these microphones move towards the edge. Well, that also means all of the coffee grounds or whatever that stuff that makes the coffee is moving towards
1:48:49the edge. And by the time that everything evaporates, all of the stuff has concentrated >> to the edge, >> right? Uh it makes total sense and it's like obvious in retrospect. >> Yeah. Yeah. Yeah. But it's such a it's such a clean argument. >> 100 100%. Yeah, 100%. This is something that I could imagine in an advanced undergrad class of fluid mechanics. Like this is something you solve like this is a homework problem that would be very nice. >> That's so good. >> You know, um the contact line is pinned basically and then the evaporation removes the solvent. So mass conservation creates this outward flow. >> Yeah.
1:49:29>> Um there this is the first treatment. Their later treatment which is this paper over here. Um this was in the physical review E in 2000 3 years later they had a much longer treatment where they developed the flow and deposit theory in much greater detail and what you can do is you can change the pinning you can change particle interactions you can change the internal flow and then you can change the pattern of the coffee state. So, so they developed it a lot more further in that paper and I think that quantification is very very important because if you're printing with some kind of functional ink, right, you might want a uniform deposit. >> If you're trying to print with an ink printer, you don't want only the edges
1:50:09to show up. >> So, the next question obviously becomes how do we prevent this >> from happening? And the way we prevent this from happening is we change the characteristics of the coloring the the coffee grounds or whatever that is inside the liquid. Um what we end up doing is in order to suppress this outward flow, you can engineer the shape of the particles inside that will that will create traffic jams >> inside the flow that will make the particles your ink or whatever thing that is coloring it >> stay put and not actually move. So maybe the water will move, right? The other fluid, but the stuff that is creating
1:50:51the coloring doesn't move because it's jammed up. You're sort of engineering the outcome >> by creating differences in the substance such that >> the only outcome that arises is the desired outcome. >> Mhm.
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