Why do puddles of coffee sludge have spikes over its perimeter at regular intervals?

Question

After I finished my coffee, I by mistake dropped my cup on the floor. The sludge as it dropped, painted circles with little spikes in gaps over it perimeter:

Why do these spikes come in (mostly) regular gaps?

Answer 1

In blood spatter forensics the shape of droplet impact patterns has been studied extensively. See for example this article. Even though blood is pronouncedly a non-newtonian fluid, the main characteristics of the stains will be most probably the same for the likely newtonian fluid "dilute coffee solution in water", especially with respect to the reasons for the regularity of the so-called "spines" and "satellite droplets". Maybe the interdependency of the parameters density, viscosity, surface tension and impact velocity differs to some extent, but the general picture should probably the same.

However, I think the quickest way to gain an impression about the reasons for the pattern you have observed is by looking at a high-shutter-speed + flash still image of a droplet impact, like for example in this article. Maybe you can also find somewhere a high-speed camera video of a droplet impact. I would explain the pattern in the following way:

• As the droplet hits the surface (no matter if the surface is solid, like in your case, or liquid, like in the article), it first gets flattened, so the outer regions of the deformed droplet gain an increasing outward-directed horizontal velocity.
• The lower regions of the deformed droplet already stick to the surface (or experience viscous friction if the surface belongs to a shallow liquid as well). Therefore the horizontal components of the momentum of the upper regions of the deformed droplet causes them to get jammed against the lower regions, while material from the center of the droplet still keeps on flowing to the periphery.
• This jamming causes an elevated circular rim at the outer regions. Under ideal impact conditions, this rim is almost exactly regular at first.
• But real fluids have surface tension, which causes them to avoid all shapes but the spherical shape. Especially the torus-like shape of the rim is unstable because it has an "excited" state of surface energy. Depending on the impact parameters and the fluid properties and size of the droplet, it might often be easier/faster to escape this excited state by forming a regular chain of droplets where the rim was, rather than by retracting to one big blob at the center of the impact.
• Finally, gravity might be so dominant in relation to the fluid's properties, that already during the process of constriction of the rim towards satellite drops, the hole elevated mass falls down back into to bulk, leaving only residual traces of the beginning droplet formation, which you will see as regular "spines" or "spikes" at the boundary of the drop stain.
• On the other hand, if the drop falls from sufficient height (with sufficient kinetic energy) the satellite drops might have enough momentum to finalize their formation and "jump over" the rest of the stain, in which case you see isolated satellite stains.
• The regularity of the satellite patterns originates from the regularity of the intermediary rim, and the fact that the cross section of the rim together with surface tension determines the size and distance of the satellite drops.

Getting all this into an analytical fluid dynamics calculation is most probably an insurmountable task. But I guess a CFD simulation (with the ability to handle free surface boundaries) could pretty easily come up with the result.

PS: interesting sidenote from my personal experience. In the past I have sometimes tried to dry wet paint with a hair dryer (sorry for that testimony of being grossly impatient and a total amateur sometimes ;-) ). With that I could also observe the formation of a rim at the boundary of the paint (although the forces in this rim are constantly driven by the hair dryer rather then coming from an initial impact momentum), and if the blow was strong enough, also the formation of regularly spaced (partial) satellite droplets. Of course this process is yet more complicated since the paint successively dries and viscosity increases, but I think this low-budget experiment can also underline the general principle.

Answer 2

you can see that the surface the coffee splashes are sitting on has a regular texture to it, a square grid of round dots... The coffee appears to avoid the "dots" and prefers to wet the spaces between them. I suggest you set up a close-up camera with a sharp lens next to the surface and place single droplets of clean water on the surface and photograph the surface before and after placing the water drops. Then post the pix here so we can get a better look at what is going on here. By the way, what exactly is the surface? is it floor tile, linoleum, vinyl or what?