Clustrelle: Cheerios Effect
Mechanics, Chaos & Fluids arc, page 104 of 193. Back to The Pixelated Physics Universe
Who they are
Clustrelle has one line, and says it often: “Lonely bubbles attract at the meniscus.”
Clustrelle is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Floating objects attract via meniscus deformation (Cheerios effect).
$$ \begin{gathered} \ell_c = \sqrt{\frac{\gamma}{\rho g}} \\ F(\ell) \propto K_1\!\left(\frac{\ell}{\ell_c}\right) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\ell_c$ | capillary length | m |
| $\gamma$ | surface tension | N/m |
| $\rho$ | liquid density | kg/m^3 |
| $g$ | gravitational acceleration | m/s^2 |
| $F(\ell)$ | attraction between two floating objects | N |
| $\ell$ | separation of the objects | m |
| $K_1$ | modified Bessel function of the second kind | — |
Sources
Crossovers
Clustrelle meets Kayella (Kaye Effect). Kayella's shampoo is shear-thinning, so it gets runnier as it is sheared. Clustrelle's floating bubbles attract because surface tension bends the liquid surface. Both are everyday puzzles where the fluid's own shape drives the motion.
Clustrelle meets Rimstain (Coffee Ring Effect). Rimstain's ring forms because evaporation at the edge pulls fluid outward, carrying particles with it. Clustrelle's Cheerios gather because the meniscus bends the surface. Both are surface-driven flows in a cup.
Wear the lore
Concept keywords: Cheerios Effect, Clustrelle, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics