Rimstain: Coffee Ring Effect
Mechanics, Chaos & Fluids arc, page 103 of 193. Back to The Pixelated Physics Universe
Who they are
Rimstain has one line, and says it often: “Evaporation puts everything at the edge.”
Rimstain 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
Coffee-ring effect: evaporation-driven outward flow deposits particles at the drop edge.
$$ \begin{gathered} J(r) \propto (R^{2} - r^{2})^{-\lambda}, \qquad \lambda = \frac{\pi - 2\theta_c}{2\pi - 2\theta_c} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $J(r)$ | evaporative flux at radius r | kg/(m^2·s) |
| $R$ | drop radius | m |
| $r$ | distance from drop centre | m |
| $\lambda$ | flux exponent | — |
| $\theta_c$ | contact angle | — |
Sources
Crossovers
Rimstain meets Clustrelle (Cheerios 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.
Rimstain meets Vaporelle (Latent Heat of Vaporization). Rimstain's outward flow happens because evaporation is fastest at the pinned edge of the drop. Vaporelle sets the energy price of every molecule that leaves: water's latent heat.
Wear the lore
Concept keywords: Coffee Ring Effect, Rimstain, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics