coalescence

A raindrop landing on an already-wet window doesn't splash and doesn't soak in — it stops being a drop and becomes film. That's the thin-film equation, and every drop below is an exact solution of it. The drop isn't in the equation; the drop is the initial condition.

hfilm thickness αroof pitch x̂downhill σsurface tension μviscosity ρdensity ggravity

integrated linearised about a flat film, h = h₀ + η

touch a slider to see which term it moves

how wet the glass already is µm

the h³/3µ in front. Drops vanish as 1/h₀³ — wetter glass erases them cubically faster.

roof pitch °

splits gravity between the two terms: sin α runs the water downhill, cos α flattens it.

how hard it rains /m²/s

not in the equation. This is the initial condition.

drop diameter mm

how close you are mm of glass

distance to the trees m

behind the glass

show the roof window

downhill drift c
drops visible at once

or ask for more or less rain

the model is not in your browser yet — asking fetches it once (~0.5 GB), and you can watch it arrive.

Write anything meaning more rain or less rain. A 0.5B model in your browser answers one yes/no question — do they want it stronger? — and that is all it is asked, because it is all it can do. It gets it right 27 times in 32 on its own, so where the wording is plain a word list overrules it, and the line above tells you when that happened.

It cannot judge how wet the glass already is: asked "is the glass wet?" and "is the glass dry?" about one sentence it answers yes to both. That slider stays yours.