Ink Drop in Water Simulator (2D)

Ink Drop

Drop size 100%

Water

Viscosity 50%

Temperature 20 °C

Click the water to drop ink.

Live Readout

Diffusion coeff. D

Spread radius

0 px

Elapsed time

0.0 s

Active particles

How it works

Each ink particle undergoes a random walk driven by countless collisions with invisible water molecules — the same Brownian motion Einstein used in 1905 to prove atoms exist. The Stokes–Einstein relation gives the diffusion coefficient D = k_BT / (6πηr): higher water temperature T speeds diffusion, while higher viscosity η and a larger effective particle radius r slow it down.

In two dimensions, the mean-squared displacement of the ink cloud grows as ⟨r²⟩ = 4Dt, so the visible spread radius grows with the square root of time, not linearly — diffusion looks fast at first and then appears to slow down, even though every particle keeps moving at the same average rate.

Drop size sets how many ink particles start clustered together; it doesn't change how fast any single particle diffuses, but a bigger drop takes longer to look "spread out" simply because it starts from a larger initial cloud.

Click or drag to drop ink · Random-walk diffusion, not just a fade