| Time since the drop | – |
| Particle speed (relative to 20 °C) | – |
| Diffusion rate (relative to 20 °C) | – |
| Spread of the ink (rms) | – |
Model: particles move faster when hotter (speed ∝ √T), and warm water is also less viscous, so ink diffuses faster: D ∝ T/η (Stokes–Einstein, with the standard viscosity of water). Each particle takes random steps; the spread grows like √(D × time). Sizes and times are not to scale.