English: Yellow food coloring spreading in water. The glass on the left contains hot water, while the glass on the right contains cold water. The food coloring was added to the cold water slightly before the coloring was added to the hot water, yet after a few seconds it has spread more thoroughly in the hot water. The frames are roughly 1 second apart (so the animation is roughly 2x real-time).
The dispersion is caused by convective mass flow due to concentration gradients, temperature gradients, bulk convective flow from localized density gradients. Currents and eddies are clearly visible. If the food coloring was to move throughout the container purely by diffussion, assuming a diffusion coeficient of 10^-12 m^2/s, it would take approximately 10^10 seconds for the dye to reach a 90% equilibrium.