Question

how does a drop of red ink get evenly distributed in water?

Answer 1

Ink diffuses in water because of the random motion of water and ink molecules. On a large scale, we don’t see the individual molecules moving. Instead we see how dark the ink is at different points in the solution, which actually indicates its concentration. You can see the ink move from areas of higher concentration to those of lower concentration, and the rate of this movement is proportional to the diffusion coefficient of the ink in water.
Diffusion Coefficient

The higher the temperature of the water, the faster the molecules move. This results in more and harder collisions. Consequently, the diffusion coefficient is proportional to the temperature. How far each ink molecule moves after a collision depends on its diameter, because bigger molecules slow down more from friction compared to smaller molecules. The intrinsic friction in a fluid is called viscosity. Thus, the diffusion coefficient is inversely proportional to both the molecule's diameter and the liquid's viscosity.

Answer 2

This happens because the particles of water have space between them.