okay, you need to look at the structures of the particles of matter in the solid, liquid and gas.
particles in a solid are in fixed positions, where they can only vibrate in those positions ( take a look at ice, or rather, a brick)
liquids have very small or rather, no spaces between them, but they can slide or rub against each other, like people in a <em>really tight</em> crowd I guess
gas particles have very large spaces between them and they move randomly. these exibit what's called brownian motion.
since water particles (and all other liquid particles) have negligible spacings and limited movement, that allows the dye particles to move from a region of high concentration to that of a low concentration. the aim for this is for the mixture/solution to reach an equilibrium, that is the mixture must get to a point where all regions have the same concentration of the dye.
