Laminar Flow

A low flow rates the layers of liquid flow over each other neatly and the dye slides between them. At higher flow rates, the shear between the different layers causes rotation in the flow this is the mixing.

The whole thing was sorted out by Osborn Reynolds in 1883.

These fluid dynamic effects are vital for planes flying, and other such stuff.

You can also get the laminar and turbulet effect from a tap. The glassy flow is laminar, the cloudy, turbulent (not dissolved water).

Now if it was moved slowly, and returned back slowly all particles will come back to their original positions, including the dyed particles.