does this make sense?
If coloured crystals of e.g. the highly coloured salt crystals of potassium manganate(VII) are dropped into a beaker of water and covered at room temperature. Despite the lack of mixing, convection etc. the bright purple colour of the dissolving salt slowly spreads throughout.

The same thing happens with dropping copper sulphate crystals or coffee granules into water and just leaving the mixture to stand.
When pollen grains are viewed under a microscope they appear to 'dance around' when illuminated with a light beam at 90o to the viewing direction. This is because the pollen grains show up by reflected light and 'dance' due to the millions of random hits from the fast moving water molecules. This is called 'Brownian motion' after a botanist called Brown first described the effect .At any given instant of time, the hits will not be even all round the pollen grain, so they get a greater number of hits in a random direction. comment asap.