This is a fun, easy and super kid friendly experiment. Now, what exactly is happening here? :)
https://www.youtube.com/watch?v=rqQSlEViNpk
on Phys.org
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He put the cotton bud in a dish soap which is very 'smooth'(Very Less viscosity). And as the dish soap is less dense than milk, it floats. Then it spreads sideways (Very less viscosity)carrying the dyes with it.
I think he avoided using water instead of milk because water would dissolve the dyes fast.