Have you a video of real experiment of mixing of two liquids?
How much the theoretical video is similar to a real picture?

Great video. Surface or boundary tensions are fractal regional effects also. The regional effects caused by the boundaries are fractal in a more general sense, although box counting could be done. I am more liberal about the term fractal than some and so i express my opinion . I think magnification of the boundaries would reveal how fractal they are, and that they are wada regions.

Boundaries actually determine the internal nature of the regions they bound, by means of a dynamic equilibrium. It is fascinating to watch different dynamic equilibriums pass though each other without mixing. The rate of pass through is too fast for osmosis to have any appreciable effect. But as soon as the boundary equilibrium matches that of another the boundary vanishes. Surface tension then is a boundary effect due to different dynamics, and a boundary forms precisely because of the different spatial dynamics.

Why can't i walk through a wall?  That seems to be down to viscosity in the main. More revealing though is if i could find a space with the same dynamic equilibrium in its boundary  i would simply merge with it! That is spooky!