This is another demonstration that falls in to the category of illustrating the order of magnitude of a process or constant that students have trouble visualizing (just like the plunger tog-o-war illustrated the magnitude of atmospheric pressure). I use this demonstration in my environmental fluid mechanics class to illustrate how slow a process molecular diffusion can be.

**Equipment**

- Fish tank half full of water
- A 10-20 ml syringe
- Salt water
- Food coloring

**Demonstration**

The demonstration takes a full class period so it needs to be started at the very beginning of class. Mix the food coloring into the salt water and fill the syringe. Slowly lower the syringe to the base of the fish tank so that the outlet is touching the base. Very slowly inject the dyed salt water along the base of the tank. The dyed salt water should spread out in a very thin layer at the base of the tank. Have the students look at how thin the layer is. At the end of the class have the students have another look at the tank and they should observe that there has been negligible thickening of the layer during the hour or so since injection. If you can, move the tank without disturbing it, or you can leave it in the class room for a prolonged period of time so you can invite students to return later in the day to see how the layer slowly thickens. If keeping it diffusing is not an option you can mix the tank up by hand at the end of the class to illustrate how rapid turbulent mixing can be by comparison.

**Analysis**

I usually use this demonstration on the first day of discussing the advection – diffusion equation. There are plenty of good write-ups on solutions to idealized diffusion problems (see for example https://engineering.dartmouth.edu/~d30345d/courses/engs43/Chapter2.pdf) so I will not write up the analysis here. The demonstration can be modeled as a finite release one dimensional diffusion problem with a reflecting boundary at the base and an infinite environment vertically (that is, the diffusing dyed salt water does not feel the effect of the water surface over the time scale of the demonstration). I try to get through this problem during the class so that we can substitute values in to see if the predicted diffusion over the class period is similar to that observed (i.e. not much). The diffusivity of salt in water is approximately 1.6×10^{-5} cm^{2}/s (http://pubs.rsc.org/EN/content/articlepdf/1954/tf/tf9545001048).

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.