My older son’s school (Willagillespie Elementary) had its annual “Math and Science Night” tonight, which is consistently great. This year, I was asked if I would do something for it, and I decided to present some demonstrations and activities about surface tension. Here’s something that I didn’t show, but that I did for my Physics of Life class, that gets at the question of what aspects of an object’s geometry govern the force of surface tension acting on it. Here are two disks, which sit atop a water surface.
The disks each have the same diameter and the same area. Will they hold the same amount of weight? (Now’s the time to make your guess…) In the movie below, I gradually add washers, one by one. Which will sink first? In class, this was remarkably suspenseful — everyone stared, completely motionless and silent!
In case you weren’t patient enough to watch the video: the many-spoked disk supports more weight before sinking. (Sometimes, I can get several more washers on this one than I was able to in the video above.) The force of surface tension depends not on area, but on the perimeter of the contact with the fluid. The geometry of surface tension is the reason why big animals (like you and me) have a very hard time walking on water, while small animals can do so easily: if an object’s length gets bigger by some factor X, its perimeter (and therefore the force of surface tension supporting it) gets bigger by X, but its mass (and therefore the force of gravity pulling it down) gets bigger by X cubed, a much larger amount!
At school, we looked at paper clips atop water, motion induced by dabs of soap, and my third-favorite demonstration of all time: placing a loop of string on a soap film…
… and then popping the film inside the loop. What will happen? This?
or this?
I strongly recommend trying this in your kitchen! (It’s a bit tricky to get the string to sit on the soap film without everything falling apart. Practice helps, as do soapy fingers.)
The activity went well, or as well as I could have hoped given that I lost my voice today and could only speak in a whisper. It occurred to me that I could mime the whole thing, but I have neither a beret nor a Breton shirt.
The Eighteenth Elephant 
So would a Koch snowflake support infinite weight? Or could we walk on water if we wore shoes of Romanesco broccoli?
Sadly, edges that are closer than the “capillary length” (about 2 mm for water) don’t separately contribute to the effective perimeter of the object, as far as being supported by surface tension goes. So much of the infinite perimeter of the snowflake wouldn’t be helpful! Still, a spindly fractal would seem like a good idea! You might like the figures in http://biomimetic.pbworks.com/f/WALKING+ON+WATER+Biolocomotion+atBush.pdf ,which are great. (In Fig. 3, the capillary length, but no fractal feet.)
By the way: Happy Birthday!