A Tense Moment

A few days ago, I was sitting on the balcony at my parents' condo, and I noticed a water droplet on the leaf of their banana tree.

 

Seeing it got me thinking about surface tension, the force that gives it the characteristic shape that small drops have.

A simple way to think about surface tension is this: each molecule of water has a certain amount of attractive force between it and its neighbors.  However, at the surface, there are no molecules on one side, so the force associated with the other molecules is stronger.  Here's a diagram (from Wikipedia):

When a droplet like this sits on a solid surface, it will be spread out slightly by the force of gravity.  The height is given by

where ϒ is the surface tension between air and water, θ is the angle the water's surface makes with the leaf, and ρ is the density of water.  Plugging in the values we have, h = 4.1 mm.  Unfortunately, my photo doesn't include any scale, so I can't check how close this is, but it sounds reasonable.

I'll be leaving for Michigan in a few days to start grad school, so there will be a pause in posting while I move in.