A nonmathematical post but nevertheless something I novel I noticed this evening and which made me think that I should probably investigate this a bit further.
I recently bought a cheap digital microscope and have been randomly looking up close at things to verify some of my previous explanations for various phenomena. One being how small droplets of liquid produce pretty vivid dots when they lie on the surface of the screen of your phone. The basic physics is that the droplets forms a semispherical lense which magnifies the individual pixels of the screen making them partially visible even from afar as illustrated by this image of a ~1mm droplet on a Samsung Galaxy S3 screen. and here slightly more magnified.
As I was applying the droplets however dipping various small thin things like needles I realized dropping the droplets from needles was no good because the droplet hangs on the tip of a needle in a rather curious way.
Or rather it doesn’t hang from the tip at all. This is to be compared with how droplets would hang from things which arent sharp at the tip like a pencil lead
and sharpening the pencil lead at the tip with a knife the same effect is produced
In a way this isn’t that strange given that one of the effects which retains the droplet is that the tip isn’t inside the droplet for if it was there would be no (discontinous) barrier towards decreasing the surface tension by simply sliding while with a blunt tip releasing to form a spherical droplet requires a discontinuous increase in surface area and I suppose the probability of it sticking at all would go down.
(Details on the formation of these droplets by the way is by means of dipping it pretty deep and have an originally even coating slide down and accumulate at the tip.)
Nevertheless I can’t quite make out the details of what the origin of the force that is fulling the droplet upwards is coming from, whether it is driven principally by surface tension or adhesion. Because it the needle is shaken a bit and the droplet pushed down a fraction of a millimeter it will climb back up.