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There’s lots of physics going on in raindrops: cohesion, adhesion, air resistance – I
mean, falling raindrops often look more like jellyfish than teardrops – but perhaps most
fascinating is the physics that makes raindrops impossible.
You might think making a raindrop is easy – just cool water vapor in the air past
its condensation point, and it condenses into liquid droplets, right? But there’s a big
problem standing, almost literally, in the way: the surface of the droplets themselves.
Liquids hate surfaces – the liquid is bound by the laws of intermolecular attraction to pull
together in an attempt to minimize the size of their surfaces. That’s why small water
droplets are spherical, why you can put a huge amount of water on a penny, and why bubbles
form the crazy shapes they do.
The technical way of saying this is that surfaces require more free energy to make than volumes.
For example, when you’re condensing water in saturated air from a gas to a liquid, every
cubic centimeter VOLUME of water you make releases energy just from its change of volume
and pressure – roughly enough to lift an apple a meter into the air. But to make each
square centimeter of the SURFACE of that water requires an INPUT of energy – not much,
but it's equivalent to lifting a fortune cookie fortune 1 centimeter.
For large amounts of water, the energy you get from the volume, which is proportional
to the radius cubed, is more than enough to make up for the energy cost due to the surface
area, which is proportional to the radius squared. Cubing tends to make things bigger
than squaring. BUT for really small radii, the opposite is true – cubing a small number
makes it smaller than squaring it. This unavoidable mathematical truth means that if a water droplet
is below a certain size, then making it bigger requires more surface area energy than is
released from volume energy, meaning it TAKES energy for the droplet to grow, so it doesn’t
– it shrinks. For pure cubic and quadratic functions, this equivalence point happens
at 2/3 – that’s when x^3 starts growing faster than x^2, but for water droplets it’s
somewhere around a few million molecules; way too many to randomly clump together in
less than the age of the universe! And thus, raindrops are impossible for the precise mathematical
fact that x squared grows faster than x cubed – for small numbers.
Ok, so obviously raindrops exist, but if you want to know HOW they sidestep this battle
between quadratics and cubics, you’ll have to go watch MinuteEarth’s video about how
raindrops form.
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Why Raindrops Are Mathematically Impossible

8737 Folder Collection
bsofade published on July 15, 2016
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