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