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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 teardropsbut 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 surfacesthe 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 youre 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 pressureroughly 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 energynot 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 cubedfor small numbers.

  • Ok, so obviously raindrops exist, but if you want to know HOW they sidestep this battle

  • between quadratics and cubics, youll have to go watch MinuteEarth’s video about how

  • raindrops form.

There’s lots of physics going on in raindrops: cohesion, adhesion, air resistance – I

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B2 US energy water centimeter volume droplet surface

Why Raindrops Are Mathematically Impossible

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    bsofade posted on 2016/07/14
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