Physics of Raindrops: Why They’re Mathematically Impossible

Teardrops – this is what most assume falling raindrops often look like. However, there is a lot of physics – cohesion, adhesion and air resistance – going on in raindrops. Falling raindrops look more like jellyfish than teardrops.

In the latest episode of MinutePhysics, Henry Reich explains the physics that makes raindrops mathematically impossible to explain.

The process of formation of raindrops seems pretty easy from our point of view. According to us, when we cool water vapour in the air, it condenses into liquid droplets once it passes its condensation point – the moment in which substance changes from its gaseous state to liquid state. But Henry says it is not that simple, because there is a big problem standing, almost literally, in the way: the surface of the droplets themselves.

While considering the surface of the liquid droplets, we need to follow another distinct set of laws of physics.

Liquids are bound by the laws of intermolecular attractions – attractions between one molecule and a neighboring molecule. So in water, all the molecules will pull together in an attempt to minimize the size of the outer surface area. Wonder why small water droplets are spherical, why you can put a huge quantity of water on a penny, and why bubbles form the crazy shapes they do? It is because of the intermolecular attraction between the molecules; or in physics way of explaining, surfaces require more free energy to make than volumes.

When we are condensing water vapour from a gas to make liquids, every cubic centimeter volume of water we have converted releases energy just from its changes of volume and pressure, but in order to make each square centimeter of the surface of that water, an input of energy is required.

For a huge amount of water, the energy we get from every cubic centimeter volume of water, is more than enough to make up for the energy cost due to the surface area. Cubing tends to make things bigger than squaring, but for a small radii, cubing a small number makes it smaller than squaring it.

If a water droplet is below a certain size, making it bigger requires more surface area energy than is released from volume energy. It means raindrops do not grow, they shrink as they fall. So if they shrink, perhaps they should disappear before they hit the ground, but why there are even rains?

“For pure cubic and quadratic functions, this equivalence point happens 25. at 2/3 – that’s when x^3 starts growing faster than x^2, but for water droplets it’s 26. somewhere around a few million molecules; way too many to randomly clump together in 27. 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,” says Henry.

If something that cannot be explained by science is called magic, should raindrops be considered magic then, just because it is mathematically impossible? Watch the video below and see if it changes your perspective about raindrops.