## Why don't clouds fall?

Clouds can hold an enormous amount of water. When this water falls as rain it clearly has a significant mass so why don't clouds fall? In fact, the small water droplets that make up clouds do fall slowly. However, the drag force of the air dominates over the gravitational force for small particles. The drag force increases as the size of an object decreases. The force needed to move a sphere through a viscous medium is given by Stokes's law,

F = 6πηRv.

Here, R is the radius of the sphere, v is the velocity, and η is the viscosity. The viscosity of air is about 0.018×10-3 Pa·s and the viscosity of water is about 1.8×10-3 Pa·s. Stokes's law is valid if the Reynolds number NReynolds = 2Rρv/η is less than about 2000. Here ρ is the mass density.

A spherical particle falling under the force of gravity will reach terminal velocity when the gravitational force matches the drag force,

mg = 6πηRv.

Solving this for the terminal velocity yields,

vterminal = 2gρR²/(9η).

A water droplet with a 10 nm radius falls at 12 nm/s in air. It would take 2.6 years for this droplet to fall one meter. It is only when the small droplets begin to coalesce into larger droplets that they fall with significant speed.

In some sense, the inverse effect to rain is the rising of bubbles in beer. Bubbles are lighter than the surrounding liquid so gravity pushes them up. They rise with a constant velocity which is described by Stokes law. If you are the type that carefully observes your beer, you will have noticed that sometimes the bubbles move down. This is because of the circulation of liquid in the beer glass. The rising bubbles in the center of the glass drag some liquid along with them. After this liquid reaches the top of the glass, it returns to the bottom along the sides of the glass. This downward flow can drag bubbles, especially small bubbles, downwards against the force of gravity.

In a similar manner, small rain drops can be pull up by air currents against the force of gravity.