Clouds are made up of tiny water or ice droplets, depending on temperature. This implies that cloud density is greater than that of dry air. Why don't clouds sink through their surrounding atmosphere rather than float by in a variety of formations?
Clouds don't start as clouds. Most of them start out as humid air, typically from evaporation from a large body of water (say, the Pacific or Atlantic ocean, and most of that between latitudes 30 degrees north and south).
Now humid air is LIGHTER (less dense) than normal air. This is because gases like to run the same number of moles (number of molecules) per cubic meter, and an H2O molecule weighs less (much less) than an N2, O2 or CO2 molecule.
So, the humid air rises until is cools at higher elevations, forming clouds. Even at this point, where the microdroplets are denser than the surrounding air, they are not so heavy that they can force their way down. They are trapped, sort of like grains of sand that get picked up in a sandstorm. At some point, though, the micro-drops collect into not-so-micro drops and start falling. As they fall they merge with other moisture and micro-drops to form rain or other precipitation.
To understand how these micro-droplets or micro-crystals can stay up so long, think about hail storms. We know now that larger hail sizes can be attributed to the initial tiny hail dropping for a distance and then being blown back up by thunderstorm updrafts. The tiny hail balls go up and down, up and down; and get coated with a new layer of ice each time, until they are finally heavy enough to overcome the updrafts and fall to the earth. At his point they may be golf ball sized or even larger. Think of it: billions of balls of hail, each the weight of a snowball, being suspended in space by atmospheric conditions. After pondering that, it is not hard to believe that micro-droplets can stay up there.
The short answer is, it's a colloidal suspension, effectively. From Scientific American:
For particles that are roughly spherical, mass is proportional to the radius cubed ($r^3$); the downward-facing surface area of such a particle is proportional to the radius squared ($r^2$). Thus, as a tiny water droplet grows, its mass becomes more important than its shape and the droplet falls faster. Even a large droplet having a radius of 100 microns has a fall velocity of only about 27 centimeters per second. And because ice crystals have more irregular shapes, their fall velocities are relatively smaller.
Upward vertical motions, or updrafts, in the atmosphere also contribute to the floating appearance of clouds by offsetting the small fall velocities of their constituent particles. Clouds generally form, survive and grow in air that is moving upward.
Air Density Calculations
Calculations with Vaisala: http://go.vaisala.com/humiditycalculator/5.0/
All calculations at a pressure of 1013.25mbar Temperature 20°C rel. humidity 0%: density: 1.2041 kg/m^3 100% 1.1936 kg/m^3 Density difference: 10.5 g/m^3
Temperature 24°C rel. humidity 0%: density: 1.1879 kg/m^3 100% 1.1747 kg/m^3 Density difference: 13.2 g/m^3
Temperature 30°C rel. humidity 0%: density: 1.1644 kg/m^3 100% 1.1459 kg/m^3 Density difference: 18.5 g/m^3
Temperature 34°C rel. humidity 0%: density: 1.1439 kg/m^3 100% 1.1264 kg/m^3 Density difference: 17.5 g/m^3
At the first glance these differences look quite small. But taking into account that fog holds less than 0.3g of condensed water as micron sized droplets it is very large. The amount of invisible water is much higher in that air. What is the effect of temperature? 20°C vs 24°C: at 0% rel. hum. Density difference: 1.2041 – 1.1879 = 16.2 g/m^3 30°C vs 34°C: at 100% rel. hum. Density difference: 1.1459 – 1.1262 = 19.7 g/m^3
Density differences because of humidity differences are in the same order of magnitude as with temperature differences and will drive instabilities. Humidity is in so far more important as condensation during up rise will release higher air temperature.
Fluid mechanics: Density differences cause pressure differences. These cause fluid motion. Navier – Stokes - Equations do not deal with “potential temperatures” …
The law of gravity states that the gravitational force exerted on a body has corrolations with its mass. Clouds are groups of very tiny water/ice particles, thus they do fall but their falling velocitz (aka terminal velocity) is much lower for one to see. Also, some atmospheric phenomena such as air streams, pressure difference, deep convection influences the terminal velocity.