Cloud Formation 

    The air is filled with millions of microscopic aerosols. Water vapor molecules in the air are continuously attaching and detaching themselves from these aerosols, forming a thin surface of liquid water around them. Aerosols are important for cloud formation. Since these aerosol particles act as embryos for the formation of cloud droplets, the number of cloud droplets that form is a function of the number of aerosols with affinity for water present in the atmosphere. How to do this requires a sophisticated idea called “Kholer Theory”.

  To enlarge the aerosol particles requires the addition of more water vapor molecules from the surroundings into the liquid water surface. However, upon further inspection, there are two conditions that must be satisfied before one can make such a statement. The first condition considers the curvature of the droplet, called the Kelvin Effect. The second condition considers the purity of the liquid water, called Raoult’s Law.

  The Kelvin Effect tells us that droplets are more likely to give away their water molecules, not accept more. And, Raoult’s Law tell us that droplets in the atmosphere, which are likely not comprised of pure liquid water, are likely to keep their water  molecules, not give them away.

  Kohler Theory combines these two effects to give us a better way to understand how aerosol droplets actually behave.

Kohler Theory

The above is a sketch of what is called a Kohler Curve. It represents graphically what happens when the Kelvin Effect and Raoult’s Law are combined. The x-axis represents the radius of the drop. The y-axis is a measure of the amount of water vapor molecules needed from the surrounding air.

Notice that the Kohler Curve has a maximum value at (rc,Sc). If we add Sc of water vapor molecules from the surrounding air (or more), aerosol particles will grow to a radius of rc and then continue to grow, forming a cloud drop.

Thus, Kohler Theory tells us that, for some determined lower-bound number of water vapor molecules from the surroundings, the aerosol particle will grow into a cloud drop. 

Rain formation

   When a cloud forms, moisture in the form of water vapor is carried into the cloud until it condenses on particles into liquid water, thus forming cloud droplets (see Figure 2, part 1). The cloud droplets are very small, however, and cannot readily fall out of the cloud, and therefore other processes must occur to grow the liquid cloud droplets large enough to fall as rain. One such process is called collision and coalescence, in which cloud droplets of a variety of sizes collide with each other and coalesce into a combined larger drop (Figure 2, part 2). This process continues until drops are large enough to overcome the updraft speed within the cloud and fall as rain. 

 [Figure 2] Hygroscopic seeding conceptual model diagram 

(reference : Research Application Laboratory, 'Aerosol and precipitation')

   However, in addition to processes that help the droplets grow, there are factors that can deplete the liquid water from eventually becoming rain on the ground, such as evaporation of the droplets or the freezing of small droplets into small ice crystals that are unable to fall as precipitation. Thus, the amount of water vapor that enters a cloud never all falls to the ground as rain. 

   Adding additional particles of larger sizes may help enhance collision and coalescence processes that are responsible for rain formation and convert more of the cloud water to rainfall. In essence, a more efficient collision and coalescence rain formation process yields more rainfall at the ground (Figure 2, part 4).