Köhler theory

Köhler theory describes the vapor pressure of aqueous aerosol particles in thermodynamic equilibrium with a humid atmosphere. It is used in atmospheric sciences and meteorology to determine the humidity at which a cloud is formed. Köhler theory combines the Kelvin effect, which describes the change in vapor pressure due to a curved surface, with Raoult's Law, which relates the vapor pressure to the solute concentration. It was initially published in 1936 by Hilding Köhler, Professor of Meteorology in the Uppsala University.

The Köhler equation relates the saturation ratio ${\displaystyle S}$ over an aqueous solution droplet of fixed dry mass to its wet diameter ${\textstyle D}$ as:$${\displaystyle S(D)=a_{w}\exp {\left({\frac {4\sigma _{d}v_{w}}{RTD}}\right)},}$$with:

• ${\displaystyle S}$ = saturation ratio over the droplet surface defined as ${\textstyle S=p_{w}/p_{w}^{0}}$, where ${\textstyle p_{w}}$ is the water vapor pressure of the solution droplet and ${\textstyle p_{w}^{0}}$ is the vapor pressure of pure water with a flat surface
• ${\textstyle D}$ = diameter of the solution droplet ("wet" diameter)
• ${\textstyle a_{w}}$ = water activity of the solution droplet
• ${\textstyle \sigma _{d}}$ = surface tension of the solution droplet
• ${\textstyle v_{w}}$ = molar volume of water
• ${\textstyle R}$ = universal gas constant
• ${\textstyle T}$ = temperature

In practice, simplified formulations of the Köhler equation are often used.