Köhler theory is a scientific concept that explains how cloud droplets form and grow in the atmosphere. Developed by the German meteorologist and physicist Hans Köhler in the early 20th century, this theory particularly addresses the processes involved in the activation of cloud condensation nuclei (CCN), which are small particles that serve as the surfaces onto which water vapor condenses to form droplets.
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The equilibrium water-vapor saturation ratio above a solution droplet combines a curvature effect, which raises vapor pressure, with dissolved-solute reduction of water activity. Its maximum defines a critical supersaturation for activation. In a dilute hygroscopicity approximation using droplet diameter and dry diameter , , where . Then . These approximate forms assume the stated diameter convention and dilute solution; composition and surface tension must be consistent.[ref]
A single parameter representation of hygroscopic growth and cloud condensation nucleus activity by M. D. Petters and S. M. Kreidenweis. Equations describing hygroscopic growth and critical activation supersaturation