Cloud condensation nucleus

An aerosol particle able to activate into a growing cloud droplet at the supersaturation attained by a cloud parcel. Activity depends on particle dry size, hygroscopicity and interfacial properties. The number active at a specified supersaturation differs from total aerosol number.

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 $D$ and dry diameter $D_d$, $s(D)\simeq A_K/D-\kappa D_d^3/D^3$, where $A_K=4\sigma M_w/(RT{\rho }_w)$. Then $s_c\simeq \sqrt{4A_K^3/(27\kappa D_d^3)}$. These approximate forms assume the stated diameter convention and dilute solution; composition and surface tension must be consistent.^[ref]

The maximum equilibrium supersaturation along a solution-droplet growth curve. Above this threshold, an aerosol particle can grow into an activated cloud droplet under the conditions of the parcel. In Köhler theory, larger dry diameter or greater hygroscopicity generally lowers the threshold; aerosol number alone does not specify it.