= Köhler theory
{c}
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.<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]{ref}
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