Dilute Köhler curve ($S_{\mathrm{eq}}(r)=1+A/r-B/r^3$)

The first-order combination of the Kelvin equation and Raoult's law for a chemical solution droplet with $A/r\ll 1$ and $B/r^3\ll 1$. Its maximum is at $r_c=\sqrt{3B/A}$, with $S_c-1=2A/(3r_c)$. For ambient saturation ratio $1<S<S_c$, the smaller equilibrium radius is stable and the larger is unstable: the sign of condensational growth is the sign of $S-S_{\mathrm{eq}}(r)$. In particular, exceeding $r_c$ alone need not activate continued growth at subcritical atmospheric supersaturation.