Dilute Köhler curve
= Dilute Köhler curve
{title2=$S_{\rm eq}(r)=1+A/r-B/r^3$}
The first-order combination of the <Kelvin equation> and <Raoult's law> for a <chemical solution> droplet with $A/r\ll1$ and $B/r^3\ll1$. 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 $S-S_{\rm eq}(r)$. In particular, exceeding $r_c$ alone need not activate continued growth at subcritical <atmospheric supersaturation>.