Raise the supersaturation past the critical value and a salty particle turns into a cloud droplet. The blue Kohler curve is the equilibrium; the yellow dot is the droplet being pushed by the ambient air (dashed line).
The science
Kohler theory. The equilibrium saturation ratio over a solution droplet is S(r) = [(r3 - rd3)/(r3 - rd3(1 - κ))] exp(a/r), with the Kelvin term a = 2σ/(ρw Rv T). Curvature raises S, dissolved salt lowers it, so S has a maximum.
Activation. At small b = κ rd3 the maximum sits at rc = sqrt(3b/a) with Sc - 1 = sqrt(4a3/(27b)). If the ambient supersaturation is above Sc the droplet passes the peak and grows without bound; below it, it settles as a haze droplet at its equilibrium size.
Growth. Water vapour diffusion and latent-heat conduction give r dr/dt = (Senv - Seq(r))/(Fk + Fd), so r2 grows linearly in time for large drops. The curve is integrated with a stable semi-implicit step.
Simplifications. Constant ambient supersaturation (a real updraft makes it change), no collision-coalescence, no kinetic effects such as the accommodation coefficient, and a single particle. Typical sizes and times are illustrative.