 Thin-plate ice-growth time

For the geometrical diffusion-capacitance analogy approximation $C=2r/\pi$, a mass law $m=\alpha r^3$ and constant ice supersaturation $s>0$, the growth law $dm/dt=4\pi Cs/F$ gives $d(r^2)/dt=16s/(3\alpha F)$. Integration yields the displayed time. Comparing to a liquid sphere must use equal mass rather than equal radius; evolving supersaturation, ventilation and surface attachment invalidate the constant-coefficient estimate.