= Thin-plate ice-growth time
{title2=$t=3\alpha F(r^2-r_0^2)/(16s)$}
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.
Back to article page
