Athermal heterogeneous nucleation of freezing: numerical modelling for polygonal and polyhedral substrates

In a number of cases of practical interest, nucleation of freezing occurs at small supercooling, on potent nucleant substrates. Nucleation is then deterministic, consisting of the onset of free growth at a supercooling related only to substrate size and shape. Existing analytical treatments have evaluated the critical supercooling only for substrates in the form of a plane circle or a sphere. We develop a numerical treatment for a substrate of arbitrary shape. Coefficients are derived to permit straightforward evaluation of the critical supercooling for shapes typical of actual nucleant particles.