In the process of cloud seeding, small "seed" particles are put into an under$-$cooled water vapor region in the sky in an attempt to nucleate water droplets, resulting in rain.

The spherical model can be used to model the nucleation process.

Assume the seed particle is a sphere of radius $r,$ which is less than the critical radius for homogeneous nucleation.

Also assume that the surface energy between the liquid and the solid seed particle is essentially zero.