Efficient approach to nucleation and growth dynamics: Stationary diffusion flux model

A new model describing the evolution of clusters in the processes of nucleation and growth is proposed. The diffusion flux in the nonstationary Fokker–Planck equation with an unknown distribution function is approximated by the closed form expression containing the steady-state solution of the Zeldovich–Frenkel equation. This is justified due to the smallness of induction time of cluster formation compared to the time scale observed in experiments. The resulting stationary diffusion flux model is valid for all cluster sizes, computationally efficient and applicable to various types of cluster formation processes. Its application to a nucleation pulse experiment shows an excellent agreement with the solution of the set of formally exact Becker–Döring equations