ABSTRACT
A multigrid algorithm has been developed enabling more efficient solution of the cluster size distribution for N-component nucleation from the Becker-Döring equations. The theoretical derivation is valid for an arbitrary number of condensing components, making the simulation of many-component nucleating systems feasible. A steady state ternary nucleation problem is defined to demonstrate its efficiency. The results are used as a validation for existing nucleation theories. The non-steady state ternary problem provides useful insight into the initial stages of the nucleation process. We observe that for the ideal mixture the main nucleation flux bypasses the saddle point.
ABSTRACT
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-Doring equations.
