Two-Group Approach to the Kinetics of Particle Cluster Aggregation

We present a numerical scheme for the treatment of particle agglomeration phenomena. The method is based on separating clusters into two groups according to size: small clusters containing up to x ^∗ particles and larger clusters with more than x ^∗ particles. In the first group, a set of equations describes the evolution of individual clusters; moment equations are derived for the second group. These two sets of coupled equations are solved numerically for, and giving good agreement with, a case where an exact solution is available. In a second step, the full distribution function is reconstructed from its moments. Here we use a nonlinear method based on the maximum entropy principle. The superiority of this method over a Gram-Charlier expansion is demonstrated for an example taken from the condensation of atomic clusters on a surface.