COARSENING KINETICS IN FINITE CLUSTERS

We address the problem of diffusional interactions in a finite sized c luster of spherical particles for volume fractions V-v, in the range 0 -0.01. We determined the quasistatic monopole diffusion solution for n particles distributed at random in a continuous matrix. A global mass conservation condition is employed, obviating the need for any extern al boundary condition. The numerical results provide the instantaneous (snapshot) growth or shrinkage rate of each particle, precluding the need for extensive time-dependent computations. The close connection b etween these snapshot results and the coarse-grained kinetic constants are discussed. A square-root dependence of the deviations of the rate constants from their zero volume fraction value is found for the high er V-v investigated. The behavior is consistent with predictions from the diffusion Debye-Huckel screening theory. By contrast, a cube-root dependence, reported in earlier numerical studies, is found for the lo wer V-v investigated. The roll-over region of the volume fraction wher e the two asymptotics merge depends on the number of particles n alone . A theoretical estimate for the roll-over point predicts that the cor responding V-v varies as n(-2), in good agreement with the numerical r esults.