H. Mandyam et al., STATISTICAL SIMULATIONS OF DIFFUSIONAL COARSENING IN FINITE CLUSTERS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(2), 1998, pp. 2119-2130
The problem of diffusional interactions in a finite-sized cluster of s
pherical particles is studied. Simulations of diffusional interactions
with size distribution and volume fraction V-v, as input parameters,
referred to as snapshot (static) simulations, are compared with dynami
c (time-dependent) simulation results. The precise size distribution i
nformation in the snapshot simulations is obtained on the basis of a p
erturbation technique proposed recently by Fradkov et al. [Phys. Rev.
E 53, 3925 (1996)]. Robust iterative solution schemes for the quasista
tic diffusion equation facilitate investigations of coarsening systems
comprised of one million particles at ultralow (10(-13)) to moderate
(0.25) volume fractions. The objective of carrying out simulations at
such low volume fractions is to analyze the first-order volume-fractio
n-dependent correction to the effective coarsening rate predicted by t
he Todes, Lifshitz, and Slyozov (TLS) theory at infinite dilution. Whe
n volume fraction is considered as an input parameter, the deviation o
f coarsening rates from that of the infinite dilution limit of TLS var
ies as (3)root V-nu for a finite cluster and root V-nu (Debye screenin
g) for an infinite system. Accurate numerical investigations of the ro
llover volume fraction ( V-nu) above which the (3)root V-nu behavior
changes to root V-nu showed that V-nu varies as n(-2),where n is the
number of particles in the spherical cluster. The deviation of coarsen
ing rates from TLS observed from dynamic simulations agrees with that
predicted by snapshot simulations for V-nu <0.01. The dynamic results
are higher than the snapshot results for V-nu>0.01. The coarsening rat
e of the average particle can be calculated directly from dynamic simu
lations and indirectly from snapshot simulations by a perturbation rel
ation. A different type of snapshot-ensemble averaging is suggested on
the basis of the functional nature of the individual particle monopol
e source or sink strengths. Dynamic and snapshot simulations with dipo
les were carried out up to a volume fraction of 0.25, and departure fr
om Debye screening behavior was observed. The inclusion of dipole term
s affects the deviations noticeably only above a volume fraction of 0.
1.