  There are two modes by which clusters of aggregating particles can coalesce:
The clusters can merge either (i) by the Ostwald ripening process in which
particles diffuse from one cluster to the other whilst the cluster centres
remain stationary, or (ii) by means of a cluster translation mode, in which the
clusters move towards each other and join. To understand in detail the
interplay between these different modes, we study a model system of hard
particles with an additional attraction between them. The particles diffuse
along narrow channels with smooth or periodically corrugated walls, so that the
system may be treated as one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form clusters. The channel
potential influences whether clusters can move easily or not through the system
and can prevent cluster motion. We use Dynamical Density Functional theory to
study the dynamics of the aggregation process, focusing in particular on the
coalescence of two equal size clusters. As long as the particle hard-core
diameter is non-zero, we find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The period of the potential
determines the size of the final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a cross-over in the dominance of
the two different coarsening modes, that depends on the strength of the
attraction between particles, the cluster sizes and the separation distance
between clusters.
