  We explore the evolution of the aggregate size distribution in systems where
aggregates grow by diffusive accretion of mass. Supersaturation is controlled
in such a way that the overall aggregate volume grows linearly in time.
Classical Ostwald ripening, which is recovered in the limit of vanishing
overall growth, constitutes an unstable solution of the dynamics. In the
presence of overall growth evaporation of aggregates always drives the dynamics
into a new, qualitatively different growth regime where ripening ceases, and
growth proceeds at a constant number density of aggregates. We provide a
comprehensive description of the evolution of the aggregate size distribution
in the constant density regime: the size distribution does not approach a
universal shape, and even for moderate overall growth rates the standard
deviation of the aggregate radius decays monotonically. The implications of
this theory for the focusing of aggregate size distributions are discussed for
a range of different settings including the growth of tiny rain droplets in
clouds, as long as they do not yet feel gravity, and the synthesis of
nano-particles and quantum dots.
