  Active oil droplets in a liquid are believed to repel due to the Marangoni
effect, while buoyancy effects caused by the density difference between the
droplets, diffusing product, and ambient fluid are usually overlooked. Recent
experiments have observed active droplet clustering phenomena due to
buoyancy-driven convection (Kruger et al. Eur. Phys. J. E, vol. 39, 2016,
pp.1-9). In this study, we numerically analyze the buoyancy effect in addition
to Marangoni flow, characterized by Peclet number $Pe$. The buoyancy effects
originate from (i) the density difference between the droplet and the ambient
liquid, which is characterized by Galileo number $Ga$, and (ii) the density
difference between the diffusing product (i.e. filled micelles) and the ambient
liquid, characterized by a solutal Rayleigh number $Ra$. We analyze how the
attracting and repulsing behavior depends on the control parameters $Pe$, $Ga$,
and $Ra$. We find that while Marangoni flow causes repulsion, the buoyancy
effect leads to attraction, and even collisions can take place at high Ra. We
also observe a delayed collision as $Ga$ increases. Moreover, we derive that
the attracting velocity, characterized by a Reynolds number $Re_d$, is
proportional to $Ra^{1/4}/(l/R)$, where $l/R$ is the normalized distance by
radius between neighboring droplets. Finally, we obtain repulsive velocity,
characterized by $Re_{rep}$, as proportional to $PeRa^{-0.38}$. The balance of
attractive and repulsive effects results in $Pe \sim Ra^{0.63}$, which agrees
with the transition curve between regimes with and without collision.
