  In this paper, we investigate the dynamics of spherical droplets in the
presence of a source-sink pair flow field. The dynamics of the droplets is
governed by the Maxey-Riley equation with Basset-Boussinesq history term
neglected. We find that, in the absence of gravity, there are two distinct
behaviours for the droplets: small droplets cannot go further than a specific
distance, which we determine analytically, from the source before getting
pulled into the sink. Larger droplets can travel further from the source before
getting pulled into the sink by virtue of their larger inertia, and their
maximum travelled distance is determined analytically.
  We investigate the effects of gravity, and we find that there are three
distinct droplet behaviours categorised by their relative sizes: small,
intermediate-sized, and large. Counterintuitively, we find that the droplets
with minimum horizontal range are neither small nor large, but of intermediate
size. Furthermore, we show that in conditions of regular human respiration,
these intermediate-sized droplets range in size from a few $\mu$m to a few
hundred $\mu$m. The result that such droplets have a very short range could
have important implications for the interpretation of existing data on droplet
dispersion.
