The current work presents a mathematical analysis of aerosol particle/droplet dynamics in periodically changing droplet-laden flows with nonzero mean velocity. The parameters for the model are taken from experimental studies reported in the literature and include the mean flow velocity and the amplitude and frequency of oscillations. On this basis, the governing equation of droplet motion is derived and solved. The solution indicates the existence of two regimes of droplet clustering. In the first regime, each droplet moves within a fixed cluster, In the other regime, the droplets can move from one cluster to another. A mathematical study helps to reveal the separate effects of various operating parameters on the droplet behavior. The two regimes are also identified in terms of a dimensionless parameter that is comprised of the carrier fluid flow characteristics and the droplet size. The performed analysis can provide an insight into the phenomena of droplet clustering, and can be useful in analyses of droplet behavior in various aerosol flows.