We have developed a numerical model that solves the time-dependent, one-dimensional, coupled continuity and momentum equations for an arbitrary number of charged and neutral particle species. The model includes production and loss of particles due to ionization, recombination, and attachment of ions and electrons by heavy aerosol particles, and transport due to gravity and multipolar diffusion. The model is used to study the response of the mesopause plasma to small-scale, aerosol particle density perturbations. We find that for aerosol structures on the order of a few meters, electron attachment and ambipolar diffusion are the dominant processes, leading to small-scale electron perturbations that can cause polar mesosphere summer echoes (PMSEs). Moreover, for small aerosol particles, with radii on the order of 10 nm or less, ambipolar diffusion leads to an anticorrelation between electron and ion densities, which is in agreement with most rocket observations. These small-scale structures persist as long as the aerosol layer persists, which will be limited by aerosol particle diffusion. For 10-nm particles, this diffusive lifetime will be on the order of hours. The few instances where rocket observations find instead a correlation between electron and ion densities can be explained either by the aerosol particles becoming large, on the order of 50 nm or more, in which case ion attachment becomes important, or by rapid evaporation of aerosol particles. In the latter case, evaporation must be sufficiently fast to overcome ambipolar diffusion.