Aerosol invariance in expanding coagulating plumes

We demonstrate that the total number of particles in an evolving aerosol plume is limited in a predictable way by the competing rates of coagulation and atmospheric dispersion, and is generally independent of the details of particle nucleation or growth. Using a simplified phenomenological model, expressions are derived from which the time variation in the total number of aerosols generated by localized sources can be calculated, as can their size distribution and local concentrations. Consideration of various microphysical processes contributing to aerosol plume development leads to the conclusion that the potential nucleation of enormous numbers of fine particles (for example, in high-altitude aircraft wakes and volcanic eruption clouds) does not affect the total number eventually dispersed throughout the atmosphere. We show that, after a suitable period of time (which is quite short relative to the time scales of regional and global dispersion), the aerosol population (total number, or concentration) is independent of the initial number, and instead depends in a simple way on the average coagulation kernel and plume dispersion rate. In terms of these basic physical parameters, we define a unique dimensionless number that fully determines the time evolution of the aerosol population, and show how this invariant number can be applied to estimate the properties of particulates emitted by high-altitude aircraft.