Particle size distributions in an expanding plume undergoing simultaneous coagulation and condensation

In previous work [Turco and Yu, 1997, 1998], analytical solutions of the equations describing aerosol coagulation in an expanding plume were derived. Those solutions were shown to depend on a single dimensionless time-dependent number, N_T, which is related to the particle coagulation kernel and the plume volume. Here these results are extended to the case in which a vapor, either primary or secondary, is also condensing on the aerosol. We show that for several important regimes of condensation encountered in the atmosphere, relatively simple empirical relations can be deduced that accurately describe the evolving particle size distribution, again in terms of N_T. In addition, the effects on the plume aerosol of entrained background particles and gases are explicitly treated. These new analytical solutions offer insights into the physics governing the evolution of aerosol plumes under atmospheric conditions, lead to a simple methodology for carrying out sensitivity studies, allow objective testing and validation of numerical codes and provide a useful means of extrapolating from plume scales to the scales appropriate for regional and global modeling.