Aerosol size distribution in a coagulating plume: Analytical behavior and modeling applications

In a previous paper (Turco and Yu, 1997), a series of analytical solutions were derived for the problem of aerosol coagulation in an expanding plume, as from a jet engine. 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, we derive a new analytical expression that describes the particle size distribution in an expanding plume in terms of N-T We show how this solution can be extended to include the effects of soot particles on the evolving volatile sulfuric acid aerosols in an aircraft wake. Our solutions apply primarily to cases where changes in the size distribution-beyond an initial period encompassing emission and prompt nucleation/condensation-is controlled mainly by coagulation. The analytical size distributions allow most of the important properties of an evolving aerosol population-mean size, number greater than a minimum size, surface area density, size dependent reactivities, and optical properties-to be estimated objectively. We have applied our analytical solution to evaluate errors associated with numerical diffusion in a detailed microphysical code, and demonstrate that, if care is not exercised in solving the coagulation equation, substantial errors can result in the predictions at large particle sizes. This effect is particularly important when comparisons between models and field observations are carried out. The analytical expressions derived here can also be employed to initialize models that do not resolve individual aircraft plumes, by providing a simple means for parameterizing the initial aerosol properties after an appropriate mixing time.