Fractal modelling of carbonaceous aerosols—application to car exhaust plumes

Most commonly, atmospheric aerosol particles are ideally modelled as spheres allowing for straightforward calculations of their geometrical properties (diameter, surface and volume) and ensuing radiative, dynamical and chemical characteristics. However, particles issued particularly from combustion processes display various structural types, from linear clusters to quasi-spherical ones. Such various shapes result in quite different physical and chemical particle characteristics: e.g. the processes of absorption, coagulation/sintering and deposition are strongly affected by the fractal morphology of such aerosols. Whereas only one discretization parameter (diameter, d) is required for the spectral distribution n(d) of spherical particles, it is necessary to use a 2D distribution n(v,a) for fractal ones, v and a being, respectively, the volume and area of particles. For the coagulation process the associated governing aerosol population balance equation not only involves a collision term but also another term for more or less complete coalescence (sintering). For example, in view of the general texture of carbonaceous aerosols proposed by Strommen and Kamens (Environmental Science and Technology 31 (1997) 2983), let us consider two colliding particles each made of elementary carbon spherules immersed within a viscous organic liquid. They tend to more or less rapidly and completely merge, according to their bulk viscosities and surface tensions. In a first limit case, particles only stick together, displaying a maximum overall area. The other limit case is obtained through full particle merging into spherical structures. The new fractal model proposed, appropriate for describing such diverse particle morphologies, is then applied to car exhaust plumes.