Fractal modelling of the carbonaceous aerosol

Most generally, atmospheric aerosol particles are ideally modelled as spheres for which it is straightforward to calculate geometrical properties (diameter, surface and volume) and ensuing radiative, dynamical and chemical characteristics. However, the particles issued in particular from combustion processes display a wide range of structures, from linear clusters to quasi spherical ones. These various shapes result in quite different physical and chemical characteristics for these particles : the processes of absorption, coagulation and deposition are strongly affected by the fractal nature of such aerosols. Whereas only one discretization parameter (diameter d) is required in 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 respectively representing the volume and the area of the particle. The corresponding governing aerosol population balance equation not only involves a collision term but also a more or less complete coalescence contribution. For example, after the general texture of a carbonaceous aerosol proposed by Strommen and Kamens [1], let us consider two colliding particles each made of elementary spherules immersed within a viscous organic liquid. They tend to more or less completely merge, according to their bulk viscosities and surface tensions. As a limit, particles can only stick together with a resulting maximum overall area. The other limiting case is obtained through full particle merging into spherical structures. The new fractal model is apt to describe such diverse particle morphologies.