Modeling Particle Formation and Growth

Abstract

The dynamics of an aerosol, i.e. the evolution of the particle size distribution by particle formation and growth, diffusion, coagulation, convection and sedimentation can be described by the general dynamic or population balance equation (GDE, see for example Friedlander 1977 and Gelbard and Seinfeld 1979). Wu and Flagan (1988) have used a discrete sectional model of the GDE to describe the formation of SiO₂ and Girshick and Chiu (1990) described MgO powder synthesis by thermal plasma. Landgrebe and Pratsinis (1990) used a dimensionless form of the discrete sectional model to find an universal correlation map for gas phase synthesis of powders and applied it to TiO₂ synthesis from TiCl₄. The GDE is a partial integro-differential equation (or a system of ordinary differential equations) which is difficult to solve. It can be replaced by a mass balance equation for monodisperse or moment models which greatly simplifies the solution (see Landgrebe and Pratsinis 1990 for a comparison of different levels of simulations). Probably, the processes best studied are flames (Biswas et al. 1997; Lindackers et al. 1997 both using coagulation models) and the mechanisms most investigated are homogeneous nucleation (e.g. Grandquist and Buhrman 1976 for Inert Gas Condensation (IGC); Panda and Pratsinis 1995 for nucleation of Al in a flow reactor or Kruis et al. 1994 for nucleation of silicon from silane) and coagulation of aerosols (e.g. Matsoukas and Friedlander 1991). Egashira et al. (1994), and Okuyama et al. (1992) described the cluster formation in the CVD production of AIN and GaAs films, respectively.