Many important physical properties of natural or man-made aerosol particles such as light scattering, electrostatic charges, and toxicity, as well as their behavior involving physical processes such as diffusion, condensation, and thermophoresis, depend strongly on their size distribution. An important aerosol behavior mechanism affecting the size distribution of aerosol particles is coagulation. Aerosol particles suspended in a fluid may come into contact because of their Brownian motion, or as a result of their relative motion produced by external forces (e.g., gravity, hydrodynamic forces, electrical forces, etc.). The result is a continuous decrease in number concentration and an increase in particle size. The theory of coagulation was originally devised for particles in liquids and was later extended to aerosols. In the case of solid particles, the process is sometimes called agglomeration, and the resulting particle clusters are known as agglomerates. Therefore in many basic and applied fields (e.g., synthesis of nanostructured material via gas-phase synthesis), the evolution of the particle size distribution because of coagulation is of fundamental importance and interest.

Aerosol coagulation is caused by relative motion among particles. When the relative motion is because of Brownian motion, the process is called Brownian coagulation. Brownian coagulation is a spontaneous and ever-present phenomenon for aerosols. When the relative motion arises from external forces such as gravity or electrical forces, or from aerodynamic effects, the process is called kinematic coagulation. Kinematic coagulation includes gravitational coagulation, turbulent coagulation, electrostatic coagulation, etc.

The objective of this chapter is to review the theories of coagulation describing how particle number concentration and particle size change as a function of time. To do that, first, an overview of some important coagulation mechanisms is presented. Next, various solution techniques for the coagulation equation are comparatively reviewed.