Coagulation of Particles

Aerosol particles collide due to their random motions and coalesce to form larger chains of flocs made up of many particles. The Brownian (thermal) motion of particles, turbulence, presence of a shear field, and external forces such as gravity and electrical forces could cause coagulation.

Coagulation of Monodisperse Spheres

 Smoluchowski was the first to develop a model for the coagulation of monodispersed spherical aerosols. He considered the reference particle to be fixed as shown in Figure 1. The other particles would then diffuse to the reference particle by the action of the Brownian motions. The concentration then satisfies the following diffusion equation:

(1)

subject to boundary conditions

(2)

(3)

Here,  is the concentration far away. Equation (2) assumes sticking of particles without rebound upon contact.

Figure 1. Schematic of Brownian coagulation of monodispersed particles.