The aerosol particle collision kernel considering the fractal model of particle motion

A method is presented in which the fractal model of particle motion, distinct from the Langevin equation of motion, has been used to determine the collision kernel of particles. The collision kernels, valid in the continuum and free molecular regions, are reformulated to be dependent on one sixth of the mean square displacement of a particle divided by time instead of diffusion coefficient and the root mean square displacement divided by time instead of the mean velocity. One generalized formula for collision kernels in the transition regime is obtained by equating the two expressions for kernels. The approaching time is calculated using equation describing the particle trajectory. For condensation and monodisperse aggregation the calculated collision kernel is the harmonic average of limiting kernels valid in continuum and free molecular regimes. It is in agreement with the experimentally verified formula of Fuchs–Sutugin. The results for polydisperse aggregation are close to those obtained by the widely accepted method of Fuchs. The obtained formula can also be used to approximate the drag force on particles in the transition regime.