Penetration of aerosol undergoing combined electrostatic dispersion and diffusion in a cylindrical tube

The deposition of unipolarly charged aerosol particles by simultaneous Brownian diffusion and electrostatic dispersion (space-charge) in laminar flow tubes has been modelled in two different ways. In the first approach, the rigorous transport equation has been solved numerically under the restriction of negligible axial components of the particle Brownian motion and of the space-charge electric field. The thus calculated theoretical penetrations agree satisfactorily with the experimental results obtained for air ions. Second, the system has also been modelled from a phenomenological point of view, based on the fact that deposition by diffusion and space-charge follows first- and second-order kinetics, respectively. The latter approach yields a simple and practical equation correlating particle penetration with tube geometry, aerosol flow rate, and particle mobility and concentration.