Solutions to the Fokker-Planck equations governing simultaneous diffusion and gravitational settling of aerosol particles from a stationary gas in a horizontal circular tube

Abstract

A method is given for calculating the solution to the Fokker-Planck equation describing the deposition from a dilute suspension of aerosol particles due to the combined mechanisms of gravitational settling and diffusion in a horizontal cylindrical tube with perfectly adsorbing boundaries. For facilitation of numerical solutions, this method is most applicable to problems in which settling effects are not large compared to diffusive effects. This general technique is applied to a solution of a particular problem in which a spatially uniform initial concentration of aerosol particles within a cylindrical tube is considered. Solutions to a pure diffusion problem and a pure sedimentation problem are given and these results are compared to the solution in which simultaneous diffusion and sedimentation effects are considered. A criterion is given describing conditions for which the solution to the problem involving simultaneous gravitational settling and diffusive effects may be approximated by a solution to a simpler problem in which only the settling effect or only the diffusive effect is considered. The technique has been applied to a problem involving a cylindrical tube but is also applicable to similar problems involving deposition in spherical chambers.