Simultaneous diffusion and sedimentation of aerosols in a horizontal cylinder

The problem of particle loss to the wall of an infinitely long horizontal cylinder filled with an aerosol of uniform concentration initially is studied. The particle movements due to the mechanisms of Brownian diffusion and gravitational settling are considered simultaneously. A series solution for the particle distribution is obtained, from which the deposition loss to the wall is calculated. However, for small time, this series solution does not converge rapidly enough for practical computation, thus, an asymptotic expression is developed for this case. The relative importance of diffusion and sedimentation on the deposition efficiency depends upon the parameter σ = v g a /2 D , where v g is the settling velocity, D the Brownian diffusion coefficient and a the radius of the cylinder. For σ