Diffusion of aerosols in the entrance region of a smooth cylindrical pipe

Abstract

The laminar fluid flow in the entrance of a circular pipe has received much attention and it is generally accepted that at a distance x≳0.150 r 0 Re (where r 0 is the radius of the pipe and Re is the Reynolds number) that Poiseuille flow has been reached. Thus, for large Reynolds number flows the pipe has to be very long before Poiseuille flow can be assumed to exist. If the concentration of particles at the pipe entrance is constant then numerous theories have been developed for solving the steady state mass diffusion equation without axial diffusion and for small values of the diffusion parameter, Δ, when the deviation of the flow from Poiseuille flow is negligible. In this paper the simultaneous development of the viscous and diffusion boundary layers on the pipe wall will be further investigated analytically and the results compared with some recent experimental data on the deposition of ultrafine particles in the upper airways of the human lung.