PARTICLE DIFFUSION WITH ENTRANCE EFFECTS IN A SMOOTH-WALLED CYLINDER

This work describes convective particle diffusion from developing flow s in smooth-walled tubes and presents a closed-form solution for parti cle deposition efficiencies. The mathematical model is used to simulat e inhaled particles in human airways for applicability to aerosol ther apy (the treatment of lung diseases) and inhalation toxicology (the ri sk assessment of air pollutants). Momentum and concentration equations initially written in cylindrical coordinates were simplified by a sca ling technique and solved analytically. A general velocity profile wit hin the boundary layer of developing flow was determined based on the reduced momentum equation. A concentration boundary layer equation, di fferent from Ingham's (1991) approach, was solved. Core flow accelerat ion was allowed in the airway lumen outside the boundary layer. Scale analyses demonstrated that the magnitude of the radial convection term in the particle concentration equation was quite small relative to bo th the longitudinal convection term and the effect of curvature (i.e., 1/r term where r is tube radius). Therefore, it could be neglected, e specially for flow in airways of small dimensions. The effects of core flow acceleration were negligible for particle diffusion studies pert inent to airways of the human lung. Our predictions were between 3% an d 75% greater than the corresponding theoretical results of Ingham (19 91) for various Schmidt numbers and were, therefore, in better agreeme nt with the experimental results of Cohen and Asgharian (1990). Consid eration of the effects of tube curvature contributed significantly to the improved accuracy of our model.