Particle diffusion with entrance effects in a smooth-walled cylinder

Abstract

This work describes convective particle diffusion from developing flows in smooth-walled tubes and presents a closed-form solution for particle deposition efficiencies. The mathematical model is used to simulate inhaled particles in human airways for applicability to aerosol therapy (the treatment of lung diseases) and inhalation toxicology (the risk assessment of air pollutants). Momentum and concentration equations initially written in cylindrical coordinates were simplified by a scaling technique and solved analytically. A general velocity profile within the boundary layer of developing flow was determined based on the reduced momentum equation. A concentration boundary layer equation, different from Ingham's (1991) approach, was solved. Core flow acceleration 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 both the longitudinal convection term and the effect of curvature (i.e., 1 r term where r is tube radius). Therefore, it could be neglected, especially for flow in airways of small dimensions. The effects of core flow acceleration were negligible for particle diffusion studies pertinent to airways of the human lung. Our predictions were between 3% and 75% greater than the corresponding theoretical results of Ingham (1991) for various Schmidt numbers and were, therefore, in better agreement with the experimental results of Cohen and Asgharian (1990). Consideration of the effects of tube curvature contributed significantly to the improved accuracy of our model.