Particle Diffusion from Developing Flows in Rough-Walled Tubes

A closed-form solution has been derived which quantitatively describes convective mass transfer in a conduit including wall irregularities and entrance effects. It permits the respective roles of the major diffusional parameters upon deposition to be formulated and examined directly. For testing, the model can be reduced to a limiting case; namely, the particle diffusion problem of Ingham (1991) for idealized (i.e., smooth-walled) short tubes. The mathematical model was used to study inhaled aerosols in the upper airways of the human tracheobronchial tree. We focused on the influences of core flow acceleration (in the lumen of an airway) and various cartilaginous ring structures (embedded in the surface of an airway). The effects of core flow acceleration on particle diffusion calculations were quite small for in vivo conditions. However, particle diffusion due to cartilaginous rings can be increased up to 32% relative to idealized tubes. The enhancement can be written in terms of the airway surface function expressed as a power of the ring shape aspect ratio hi b where h is the amplitude of the surface wave and b is its wavelength.