A simple model for gravitational deposition of non-diffusing particles in oscillatory laminar pipe flow and its application to small airways

Gravitational deposition of non-diffusing particles from oscillatory laminar flows in a horizontal pipe is studied. Developing a simple mathematical model, we demonstrate that when the time for gravitational sedimentation (T _d) becomes appreciable relative to the time for flow oscillation (T), the gravitational deposition may no longer be approximated by the classical solution based on steady flow (J. Aerosol Sci. 3 (1972) 351). The analysis shows that an error caused by this approximation increases with the ratio of T_d/T (for instance, the errors in the estimation of deposition site are 1.5%, 5.9%, and 128% for T_d/T=0.05, 0.1, and 0.5, respectively); the application of the commonly used steady flow-based solutions to dominantly oscillatory flows, such as tidal breathing in lung airways, may therefore significantly underestimate local deposition density. We conclude that the oscillatory nature of tidal airflow must be taken into account when one calculates gravitational deposition of micrometer size particles in small airways of the human lung.