Density and Shape Factor Terms in Stokes' Equation for Aerodynamic Behavior of Aerosols

Pharmaceutical aerosols are used to treat many pulmonary diseases. The use of low-density powders has proven useful to support efficient drug delivery. Measurements must account for the low-density, spherical particle features contributing to aerodynamic behavior. Ideally, the aerodynamic particle size distribution (APSD) is measured experimentally. Without formal measurement of APSD, calculations may be performed using surrogate measures such as bulk or tapped density and dynamic shape factor in Stokes' equation. However, the particles' low density must be established independently for this approach to be valid. In addition, where particles deviate from sphericity, the dynamic shape factor must be estimated from aerodynamic measurement not from geometric imaging of morphology. Finally, geometric sizing from particle images results in number distributions that exhibit smaller median sizes than mass distributions for the same polydisperse system. Simply applying density and shape factor corrections to geometric particle sizes does not convert number distributions to mass distributions. For log-normally distributed particle size distributions, Hatch-Choate equations, employing both median size and geometric standard deviation terms, may be used to convert number to mass distributions. Assigning small APSDs from calculations based on erroneous assumptions will result in serious interpretive flaws in subsequent in vitro and in vivo data.