Transient aerodynamic atomisation model to predict aerosol droplet size of pressurised metered dose inhalers (pMDI)

Pressurised metered dose inhalers (pMDI) produce large numbers of droplets with size of smaller than 5 μm to treat asthma and other pulmonary diseases. The mechanism responsible for droplet generation from bulk propellant liquid is poorly understood, mainly because the small length scales and short time scales make it difficult to characterise transient spray formation events. This paper describes the development and findings of a numerical atomisation model to predict droplet size of pharmaceutical propellants from first principles. In this model, the velocity difference between propellant vapour and liquid phase inside spray orifice leads to formation of wave-like instabilities on the liquid surface. Two variants of the aerodynamic atomisation model are presented based on assumed liquid precursor geometry: (1) cylindrical jet-shaped liquid ligaments surrounded by vapour annulus, (2) annular liquid film with vapour flow in the core. The growth of instabilities on the liquid precursors surfaces and the size of the subsequently formed droplets is predicted by numerical solutions of dispersion equations. The droplet size predictions were compared with Phase Doppler Anemometry (PDA) data and the predictions were in good agreement with the number mean diameter D10, which is representative of the respirable droplets. The temporal behaviour of droplet size production was captured consistently well during the period of the first 95% of the propellant mass emission. The outcome of our modelling activities also suggests that, in addition to saturated vapour pressure of the propellant, its viscosity and surface tension are also key properties that govern pMDI droplet size.