A mathematical model for the evaporation of micro- and nano-sized solution droplets is developed. This model is used to predict whether the particles produced by spray drying and pyrolysis are fully filled or hollow. The model includes the non-continuum effects on the droplet evaporation. This is achieved by combining an interpolation formula based on the numerical solution of the Boltzmann equation for the transition regime with the continuum based governing equations. Results show that the non-continuum effects can be significant for the evaporation of submicron and nano-sized droplets in atmospheric pressures. Correlations for the final particle size and its wall thickness in terms of reactor temperature and pressure and the initial solution concentration are developed. The predictions are in good agreement with experiments performed on the submicron zirconia particles, prepared by spray pyrolysis.