Development of a systematic theory of suspension inhalation aerosols. II. Aggregates of monodisperse particles nebulized in polydisperse droplets

Abstract

Using the previously developed statistical framework to study the aggregation of primary drug particles in droplets formed on nebulization of suspensions, we have computed the expected size distributions of clusters of monodisperse primary drug particles obtained after drying of log-normally distributed polydisperse aerosol droplet sprays. In systems with a high ratio of droplet to primary particle diameters and relatively high average number of particles per droplet, the cluster size distributions were found to be essentially log-normal with the same geometric standard deviations as the droplets, and the mass median (aerodynamic) diameters were accurately predictable on the basis of assumption of uniform distribution of the solid throughout the liquid phase. In systems where the average number of primary particles per droplet was less than one, the cluster size distributions showed markedly non-linear behaviour on log-normal probability graphs. However, the mass median (aerodynamic) diameters could be still predicted quite reliably assuming uniform distribution of the solid among the fraction of the droplets expected to be occupied by the solid particles (i.e. excluding the empty droplets from the calculations). When the ratio of the droplet to primary particles was small and the concentration of the suspension was high, the size distributions of the aggregates deviated markedly from the log-normal function, particularly when the droplet sprays were narrowly distributed. Calculation of the mass median (aerodynamic) diameters and geometric standard deviations using the uniform distribution assumption could lead to grossly erroneous results in these systems. The reason for this behaviour is that (i) spherical particles cannot fill space completely and (ii) a significant portion of the log-normally distributed droplets is too small to accommodate the number of primary particles which would be computed for these droplets on purely statistical grounds. This ‘exclusion’ effect, however, becomes marked only at high concentrations which are beyond the range used in current therapeutic aerosols and outside the regions of validity of some of the assumptions of the present theory. Thus, assuming uniform distribution of solid in the droplets of aerosol sprays, it is possible to estimate the significance of formation of solid aggregates arising for purely statistical reasons (i.e. without taking into account any forces of attraction causing flocculation or coagulation). Outside the regions of validity of the assumption of uniform distribution, the full computational model developed in this paper has to be used to find the median size and the shape of the distribution of the solid clusters.