Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψ a is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops ( f single) and the fraction of the powder surface covered by drops ( f covered) as a function of Ψ a. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψ a, f single and f covered are related. The Monte-Carlo data was an excellent match with analytical solutions of f covered and f single as a function of Ψ a. At low Ψ a, the proportion of the surface covered by drops ( f covered) was equal to Ψ a. As Ψ a increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops ( f single) falls exponentially with increasing Ψ a. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for f single by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.