Self-similar inverse population balance modeling for turbulently prepared batch emulsions: Sensitivity to measurement errors

We investigate the sensitivity of an inverse population balance equation (PBE) modeling technique for extracting single particle functions from transient size distribution measurements. A dynamic PBE model of a turbulently agitated batch emulsification vessel is used to generate volume size distribution data under the assumption of negligible drop coalescence. The distribution data are subjected to various types of error consistent with available measurement technologies and then introduced as input data to the inverse PBE modeling algorithm, which includes validation of the self-similar assumption. The errors considered include measurement noise, data skewed towards smaller or larger drops, skewed data due to the presence of large dust peaks, and reduced resolution caused by data binning. For each case, the computed functions for the drop breakage rate and the distribution of daughter drops are compared to the actual functions to assess the impact of input data errors on the effectiveness of the inverse PBE modeling approach. The type of measurement errors considered generally lead to underprediction of the breakage rate and, consequently, to overprediction of the number of large drops. Because the estimated and actual breakage rates tend to converge at small drop sizes, the inverse algorithm generates accurate predictions of the drop size distribution at sufficiently long batch times when small drops dominate. Implications for our future work on PBE modeling of drop size distributions in pharmaceutical emulsions prepared with high pressure homogenization are discussed.