Statistical Analysis and Nucleation Parameter Estimation from Nucleation Experiments in Flowing Microdroplets

We have studied the primary nucleation of adipic acid from aqueous solutions in thousands of microdroplets generated in a fully automated microfluidic setup. By varying supersaturation in solution and residence time, we were able to estimate nucleation rates and growth times, while accounting for the stochastic nature of nucleation, the variability in microdroplet volumes (which is kept below 2%, thanks to a carefully designed experimental protocol), and the uncertainty in the automated image analysis procedure. Through a thorough statistical analysis we have obtained exact expressions for the expected values and the variances of all the random variables involved, all the way to the nucleation rate and the growth time associated with each supersaturation level explored and to the model parameters appearing in the corresponding constitutive equations. We have analyzed what controls the overall uncertainty in the estimation of the physical quantities above. We have shown that the distribution of droplet volumes at the level observed here is not limiting, whereas the detection technique and the image analysis algorithm play a critical role, together with the fact that the supersaturation levels and residence times that can be reasonably explored are limited. The tools and methods presented and made available to the scientific community will help in making microfluidics-based studies of nucleation more effective.