Applicability of Probabilistic Nucleation Modelling for the Analysis of Microfluidics Data

Microfluidics tools have been developing rapidly over the past decade, as they offer unparalleled ability for controlling nucleation and tracking crystallisation events inside very large numbers of individual nanolitre-size droplets. They have demonstrated a significant potential for screening protein crystallization conditions and for the direct determination of inorganic products solubility curves. The accepted basis for analysing microfluidics data is the probabilistic nucleation model originally proposed by Pound and La Mer (1952). Given the significance of this model for the purpose of analysing microfluidics data, the paper conducts a review of its hypotheses, usage and applicability. A step-by-step derivation of the model equations confirms that the time variation of the proportion of empty droplets which microfluidics experiments can provide with high accuracy is indeed the recommended method for estimation of nucleation kinetic parameters from microfluidics experiments. The paper shows that, depending on its implementation, the model predicts different rates of appearance of crystals inside individual droplets. The paper focuses on two distinct implementation modes, referred to as constant supersaturation and single nucleation event modes. By confronting model prediction with microfluidics measurements for eflucimibe in octanol, the paper finds that both modes yield different model predictions, shedding light on the potential and limits of the probabilistic nucleation model for the analysis of microfluidics data.