A Stochastic Model for Nucleation Kinetics Determination in Droplet-Based Microfluidic Systems.

Area of Science:

• Chemical Engineering
• Materials Science
• Physical Chemistry

Background:

• Deterministic models fail to capture stochastic induction times in microfluidic crystallization.
• Accurate modeling is crucial for pharmaceutical and protein crystallization processes.

Purpose of the Study:

• To develop a stochastic model for crystal nucleation in droplet-based microfluidics.
• To provide analytical solutions for nucleation probability, crystal counts, and induction time distributions.
• To establish methods for determining nucleation kinetics from experimental data.

Main Methods:

• Formulation of a stochastic Master equation for crystal nucleation.
• Derivation of analytical solutions for nucleation dynamics under time-varying supersaturation.
• Experimental validation using paracetamol and lysozyme crystallization in a high-throughput platform.

Main Results:

• The stochastic model accurately describes nucleation probability and induction time distributions.
• Determined nucleation kinetics from experimental data showed low prediction errors for varying conditions.
• The model successfully predicts mean, most likely, and median induction times.

Conclusions:

• The proposed stochastic Master equation provides a robust framework for modeling crystal nucleation in microfluidic systems.
• This approach enhances the prediction of nucleation kinetics and induction times for active pharmaceutical ingredients and biomolecules.
• The model is applicable to diverse microfluidic crystallization platforms and nucleation types.