A stochastic model for nucleation kinetics determination in droplet-based microfluidic systems

Limay Goh, Kejia Chen, Venkateswarlu Bhamidi, Guangwen He, Nicholas C.S. Kee, Paul J.A. Kenis, Charles F. Zukoski, Richard D. Braatz

Research output: Contribution to journalArticlepeer-review


The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.

Original languageEnglish (US)
Pages (from-to)2515-2521
Number of pages7
JournalCrystal Growth and Design
Issue number6
StatePublished - Jun 2 2010

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics


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