Modelling the stochastic behaviour of primary nucleation.

Area of Science:

• Chemical Engineering
• Physical Chemistry
• Materials Science

Background:

• Stochastic primary nucleation significantly impacts crystallization processes, leading to variable crystal detection times under identical conditions.
• Existing literature shows abundant experimental evidence of this phenomenon, yet a clear theoretical understanding and robust modeling approach remain elusive.
• Understanding nucleation variability is crucial for controlling crystallization outcomes across various scales.

Purpose of the Study:

• To present and compare two distinct models for batch cooling crystallization that capture the interplay between stochastic nucleation and deterministic crystal growth.
• To estimate nucleation and growth rates using experimental data from paracetamol crystallization.
• To evaluate the applicability and limitations of these models under diverse operating conditions and scales.

Main Methods:

• Development of two mathematical models for batch cooling crystallization, differing in their representation of stochastic nucleation.
• Estimation of nucleation and growth rates through experimental measurements of paracetamol crystallization in a 1 mL vessel.
• Application and comparative analysis of both models to crystallization processes under varied volumes, initial concentrations, and cooling rates.

Main Results:

• Both models successfully describe the batch cooling crystallization of paracetamol, with estimated nucleation and growth rates.
• The study illustrates the advantages and disadvantages of each modeling approach when applied to different operating conditions.
• Model performance is discussed concerning their utility across varying scales of nucleation rates, particularly in micro-scale crystallizers.

Conclusions:

• The presented models offer valuable frameworks for understanding and predicting stochastic nucleation in crystallization processes.
• The choice of model depends on the specific application, desired accuracy, and the scale of the crystallization system.
• This work contributes to bridging the gap between experimental observations and theoretical modeling of nucleation phenomena in crystallization engineering.