Understanding the role of fluid shear in secondary nucleation

Crystallisation is an important unit operation used in the production of Active Pharmaceutical Ingredients (API’s) (Yousuf and Frawley, 2018). Crystallisation is typically carried out using seed crystals in a process called secondary nucleation, so that the crystal quality attributes can be controlled. The mechanism of secondary nucleation is still not well understood. Often several mechanisms of secondary nucleation may be occurring at once in a crystallisation vessel making it difficult to determine the contribution of each mechanism (Tyrrell, 2019). A model of crystal nuclei breeding was proposed by (Anwar et al., 2015) to describe the mechanism of shear secondary nucleation. This describes pre nuclei clusters forming in solution adjacent to seed crystals. The nucleated clusters are described as being weakly bound to the surface and easily removed by fluid shear. However, the mechanism by which crystals are removed by shear is not described.

This project investigates how fluid shear impacts secondary nucleation in two ways: firstly, the influence of shear flow on the removal process of crystal nuclei from parent crystals was investigated computationally and secondly the turbulent shear stress in crystallisation vessels was quantified experimentally.

A computational study of the departure process of crystal nuclei from parent crystals during secondary nucleation was carried out. The purpose of this study was to determine the role of Brownian motion and shear flow in this process. A Monte Carlo method was used to compute the probability density function of the future position of a crystal nucleus undergoing Brownian motion after it forms on the surface of a parent crystal. Two types of parent crystals are considered; an infinite stationary flat seed crystal in shear flow, and a parent crystal that is freely suspended in shear flow. For both types of parent crystals, it is found that shear flow alone results in negligible motion of the nucleus from the surface, when compared to Brownian motion with and without shear. The impact of the starting position of a nucleus on the surface of a spherical parent crystal was investigated. Nuclei that start on the equator of the parent crystal disperse faster than nuclei that begin at the pole. Larger crystal nuclei experience a lesser amount of Brownian motion and move away from parent crystals slower. Secondary nuclei are therefore expected to move away from parent crystals while they are small enough to experience significant Brownian motion. The results indicate that Brownian motion plays a significant role in the dispersion of nuclei during secondary nucleation.

Particle image velocimetry was used to measure the turbulent shear stress in a one litre round bottomed crystallisation vessel. The maximum turbulent shear stress was measured for four different impeller types across a range of agitation speeds. To ensure the accuracy of measurements, preliminary PIV experiments were carried out to determine the optimum parameters for tracer particle size, and spatial resolution. Dimensional analysis using the Buckingham pi theorem was carried out to create an equation relating the maximum turbulent shear stress in a crystallisation vessel to the process parameters, including fluid properties, impeller properties, agitation speed, and vessel geometry.

Two approaches were taken when characterising the impeller. Firstly, the impeller was characterised by its power number and secondly by its geometry and impeller blade drag coefficients. Correlation analysis was used to determine which terms in each equation contribute most to the maximum turbulent shear stress. Terms with low correlation were removed from the equation. Multiple non-linear regression was carried out in python to determine the exponents for each equation based on experimental data. The result was an equation that can predict the maximum turbulent shear stress in a crystallisation vessel based on the process parameters.

The equation which characterised the impeller based on its geometry and blade drag coefficient predicted the maximum TSS with an average error of 6%.