Computational Fluid\nDynamics for Determining the Interplay\nbetween Stirring Conditions and Crystal Size Distribution in Small\nLaboratory Devices

A computational fluid dynamics method has been developed\nto describe\nthe hydrodynamics of different stirring devices, which are commonly\nused in the development stage of protein crystallization. The experimental\nsetup consisted of minicrystallizers in which the crystallization\ncocktail was stirred using a magnetic stirrer, mechanical agitator,\nshaker, or rotating mixer at different rotational frequencies. The\nhydrodynamics of the setups was determined with respect to local and\naverage values of flow velocity, turbulent dissipation rate (ε),\nturbulent kinetic energy (<i>k</i>), and shear rate (γ̇).\nThe calculations were performed by using the ANSYS Fluent software,\nin which the <i>k</i>-ε RNG turbulence model was implemented.\nThe model was used to determine the probability density functions\n(PDFs) of the hydrodynamic parameters, which were correlated with\nthe morphology of the protein crystalline phase obtained in the crystallization\nexperiments. Lysozyme was used as a model protein, which was crystallized\nfrom sodium chloride solutions. For the shaker and rotating mixer,\nthe dependence of the crystal size distribution on the <i>k</i>-PDF or γ̇-PDF distributions followed a similar pattern.\nFor the mechanical agitator, a minor discrepancy was observed from\nthat pattern at higher rotational frequencies. The correlation could\nnot be validated for the magnetic stirrer, in which no crystalline\nphase was obtained under the crystallization conditions used. This\nwas attributed to the pulverization of the solid phase caused by the\nmagnetic bar.