While supporting customers who apply DynoChem for crystallization modeling, we have seen several cases where some of the familiar quantiles of the PSD (D10, D50, D90) reduce with time during at least the initial part of the crystallization process.
On reflection one should not be that surprised: these are statistics rather than the sizes of any individual particles. In fact, all particles may be getting larger but the weighting of the PSD shifts towards smaller sizes (where particles are more numerous, even without nucleation) and in certain cases, this causes D90, D50 and maybe even D10 to reduce during growth.
Last week we had an excellent Guest Webinar from Orel Mizrahi of Teva and Ariel University, who characterized a system with this behaviour, with modeling work summarised in the screenshot below.
In this illustration, the reduction in D50 can be seen briefly and the reduction in D90 continues through most of the process. From the changing shape of the curve, with most of the movement on the left hand side, most of the mass is deposited on the (much more numerous) smaller particles.
We see this trend even in growth-dominated systems, when the seed PSD is wide.
On reflection one should not be that surprised: these are statistics rather than the sizes of any individual particles. In fact, all particles may be getting larger but the weighting of the PSD shifts towards smaller sizes (where particles are more numerous, even without nucleation) and in certain cases, this causes D90, D50 and maybe even D10 to reduce during growth.
Last week we had an excellent Guest Webinar from Orel Mizrahi of Teva and Ariel University, who characterized a system with this behaviour, with modeling work summarised in the screenshot below.
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| D10, D50 and D90 trends in a seeded cooling crystallization: measured data (symbols) and model predictions (curves). |
There was a good discussion of these results during Orel's webinar and we decided to make a short animation of a similar system using results from the DynoChem Crystallization Toolbox to help illustrate the effect.
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| Cumulative PSD from the DynoChem Crystallization toolbox, showing the evolution of PSD shape during growth from a wide seed PSD. The movement of quantiles D10, D50 and D90 is shown in the lines dropped to the size axis of the curve. |
We see this trend even in growth-dominated systems, when the seed PSD is wide.