Crystal growth rate dispersion

Abstract

Recent developments in the phenomenon of growth rate dispersion are surveyed with a particular emphasis on its characterisation. Most of the characterisation work concerning growth rate dispersion has been carried out under negligible nucleation conditions in batch configurations. Analytical solutions to the population balance equation for an MSMPR crystallizer under transient and steady state conditions are presented and their use in model discrimination and/or characterisation is discussed.

Modeling the facet growth rate dispersion of β l-glutamic acid—Combining single crystal experiments with nD particle size distribution data

“…While the underlying, physical mechanisms leading to dispersed growth rates are still debated (cf. Section 3.1), the consequence of GRD for crystallization processes is well-known: an otherwise unexpected broadening of the particle size distribution during growth (Wright and White, 1969;Janse and de Jong, 1976;Tavare, 1985).…”

“…It is thus likely that in a comparably large number of instances, the effects of growth rate dispersion are falsely attributed to either agglomeration, breakage, spatial variations in the continuous phase within the crystallizer or size dependent growth or vice versa, a fact which has been acknowledged by multiple authors (Garside, 1985;Tavare, 1985;Klug and Pigford, 1989;Ulrich, 1989;Rojkowski, 1993;van Peborgh Gooch et al, 1996;Ma et al, 2002). The role of a correct identification step becomes more apparent given recent efforts in the area of model-based optimization and control of processes (Ma and Wang, 2012;Majumder and Nagy, 2013;Ochsenbein et al, 2013), where model mismatches may lead to unpredicted and undesired behavior of the system when subjected to inputs that have been derived based on an incomplete model.…”

Growth rate dispersion — a review

“…The same idea was followed by TAVARE (1985), GIROLAMI, KOUSSEAU (1985), and GARSIDE, TAVARE (1984). Today the model is called the Ran-…”

Crystallization from Solutions Containing Multiple Conformers. 2. Experimental Study and Model Validation

“…This was attributed to higher kink densities in larger particles due to higher crystal surface stress and higher surface defects originating from collisions. Higher (kinetic) solubility for smaller crystals due to the Gibbs–Thompson effect and increasing internal stress with decreasing crystal size: , This behavior translates into lower supersaturation for smaller crystals (as compared to larger ones), which results in lower growth rate. This situation is only expected to affect submicrometer particles and hence is unlikely to impact crystal growth in the size range normally encountered in industrial crystallization. Crystal growth dispersion can also be the source of size-dependent crystal growth as reported by various researchers since the early 1970s. − In most growth rate dispersion theories, the type of size-dependence of crystal is also size-dependent, but there are few accounts of size-independent rates as reported by Ristic et al for sodium chlorate. Growth rate dispersion can also lead to an apparent rate size-dependence as pointed out by Zumstein and Rousseau …”

“…Crystal growth dispersion can also be the source of size-dependent crystal growth as reported by various researchers since the early 1970s. − In most growth rate dispersion theories, the type of size-dependence of crystal is also size-dependent, but there are few accounts of size-independent rates as reported by Ristic et al for sodium chlorate. Growth rate dispersion can also lead to an apparent rate size-dependence as pointed out by Zumstein and Rousseau …”