A Mathematical Model for Crystal Growth Rate Hysteresis Induced by Impurity

Abstract

The growth rate of a crystal in the presence of impurity depends on the history of supercooling. This behavior is called growth rate hysteresis (GRH). In this paper, GRH is described by using a mathematical model. This mathematical model is devised by considering the pinning mechanism of Cabrera and Vermilyea, the two-dimensional Gibbs−Thomson effect on step movement and slow adsorption of impurity species on a crystal surface. The model explains, reasonably but qualitatively, experimental literature data on GRH that its magnitude becomes large as the supercooling-changing rate R is decreased or the impurity concentration c is increased. The model also shows a possibility that the reverse effect of these two factors (R and c) on GRH may occur in the range of their small values and it predicts the GRH behavior over a wide range of experimental conditions. Limitations of the model are also discussed.

Removal/Dissolution of Mineral Scale Deposits

“…For precipitation, this is given by the difference between the chemical potential of a given substance in the stable and metastable/labile region [11]. For precipitation, this is given by the difference between the chemical potential of a given substance in the stable and metastable/labile region [11].…”

“…11 Representative schematic structures of some important mineral scale inhibitors with symbol abbreviations as follows: PAA, polyacrylic acid; PMAA, polymethacrylic acid; PMA, polymalic acid; PAM, polyacryamide; CMI, carboxymethylinulin; PAMAM, poly(amidoamine) dendrimer (Generation 1).…”

Monitoring industrial pharmaceutical crystallization processes using acoustic emission in pure and impure media

“…From a physical point of view, it is therefore reasonable to think that measuring the time variations of the acoustic parameter )) t ( C ( S abs E 1 might allow some evaluation of the solid generation process in with and without inhibiting effects of impurities present 520 in solution. For example, it is well known that impurities present in industrial mother liquor entail apparent final supersaturation thresholds and, consequently, lead to the reduction of the yield of solid (Kubota et al, 2003;Kubota, 1997). In such a context, AE might provide data for estimating the inhibiting effects of impurities on the overall crystal growth and, therefore, allow designing appropriate feedback control policy for reducing losses of final solid.…”

Unsteady-state transfer of impurities during crystal growth of sucrose in sugarcane solutions

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