Models of secondary nucleation attributable to crystal‐crystallizer and crystal‐crystal collisions

Abstract

Collisions and Crystal-Crysta IThe rate of secondary nucleation of ice, assumed to be proportional to the product of collision frequency and impact energy, has been quantitatively modeled using idealized representations of collisions between crystals and either other crystals or surfaces in the crystallizer. The crystal-crystallizer collisions were assumed to be driven by either steady or turbulent fluid motion and the crystal-crystal collisions were assumed to be driven by either gravitational forces or turbulent eddies. The models predict to a good approximation the experimentally determined dependence of the secondary nucleation of ice on crystal size, ice concentration, and agitation power. T. W. EVANS SCOPEIn many practical crystallizers the nucleation rate is dominated by interaction of crystals with their environment, that is, by secondary nucleation processes. Secondary nucleation is poorly understood and heavy reliance has been placed on empirical correlations of nucleation kinetics, Without a fundamental understanding of the processes governing secondary nucleation, the form of the function that can best correlate experimental results cannot be well established. Hence there is no sound basis for extrapolating results from one set of experimental conditions to others. As examples of the wide choice of functions available to correlate secondary nucleation, simplistic models based on the assumptions that secondary nucleation is proportional to the number of crystals, crystal perimeter, area, or mass would suggest that the nucleation rate should be proportional to the zeroth, first, second, or third moment of the crystal size distribution, that is,where N is the nucleation rate and p, the nth moment of the crystal size distribution. Other models of crystallization involve collision of crystals with each other, in which case the nucleation rates would be expected to be proportional to the square of the moments of the particle size distribution. Little can be said about which moments should be used without a statement of mechanism. Additional motivation for developing mechanistic models of secondary nucleation is provided by the need to determine the dependence of nucleation rate on design parameters such as agitation rate, scale of equipment, etc.In a previous paper (Evans et al., 1974), it has been shown that the factors influencing crystal surface morphology can be separated from those influencing collisions. In this paper, following leads provided by Clontz and McCabe (1971) and Ottenj and co-workers (1972, 1973), this concept is extended. Expressions are derived for the kinetics of secondary nucleation under the assumption that the rate of nucleation is proportional to collision frequency and collision energy for each of four idealized collision mechanisms. These include (1) collision of crystals with an impeller as the crystals are swept by the impeller in steady flow, (2) collision between crystals in a turbulent flow field and various surfaces in the crystallization, (3) collision between crystals ...

Secondary nucleation of two fast growth systems in a mixed suspension crystallizer: Magnesium sulfate and citric acid water systems

“…B" is predicted independent of impeller RPM (as found in this study), since collision frequency does not limit the formation of nuclei, The observed proportionality between B" and M T would also be expected because the number of dendritic sites depends on the amount of crystals present in suspension. The growth limited nucleation proposed by Wang and Estrin is in direct contrast to removal limited nucleation model proposed by Evans et al (1974). The latter formulation predicts B" to be strongly influenced by the agitation level as found in the study of potassium sulfate .…”

“…Bennet, Fiedelman, and Randolph (1973) ; Ottens and de Jong (1973) ;and Evans, Sarofim, and Margolis (1974) derive similar power-law expressions using a semiempirical approach. If the growth rate of crystals is size independent, the following power-law model can be used to express its dependence on supersaturation G = k , .…”

Mathematical modelling and experimental validation of a novel periodic flow crystallization using MSMPR crystallizers

“…For example, herein, a secondary nucleation model based upon the work of Ref. 29 was used to describe the nucleation effect due to attrition. And for crystal agglomeration effect, the A 50 parameter was introduced to represent the combined effect of material strength, point of contact between two crystals and vessel geometry.…”

Determination of the dynamic metastable limit for α-lactose monohydrate crystallization

“…At this stage, the limiting step is the removal of nuclei from the surface of the existing crystals after each collision or unit of abrasion (Evans et al, 1974a). Higher agitation promoted both crystalcrystallizer and crystalecrystal collisions (Evans, Sarofim, & Margolis, 1974b), leading to higher collision frequency and Fig. 7.…”