On the Size Distribution of Fragments Generated by Crystal Collisions

Abstract

The present work reports the results Or50 called "impact experiments" on nine different kinds of crystals, five inorganic salts and four organic acids, performed by letting ten crystals fall through an evacuated tube onto a glass plate. The ratio between the abraded volume ofa crystal and the volume ofthecrystal itselfis inversely proportional to the plasticity index of the material. The size distribution of the fragments, in terms of number density function vs. size, is well fitted for all the systems by a power law equation with an order equal to -2.82.For one of the system examined, potassium sulphate, the size distributions of fragments obtained by the impact experiments have been successfully compared with those of the fines produced during batch seeded crystallizations carried out at low supersaturations. It therefore appears that the size distribution of the fragments generated by crystal attrition in a crystallizer may be generally predicted by means of the proposed power law equation.

Detailed simulations of particle breakage as a result of agitation

“…The assumption that particles break in two parts of equal volume is a major simplification. It will be interesting to study the sensitivity of this assumption by including a probabilistic model that captures the statistics of the fragment size distribution upon breakage [1], or -better -to involve experimental data on fragment size distributions of particles that break in a collision. We do not feel that the assumption that breakage products are considered spherical particles is a major simplification.…”

“…This paper focuses on particle breakage and does so by means of numerical simulations. Breakage in agitated solids-liquid suspensions has been studied extensively with important papers on experimental work by Mersmann and co-workers [1][2][3] and Asakuma et al [4]. They identified collisions of crystals as the predominant cause of their breakage.…”

Population Balance Modeling of Growth and Secondary Nucleation by Attrition and Ripening

“…In this contribution, we are going to focus only on the first mechanism, i.e., formation of secondary nuclei by attrition. Mersmann and co-workers have analyzed in detail secondary nucleation by attrition, and they were able to develop a comprehensive quantitative theory, validated by experiments, − of how secondary nuclei form from a single crystal upon collision with the reactor stirrer, and to analyze whether these tiny fragments (fines), once separated by the parent crystal, grow or dissolve. ,, Such a first-principles model was then embedded in a PBE framework by Bermingham in his Ph.D. dissertation . It is worth noting that such description of secondary nucleation by attrition is in principle not consistent with the empirical constitutive equation for its rate that we have summarized above.…”

“…By addressing the former and elucidating the latter, we will be able to achieve a better insight into secondary nucleation by attrition. With this conceptual and theoretical scope in mind and for the sake of brevity, we have refrained from including in this work any experimental study, especially because Mermann’s theory has already been investigated and validated experimentally in the literature. − …”

A fragmentation model for crystal attrition

“…The consequences of such collisions are multifold, in that they reduce the average particle size, change the particle size distribution, and modify the particle morphology. The influence of operating conditions on attrition phenomena occurring during crystallization processes has been the object of considerable research [12][13][14][15][16][17][18][19]. Most concerns the influence of parameters such as time, stirring intensity, crystal size and concentration, and supersaturation on fragment generation rate or on their size distribution.…”