Abstract Calculation of the crystal nuclei number density as a function of both nucleation time and supersaturation is enabled by newly devised formula. A theoretical treatment of crystal polydispersity and size distribution is presented. It is supposed that the prime cause for the inherent propensity to polydispersity of assembles of growing crystals is the prolonged nucleation period. During the subsequent crystal growth in unstirred solutions, the polydispersity arising out of the nucleation stage is increased due to two gravity instigated effects: (1) solution replenishment resulting from the convection driven plumes that form above sufficiently large crystals, and (2) sedimentation of such crystals, which brings them in non-depleted solution areas. It is shown that, although increasing the polydispersity, these factors hardly alter the bell-shaped distribution of crystal number density on crystal sizes inherited from the nucleation stage. This conclusion is in accord with experimentally determined bell-shaped normalized numbers of lactose crystals vs. their diameters. Also, the mean size of the growing crystals is calculated, and the effect of the convection plumes and crystal sedimentation on the crystal size distribution (CSD) and on the quality of the grown crystals is considered.

中文翻译：

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分批结晶中生长的晶体数量和尺寸之间的关系：核数密度、成核动力学和晶体多分散性

摘要 新设计的公式可以计算作为成核时间和过饱和度的函数的晶核数密度。提出了晶体多分散性和尺寸分布的理论处理。据推测，生长晶体的集合具有多分散性的固有倾向的主要原因是成核时间延长。在未搅拌溶液中随后的晶体生长过程中，成核阶段产生的多分散性由于两种重力激发效应而增加：（1）由在足够大的晶体上方形成的对流驱动羽流导致的溶液补充，以及（2）这种晶体，使它们进入非耗尽溶液区域。结果表明，虽然增加了多分散性，这些因素几乎不会改变从成核阶段继承的晶体尺寸上晶体数量密度的钟形分布。该结论与实验确定的乳糖晶体的钟形归一化数与它们的直径相一致。此外，计算了生长晶体的平均尺寸，并考虑了对流羽流和晶体沉降对晶体尺寸分布 (CSD) 和生长晶体质量的影响。