On the stability of a well stirred isothermal crystallizer

✍ Scribed by Byron E. Anshus; Eli Ruckenstein

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 944 KB
• Volume: 28
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(73)80047-8

✦ Synopsis

Theoretical information is obtained concerning the cycling process occurring in stirred crystallizers. This is found on the basis of a linear stability analysis of the equations describing the crystal size distribution and the solute supersaturation. Instead of utilizing the method of moments as several others have done, we apply the Laplace transform directly to the size distribution equation. The information concerning the stability is obtained from the Laplace transform in two cases: (1) the case in which the rate of growth is size independent and (2) the case in which the rate. of growth is size dependent for small crystals and size independent for large crystals. The second case has not been previously treated. In the first case instability occurs when the steepness of the nucleation curve b divided by the steepness of the growth-supersaturation curve g is larger than 2 1. In the second case the critical value of the ratio b/g is smaller than 2 1 and depends upon the specific form of the growth rate. The cycling time is in the first case approximately 2.5 times the residence time, while in the second, this cycling time is increased.