On the complete similitude of technical precipitation. Part II: Stirred-tank reactors

Abstract

The particle size distribution (PSD) of precipitated products is often influenced by mixing. This poses a serious challenge if stirred-tank reactors (STRs) are applied, because the complex fluid dynamics in STRs impedes process development and scale-up. Previous research has been limited to investigating the impact of dimensional physical or chemical parameters because their governing Π groups remained unclear. We aim within this work to fill this gap by transferring our recently developed theory of complete similitude to STRs. Hence, we propose that the dimensionless PSD depends solely on the STR’s Reynolds number, Re, the solids formation Damköhler number, Dasf and the feed velocity ratios, ζj if the same materials, educt concentration ratios and geometrically similar reactors are applied. Barium sulfate precipitation experiments in two semi-batch STRs with 0.4 and 10.8 L are conducted to validate this hypothesis. In addition to proving that complete similitude is possible for STRs, the results indicate that Re does not impact the dimensionless PSD for flows dominated by meso or macro mixing. This finding is further supported by a timescale analysis revealing that, contradictory to literature, meso and macro mixing are independent of Re. Furthermore, we demonstrate that complete similitude represents a fundamental framework from which other novel and established scale-up criteria can be derived.