Dimensional analysis for planetary mixer: Modified power and Reynolds numbers

Abstract

AbstractMixing times, power consumption, heat transfer, and scale‐up predictions in an agitated vessel require the use of correlations between dimensionless groups such as Prandtl, Nusselt, Power, and Reynolds numbers. These dimensionless numbers are now well established for an agitated vessel equipped with a vertically and centrally mounted impeller in the tank for both Newtonian and non‐Newtonian fluids. To our knowledge, there is more ambiguity as to the definition of the characteristic speed and dimensions, which should be taken into account in the dimensional analysis of planetary mixers. The aim of this paper is twofold: (1) to propose modified Reynolds and Power numbers for planetary mixers and (2) to ascertain the reliability of the modified dimensionless number proposed for a particular planetary mixer, The TRIAXE®, which uses a combination of rotation and gyration of a pitched blade turbine to achieve mixing. The modified Reynolds and Power numbers proposed involve the maximum tip speed as characteristic velocity and are consistent with the definition of traditional Reynolds and Power numbers when only a single revolution around the vertical axis of the mixing device occurs in the vessel, as is the case for a standard mixing system. Experimental power measurements carried out with a planetary mixer when mixing highly viscous Newtonian fluids show that the modified Reynolds and Power numbers proposed succeed in obtaining a unique power curve for the mixing system independently of the speed ratio. This close agreement proves that the modified Reynolds and Power numbers are well adapted for engineering purposes and can be used to compare the power‐consumption performances of planetary mixers with well‐established technologies. © 2005 American Institute of Chemical Engineers AIChE J, 2005