in Wiley InterScience (www.interscience.wiley.com).
Mixing 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 TRI-AXE ® , 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 ChemicalEngineers AIChE J, 51: 3094 -3100, 2005 Keywords: mixing, planetary mixers, dimensional analysis, power consumption, Newtonian viscous fluids
IntroductionIn the second half of the twentieth century, the systematic use of dimensional analysis to investigate mixing processes has allowed this field to evolve from "arts into sciences." Today the whole field of classical stirring technology (here, the word classical refers to impellers vertically and centrally mounted in the tank) has been examined, so that the definition of significant dimensionless groups has now become well established.Thus, for any stirring operation (heat transfer, blending, and so on), depending on the flow regime and the mixing systems investigated, numerous correlations involving various dimensionless numbers have been proposed in the open literature for both design and/or scale-up. Consequently, a deeper process understanding and/or better or reproducible products can be achieved. This is not yet the case for the planetary mixers. Indeed, for this kind of mixing equipment, the literature is relatively scarce. [1][2][3][4][5][6] In addition, some dimensionless numbers still suffer from ambiguity with respect to the characterist...
