Derivation of dimensionless relationships for the agitation of powders of different flow behaviours in a planetary mixer

This study investigates the bulk agitation of free flowing or nearly cohesive granular materials in a pilot-scale planetary mixer equipped with a torque measurement system. Our major aim is to investigate the effect of the flow properties of several powders, as well as that of the set of experimental conditions (engine speeds NR and NG), on the power consumption of such a mixer. Thanks to a previous dimensional analysis of the system, this influence is studied through the variations of the power P with a characteristic speed uch, defined from engine speeds and geometrical considerations. Two relationships involving dimensionless numbers are derived to describe the agitation process: N pG = f F r G , N R N G and NpM = f(FrM). For free flowing powders, a linear relationship is observed when plotting P against uch, and the resulting process relationship linking dimensionless numbers is NpM = 15FrM− 1. In the more cohesive case, power values vary around an average value (P = 54 W) and the resulting process relationship is NpM = 1.8072FrM− 1.467. It is argued that the exponent in the representation of NpM against FrM may be a useful parameter for powder classification, and should be linked to powder rheometrical considerations.