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

摘要

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 N_R and N_G), 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 u_(ch), defined from engine speeds and geometrical considerations. Two relationships involving dimensionless numbers are derived to describe the agitation process: N_(pG) = f (Fr_G, (N_R)/(N_G) and N_(pM) = f (Fr_M). For free flowing powders, a linear relationship is observed when plotting P against u_(ch) and the resulting process relationship linking dimensionless numbers is N_(pM) = 15 Fr_M~(-1). In the more cohesive case, power values vary around an average value (P = 54 W) and the resulting process relationship is N_(pM) = 1.8072 Fr_M~(-1.467). It is argued that the exponent in the representation of N_(pM) against Fr_M may be a useful parameter for powder classification, and should be linked to powder rheometrical considerations.