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

Abstract : 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 rich, defined from engine speeds and geometrical considerations. Two relationships involving dimensionless numbers are derived to describe the agitation process: N-pG = f (F-rG, Nu(R)/Nu(G) )and N-pM = f(Fr-M). For free flowing powders, a linear relationship is observed when plotting P against u(ch), and he resulting process relationship linking dimensionless numbers is Np-M = 15Fr(M)(-1). In the more cohesive case, power values vary around an average value (P = 54W) and the resulting process relationship is Np-M = 1.8072Fr(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.
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C. Andre, Jean-François Demeyre, Cendrine Gatumel, Henri Berthiaux, G. Delaplace. Derivation of dimensionless relationships for the agitation of powders of different flow behaviours in a planetary mixer. Powder Technology, Elsevier, 2014, 256, p.33-38. ⟨10.1016/j.powtec2014.02.002⟩. ⟨hal-01625038⟩

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