Studies on granular materials. IV. Calculation of the shaft torque for mixing granular materials

Abstract

The shaft torque of a simple paddle mixer was measured when mixing granular materials in a cylindrical vessel in dependence on the material properties and certain geometrical parameters. The results were correlated semi-empirically and relations were found for determining the critical depth and critical moment of the granular bed. A dimensionless equation was found by dimensional analysis for determining the shaft torque of the mixer for subcritical depths of bed and by extrapolation to blades of infinitely large diameter the correctness of the derivation was shown.The shaft torque required in mixing granular materials is important not only in designing mixing equipment but also yields information about the force relations in the granular material. There are only a few articles in the literature dealing with this problem: Weighardt\ Iiyama and Aoki2, Lastovcev and Chvalnov 3 .The main contribution of this paper consists in using the theoretically derived value of the stress on the mixer blade in deriving . the semi-empirical correlations. This stress was obtained from the shapes of the slip surfaces in the vicinity of the blade 4 . Further the interesting concept of the critical depth of the granular bed and the corresponding critical torque are introduced. Experimental ApparatusFor the experimental work we modified a drill press (Fig. 1) to serve as the basis of the mixing unit. The mixer shaft 1 was driven by an el-motor 9. The system of V-belt transmissions enabled us to change the shaft rpm's over the range 1 to 400 rpm. The mixing shaft torque was measured indirectly by measuring the torque exerted on the mixing vessel 1 0 which was mounted on the rotable shaft 3. The principle of measuring the torque by a balance is clear from the figure. The

A review on the continuous blending of powders

“…Novosad (1964aNovosad ( -c, 1968) and Novosad and Standart (1965) attempted to theoretically predict the slip planes (and the accompanying failure zones) for non-segregating, freeflowing powders. A blade rotating in a bed of powder was visually examined from outside and the slip planes were predicted using classical powder mechanical constructions.…”

Experimental Study of Flow and Heat Transfer in Granular Media

“…The force network inside a granular bed is necessary to be investigated for better understanding of the granular flows. The understanding of the force network between particles along with the torque required to rotate the impeller is necessary for design and improvement of mixing equipment [2]. Granular flows need to be investigated using both simulations and experiments to develop a knowledge base as granular flows and powder media have less developed mechanics compared to fluid flows [3].…”