(86b) Establishment of a General Correlation Accounting for Impeller-to-Wall Distance in a Bladed Powder Mixer Operating in the Cataracting Regime

As for any unit operation, the search and establishment of correlations between dimensionless numbers is essential to equipment design, scale-up, scale-down, energy minimization and of course operation. In the case of powders, two main issues are arising quickly:

• Dimensional analysis is extremely tedious as powder characterization is still a work-in-progress. As a consequence, the correlations that have been derived are strongly powder-dependent.

• According to rotational speeds and powder flowability, typically free-flowing or cohesive, different mechanisms and flow regimes can take place: rolling, cascading, cataracting, fluidized. Correlations have then to be adapted for the case considered, the usual limit between rolling and cataracting corresponding to a value of the Froude number equal to 1.

Together with tumbler mixers, convective mixers are widely employed throughout the industry to mix powders of different nature. They are mostly designed through a set of blades mounted on a shaft that rotates in a certain range of speeds. In the cataracting regime, the powder is taken by the blade and is projected towards a direction that depends on its inclination. The shear that is enhanced by the blade, together with the projection effect, makes it a suitable mechanism to promote in the case of cohesive systems as a way to disrupt the particle-particle interactions that are counteracting the mobility of individual particles. As a consequence, impeller-to-wall distance in the case of single-impeller shafts, or impeller-to-impeller distance for multiple-impeller systems is an important geometrical parameter to account for in the establishment of a correlation. In the present work, we report an experimental study for which the influence of the impeller-to-wall distance has been considered in the establishment of a correlation between the Froude number and the Newton number in the case of a polyvalent bladed mixer of our conception. Several cohesive powders have been investigated, so as to give a more general projection to the correlation.

The mixer considered is a 4-blade system that is mounted on a shaft in a vessel of cylindrical shape. In addition to process variables such as fill level or rotational speed of the stirrer, the equipment itself has multiple options: blade angle, equipment angle, mixing volume, distance between wall and blades … that can all be set initially at different values [1]. Removable disk-shaped walls can be placed at different positions inside the cylinder, either symmetrically or asymmetrically with respect to the blade system. This gives rise to different mixing volumes for a given filling ratio, that can be figured out by the impeller-to-wall distance L, or in dimensionless representation the ratio between blade radius R and L. Four different lactose cohesive powders (Flowlac 100, Granulac 140, Granulac 230, Tablettose 70) are studied and characterized through the help of a FT4 rheometer, as well as a tap-tap volumenometer and LASER-diffraction particle size analyzer. Stirrer’s rotational speed is varied, as well as blade-to-wall distance, the filling ratio being the same for all the experiments conducted.

A torque-meter is placed along the shaft and allows recording the torque exerted by the powder, and therefore the power that is consumed at a given rotational speed. The Newton number Ne, that is the ratio between the torque and the product MgR, where M is the powder mass, is calculated and employed to derive correlations between Ne, Fr and R/L.

Results show that a single correlation of the form Ne = k (R/L)^a Fr^b can be derived for all the powders studied as long as the mixer operates in the cataracting regime, coefficients a and b being invariants: a = 1 and b=0.3. This holds true for a free flowing powder that has been considered to complete the study, and suggests that the cataracting motion of the powder is governed by the blade system itself, regardless of the powder flowability, or at least at a much lesser level than in the rolling mode. This also gives a much precise idea of the blade’s zone of influence that can serve as guidelines for multiple impeller system’s location along the shaft.

[1] Legoix L., Gatumel C., Milhé M., Berthiaux H., Mizonov V. Powder flow dynamics in a horizontal convective blender: tracer experiments, Chemical Engineering Research and Design, 121 (2017), pp 1-21.