(82e) Experimental Investigation of the Scale up of Turbula Mixers on the Basis of Kinematic and Dynamic Similarities

Many processes from a wide range of industries (cosmetic, pharmaceutical, food) use powders as raw materials. In most of these, mixing or premixing of dry particles is a critical step, the mixture quality being known to have an influence on the taste of a food product or the bioavailability of a drug. To meet the specifications of the finished product, the choice of the mixing technology and its operating conditions is therefore a key factor for the process.

However, the complexity of granular materials leads to difficulties in predicting the behavior of powders inside a blender. Simulations are now used to understand the mixing mechanisms inside a blender in oder to improve design or operations. But these data are difficult to transpose to a real material, where shapes and sizes of particles are widely dispersed. Therefore, the analysis and the optimization of a mixing process for a given mixture cannot be performed without an experimental work that is usually tedious. The cost and the quantity of raw materials needed to conduct these studies imply that such work is often done at the laboratory scale. The main challenge lies then in the extrapolation of results from lab scale to pilot or industrial scale with a small number of tests. Although powder systems are hard to accurately describe by dimensionless numbers, scaling-up is rather based on principles of similarities that can be either geometric [1], kinematic [2] or dynamic through the use of the Froude number [3].

 The work presented here is concerned with the scaling-up of Turbula mixers, commonly used in both industry and research. The efficiency of this mixer is based on the interaction of rotation, translation and inversion as per the geometric theory developped by Schatz. This combination results in a three-dimensional chaotic motion that allow to obtain a homogeneous mixture rapidly for many granular systems [4]. Experimental results were based on the kinetics of mixing obtained by following the time-evolution of the coefficient of variation for two different powder systems. Three Turbula scales were investigated, namely laboratory Scale – Turbula T 2F, pilot scale – Turbula T 10 B, industrial scale – Turbula T 50 A. Geometric, kinematic and dynamic studies were performed thanks to a Solidwoks simulation for the three scales. The geometric study showed that there is a constant ratio between two key lengths for the 3 Turbula sizes. Amplitude velocities and acceleration for a point at the bottom of the tank was extracted from simulations. Intensity of segregation [5] was compared for kinematic or dynamic similarities  on the basis of equal velocities or acceleration for a point at the bottom of the tank. The dynamic criterion appears to lead to a better correlation between results obtained in terms of homogeneity of powder mixtures, whatever the mixer size considered.

[1] W. Entrop, 1978, International Syposium on Mixing, Mons, D1, pp 1-14

[2] Albert Alexander, Troy Shinbrot, and Fernando J. Muzzio, 2002, Scaling surface velocities in rotating cylinders as a function of vessel radius, rotation rate, and particle size. PowderTechnology, 126(2) :174–190

[3] Y. L. Ding, R. N. Forster, J. P. K. Seville and D. J. Parker, 2001, Scaling relationships for rotating drums. Chemical engineering science, 56:3737-3750

[4] Wohlhart, K., 1981, A Dynamic analysis of the Turbula, International Symposium on Gearing & Power Transmissions, Tokyo.

[5] P. Danckwerts, 1952, The definition, measurement and some characteristics of mixtures, Applied scientific research. Section A, 3, 279-296