(302g) Towards a Markov Chain Model for a Planetary Mixer

L. Legoix¹, C. Gatumel¹, M. Milhé¹, H. Berthiaux¹, V. Mizonov²

¹ Université de Toulouse, centre RAPSODEE, Ecole des Mines dâ??Albi-Carmaux, campus Jarlard, 81013 Albi Cedex 09, France

² Department of Applied Mathematics, ISPEU, Rabfakovakaya 34, 153003 Ivanovo, Russia

cendrine.gatumel@mines-albi.fr / leonard.legoix@mines-albi.fr / mathieu.milhe@mines-albi.fr / henri.berthiaux@mines-albi.fr / mizonov46@mail.ru

The annual amount of powder mixed in the industry is high and the quality level required for the blends is increasing as formulations become more complex. The connection between powder characteristics, process parameters, intensity and scale of segregation and energy consumption is generally accepted without being clearly attested. As far as there is no constitutive relation predicting the result of agitation from materials properties and operating conditions, mixing process parameters are often derived from experiments. This process conception task may become tedious and dispendious for companies. In this context there is a need to develop models to predict agitation and mixing of powders, taking into account the powders physical properties. This work focuses on planetary blenders, which are of wide interest because of their versatility and ability to process cohesive powders efficiently.

Markov models offer the advantage of short calculation times and have proved their efficiency in many powder mixing studies. We can cite for example simulations of a hoop mixer [1], static mixer [2] and continuous mixer [3]. The aim of this work is to develop a homogeneous Markov-chain model for mixing simulation in a pilot-scale planetary blender. In such equipment, mixing is carried out by combining rotation and gyration of the impellers, so the model is composed of two chains modeling separately the effects of the rotation and gyration of the blade.

For the needs of the study, a transparent multi-position cylindrical mixer agitated by means of a four bladed propeller was built. Its purpose is to figure rotation when put in horizontal position or gyration in vertical position. We first mapped the different agitation regimes observed with different powders in this device, in relation to that observed previously in the planetary blender. Stirring experiments are carried out with semolina as a free flowing powder and with lactose as a cohesive one. In the model, the mixer volume is divided into states and the objective is to determine the rates at which a particle can move from a state to another in order to build a matrix of transition probabilities. For a given agitation regime and powder cohesion, the transition coefficients are determined thanks to powder tracing experiments.

References

[1] M. Aoun-Habbache, H. Berthiaux, V. Mizonov. An experimental method and a Markov chain model to describe axial and radial mixing in a hoop mixer, Powder Technology, 128/2-3 (2002) 159-167

[2] D. Ponomarev, V. Mizonov, H. Berthiaux, C. Gatumel, J. Gyenis, E. Barantseva. A 2D Markov chain for modelling powder mixing in alternately revolving static mixers of Sysmix® type, Chemical Engineering and Processing: Process Intensification, Volume 48, Issue 11-12, November 2009, 1495-1505

[3] C. Ammarcha, C. Gatumel, J.L. Dirion, M. Cabassud, V. Mizonov, H. Berthiaux. Predicting bulk powder flow dynamics in a continuous mixer operation in transitory regimes. Advanced Powder Technology, Volume 23, Issue 6, November 2012, 787-800