Predicting bulk powder flow dynamics in a continuous mixer operating in transitory regimes

Over recent years there has been increasing interest in continuous powder mixing processes, due mainly to the development of on-line measurement techniques. However, our understanding of these processes remains limited, particularly with regard to their flow and mixing dynamics. In the present work, we study the behaviour of a pilot-scale continuous mixer during transitory regimes, in terms of hold-up weight and outflow changes. We present and discuss experimental results concerning the start-up dynamics of a Gericke GCM 500 mixer, for which a specific experimental protocol has been developed to determine the evolution of the hold-up in the mixer and the real outflow. Empirical relationships are derived so as to link hold-up weight variations with operating conditions. A simple stochastic approach, based on a non-homogeneous Markov chain, is developed to simulate the bulk particle flow and transport in the continuous mixer at a macroscopic level. Although this simple model is only based on the start-up behaviour, it provides a full description of the mixer dynamics in response to strong perturbations on the flow rate or on the rotational speed of the stirring device, such as negative or positive steps. This model is validated experimentally for a wide range of operating conditions, and constitutes a first approach to process control

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

International audienceThis 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

Dimensional analysis of a planetary mixer for homogenizing of free flowing powders: Mixing time and power consumption

International audiencePowder mixing is crucial to the processing stages in many industries. However, there is still a paucity of information about the effects of process parameters on mixing efficiency. This paper investigates the homogenization of free flowing granular materials with a planetary mixer, TRIAXE (R), examining the effect of the ratio of impeller rotational speeds (N-R/N-G) on the mixing process. First, a dimensional analysis carried out with mixing time and power consumption as target variables, established that both a Froude number and N-R/N-G controlled the process for the given free flowing powder mixture and planetary mixer. A further theoretical approach also suggested that these two dimensionless ratios which control hydrodynamics can be reduced to a modified Froude number providing that the maximum linear velocity achieved (mu(ch)) by the planetary mixer is introduced, replacing the dual impeller rotational speeds (N-R and N-G). Mixing time and power experiments validated the above hypothesis. Homogeneity tests performed in a granular media showed that the length of path achieved by the impeller governs the obtained mixing level. Finally, this work reflected that (i) dimensional analysis was also well suited to model powder homogenization with a planetary mixer. (ii) A concise set of dimensionless numbers governing mixing phenomena can be deduced through the introduction of the maximum linear velocity as obtained in previous studies on gas/liquid and miscible liquids mixing processes

Approximate calculation of breakage parameters from batch grinding tests

International audienceA mathematical treatment, based largely on the work of Kapur, has been developed to obtain breakage and selection matrices from batch grinding tests which are valid for the initial period of the process. The method is illustrated using experimental results for the grinding of hydrargillite and carbon in a laboratory scale stirred bead mill for 15 min and it is shown that this restriction still allows application of the method to continuous grinding processes in the mill. The breakage and selection functions determined by the method are shown to give a good representation of the grinding kinetics and to lead to a normalized breakage function

Modelling fine grinding in a fluidized bed opposed jet mill Part II: Continuous grinding

International audienceAn overall model of a continuous grinding process is proposed which combines experimentally‐determined breakage kinetics, a model of solids flow in the active zone and the grade efficiency curve of the classifier. This model is developed and tested for an Alpine 100 AFG fluidised bed opposed jet air mill with an integral classifier. The classifier appears to have a predominant role with respect to the product quality and the efficiency of the process but the existence of a draw off results in a dead flux of particles less than 4 mu m. The solids flow in the mill is represented by a model consisting of two zones: a perfectly mixed zone where grinding takes place, followed by a plug flow transport zone where no grinding takes place. The single adjustable parameter model appears to give a good representation of the change in particle size distribution in the process, expressed in terms of the residual fraction (a concept introduced in part I). The a posteriori calculation of the space time in the grinding zone supports the value used for the time range used in the batch grinding kinetics

Prediction of the product size distribution in associations of stirred bead mills

9th European Symposium on Comminution and Classification, ALBI, FRANCE, SEP 08‐10, 1998International audienceIn order to determine the operating conditions leading to a product with a given particle size distribution, a study has been made of the influence of the operating parameters (stirrer speed, solids concentration, bends diameter) on the particle size distribution of the product obtained in wet fine grinding in a stirred bead mill. Combination of the results of this study with a flow model through the mill leads to a model of the continuous grinding process. This model suggests that the spreading of the particle size distribution could be reduced either in multiplying the number of mills associated in series, nor in multiplying the number of passages through the same mill. Experiments made with the same overall residence time confirm this assumption

A markov chain model to describe the residence time distribution in a stirred bead mill

International audienc

A markov chain model to describe the residence time distribution in a stirred bead mill

International audienc