Henri Berthiaux

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

Abstract In 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, beads 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.

Analysis of grinding processes by Markov chains

After reviewing the wide field of application of stochastic processes in Chemical Engineering, with specific attention to particulate processes, the definition of a Markov chain is given and commented upon using an example. Batch grinding processes are then analysed from this point of view, emphasizing the link that exists between both stochastic and deterministic (based on population balance) approaches. Breakage and selection functions appear to be clearly linked to the transition probabilities of a Markov chain via the definition of a time interval characteristic of the grinding process. This provides a physical significance for the time interval. An identical analysis is made for continuous grinding processes which underlines again the similarity between both approaches. These concepts are illustrated by the use of experimental grinding data obtained in a stirred bead mill which shows the high degree of fit of the Markov chain model for both continuous and batch experiments.

Modeling continuous powder mixing by means of the theory of Markov chains

This article demonstrates the efficiency of the application of the theory of Markov chains as a tool to model and simulate continuous powder mixing to aid in better design of such equipment. Markov chain models allow calculating practically all parameters of the process necessary for its characterization, and in particular those related to particle residence time distribution (RTD). Some numerical examples from the model, which are important for better understanding the process, are also included. It is shown that the main factor defining the efficiency of continuous mixing, through the variance reduction ratio (VRR), is the ratio of the mean residence time and the period of inflows fluctuation, rather than the variance of the RTD. Also, the influence of the dimensions of the mixer outlet on the mean residence time, and in turn on the VRR, is examined as another way of improving the design.

A dynamic study of static mixing using on-line image analysis

In this paper, we try to develop a general methodology for defining and characterising homogeneity at the outlet of any continuous mixer based on auto-correlation of samples. We also emphasize on the necessity of developing on-line non-invasive techniques, as well as systemic model of the powder flow. This is further applied for the case of a static mixer, using a special set-up that allows following the evolution of a typical homogeneity length by image analysis. Mass flow perturbations performed with binary mixtures of aspirin and semolina are studied by examining the variations of the correlograms obtained. The absence of axial dispersion of the signal is finally assessed.

An experimental method and a Markov chain model to describe axial and radial mixing in a hoop mixer

An experimental methodology is developed to investigate the simultaneous axial and radial mixing of particles in a hoop mixer. This involves following the migration of a colored tracer, with flow properties identical to that of the bulk using tracer detection by image analysis. The particle transitions from all initial tracer positions inside the mixer are calculated and the experimental conditions are established which improve the homogeneity of the mixture. Finally, a Markov chain model is derived which gives a good representation of the experimental data.

Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer

As increasingly commented by the literature during the last 5 years, estimating the homogeneity of a powder mixture and following powder mixing processes is not a simple task. In this paper, we present the development and statistical validation of a sampling methodology for defining the number of samples required to provide a reasonable estimation of the homogeneity attained in a laboratory scale tumbler mixer. This method is then used to follow the mixing kinetics of a dilute binary powder mixture in a hoop mixer. Special attention is paid to the statistical meaning of the values obtained and the influence of the physical characteristics such as particle size and shape. The role of the particle shape of the majority powder is particularly emphasised and it is quantitatively demonstrated that spherical particles are harder to mix and more ready to segregate than particles with irregular shapes. The different mixing mechanisms at play are identified; the practical limits of use of such tumbler mixers with pharmaceutical powders are discussed.

The Development and Use of a Static Segregation Test to Evaluate the Robustness of Various Types of Powder Mixtures

Particle segregation usually appears as the counterpart of any mixing operation involving particles of different physical properties. However, little attention has been paid in the literature to this problem and especially to quantifying the stability of powder mixtures to segregation during the conveying and handling operations following a mixing process. This paper gives a theoretical definition of the ‘robustness’ of a powder mixture based on knowledge of the quality of a mixture before and after a segregation test. Specific attention is paid to the problem of homogeneity estimation through sampling. A simple static segregation device, specially developed for this study, is then used for evaluating the robustness of pharmaceutical powder mixtures. The effect of using an excipient, of the same chemical nature but different physical properties, is investigated from the point of view of size and shape of the particles. In the experiments performed here it is found that particle size has practically no influence on robustness, but it is demonstrated that particle shape has an important effect. Replacing irregular-shaped particles in a powder mixture by spherical-shaped particles (such as those produced by spray-drying) can provoke a dramatic disruption of the structure of a mixture by a simple pouring. Finally, the static segregation device is used as a relative measurement of homogeneity of complex blends consisting of animal feed and aroma. The evaluation of the effect of a premix step leads to the conclusion that the process time devoted to premixing should be optimized with respect to the overall mixing.

A numerical model to identify the structure of a high-dilution powder mixture

Abstract The study of low diluted powder mixtures poses problems due to the difficulty of accurately observing the evolution of the mixing process thus making it essential to have structural information of the mixture. A new systemic model is presented here, based on the definition of homogeneous regions, where the deviation from a pure random mixture is expressed in terms of the relation between standard deviation and sample size. A one-dimensional example is provided and applied to experimental work for the case of a 1% binary mixture. The numerical results together with the determination of the autocorrelation function leads to a complete identification of the mixture structure.

Modeling classifier networks by Markov chains

Abstract The applicability of probabilistic ideas to processes involving particles is first presented and followed by a general definition of a Markov chain which is illustrated by a simple example. The stochastic nature of the concept of grade efficiency in separation processes is demonstrated by assuming a particle of size x to be the system and the grade efficiency function to be a transition probability. This is used to calculate the overall grade efficiency for various classifier networks showing the evolution of the probability of presence of a particle at each point of the circuit as a function of the number of steps. Finally, performing the calculation with indefinite number of classifiers and taking into account dead flux, we emphasize the possibility of modelling complex particle flow in hydrocyclone.

Experimental Evidence of Mixture Segregation by Particle Size Distribution

In this study, we discuss experimental segregation results obtained for two industrial cases, namely, ammonium perchlorate and a polymeric resin. These results show a segregation effect due to particle size distribution rather than particle size itself. We used a heap-pouring device as a tester, for which a visual knowledge of the segregation state was observed. The analysis of segregation is based on various coefficients of variations related to the size fractions or particle size distributions global characteristics, indicating heterogeneities in the heaps formed. Both cases indicate that wide particle size distributions, as opposed to narrow ones, are limiting segregation risks. This collective, and maybe astonishing, effect is extremely marked for the cases studied, and demonstrates again the mesoscopic nature of granular media.