Rubber and plastics companies are using mixing equipment (‘internal mixers') which was invented by Banbury in 1916 and which has hardly evolved since then. There is an urgent need for the modernization of such equipment and the market is demanding higher and higher performances for rubber goods. The physics of the dispersion of porous or fibrous agglomerates in a flow field has not been widely addressed in the past, despite of its importance. This is mainly due to the technical difficulties associated with the observations of the kinetics of this disagglomeration and the wide range of size that must be probed. Two mechanisms are recognized : erosion and rupture. Actually, different software solutions to simulate the 3D transient behavior of a flow in internal batch mixer are available. In all existing codes, it is assumed that mixing and flow calculations are decoupled : the analysis of the mixing (distributive or dispersive mixing) is performed after the calculation of the flow. To sum-up, hierarchical modeling including micro-macro models is considered in this work. In this thesis, we developed new distributive tools and new dispersive mathematical model. We compared the numerical prediction with several experiments. Finally, we use this model to design a new rotor shape in the framework of a European project.

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The mixing of additives into a plastic is an extremely important step in the plastics industry, necessary for the manufacture of almost every conceivable product. Therefore the costs in developing new products can prove very expensive as the testing is usually carried out using full scale machines, usually using twin screw extruders because they are able to provide good dispersive and distributive mixing. This is particularly important when compounding difficult to disperse additives and nano-additives. What is required is a machine that can replicate the mixing abilities of a twin-screw extruder but on a laboratory scale. There have been attempts by industry to develop smaller machines, such as the Thermo Scientific HAAKE Minilab II Micro Compounder which processes on the scale of 7 cm3 of material volume. This can be too small for some needs and therefore a machine is required to produce material on the 10g to 100g scale. To this end a laboratory mixer of novel design was devised and its mixing performance was assessed using conductive carbon black and compared against the Thermo Scientific HAAKE Minilab II Micro Compounder, a 19 mm co-rotating twin-screw extruder and a 40 mm co-rotating twin-screw extruder. Carbon black was used because mixing performance can be assessed by measuring the minimum carbon loading necessary to induce electrical conductivity. It was found that the minimixer was able to induce electrical conductivity at loading of 5.75% but the comparison with the other machines proved difficult as the achievement of the threshold at which semi-conductivity occurred appeared independent of shear rate and mixing duration.

Dans cette thèse, nous avons voulu exploiter et étendre les outils de simulation à notre disposition pour proposer des méthodes de caractérisation et de prédiction du mélange à différentes échelles. À l'échelle locale d'écoulements macroscopiques, nous avons voulu exploiter les possibilités offertes par le logiciel de simulation 3D éléments finis XimeX® et y apporter des améliorations dans le but d'obtenir un outil d'étude du mélange distributif de particules dans un polymère par extrusion bivis. Nous avons ainsi enrichi la méthode éléments finis existante à l'aide de la bibliothèque éléments finis CimLib© du Cemef pour atteindre une plus grande précision de calcul, puis nous avons testé plusieurs méthodes de lâchers de particules afin de simuler le déplacement de charges dans la matrice polymère au cours du mélange. Nous avons ensuite appliqué quelques méthodes de caractérisations du mélange, dont une inédite, à ces lâchers de particules, et ce dans le cas de plusieurs géométries de vis. À l'échelle de la particule, on s'est intéressé aux mécanismes conduisant à la casse de fibres rigides, telles que les fibres de verre, lors du mélange avec un polymère en extrusion bivis. Nous avons choisi de faire des hypothèses assez importantes afin de simplifier ce problème extrêmement complexe et nous avons proposé une méthode de simulation de l'évolution de la distribution des longueurs de fibres le long de l'écoulement basée sur la conservation de la masse des fibres. Nous avons utilisé comme paramètres de cette simulation les résultats de calcul 1D obtenus par le logiciel Ludovic® qui repose sur des approches de type ALH. Nous avons ensuite comparé quelques résultats de calcul à des distributions de longueurs mesurées sur des échantillons prélevés le long d'une extrudeuse bivis. / In this thesis, we have attempted to use and to extend previously developed simulation tools to propose characterisation and mixing prediction methods at different scales. At a local macroscopic flow scale, we attempted to use the possibilities given by the 3D finite element software XimeX® and to improve it in order to obtain a tool for mixing simulation of filled polymers in twin-screw extruders. Thus we have enriched the existing finite element method using the Cemef finite element library CimLib© in order to achieve a greater computation accuracy. Then we have tested several particle tracking methods to predict the fillers displacement into the matrix during mixing. Furthermore, we have applied several characterisation methods to these particles tracking results for different screw geometries. At the particle scale, we have focused on the mechanisms leading to rigid fibres (such as glass fibres) breakage during mixing with polymer in twin-screw extruders. We have some assumptions in order to simplify this extremely complex problem. We then have proposed a simulation method of the evolution of the fibres length distribution along the flow. This method is based on the fibres mass conservation. We have used the results of the Ludovic® software 1D computations based on lubrication theory as impute parameters for this simulation. Then we have compared some computational results to length distributions measured on experimental samples taken along a twin-screw extruder.

The mixing of additives into a plastic is an extremely important step in the plastics industry, necessary for the manufacture of almost every conceivable product. Therefore the costs in developing new products can prove very expensive as the testing is usually carried out using full scale machines, usually using twin screw extruders because they are able to provide good dispersive and distributive mixing. This is particularly important when compounding difficult to disperse additives and nano-additives. What is required is a machine that can replicate the mixing abilities of a twin-screw extruder but on a laboratory scale. There have been attempts by industry to develop smaller machines, such as the Thermo Scientific HAAKE Minilab II Micro Compounder which processes on the scale of 7 cm3 of material volume. This can be too small for some needs and therefore a machine is required to produce material on the 10g to 100g scale. To this end a laboratory mixer of novel design was devised and its mixing performance was assessed using conductive carbon black and compared against the Thermo Scientific HAAKE Minilab II Micro Compounder, a 19 mm co-rotating twin-screw extruder and a 40 mm co-rotating twin-screw extruder. Carbon black was used because mixing performance can be assessed by measuring the minimum carbon loading necessary to induce electrical conductivity. It was found that the minimixer was able to induce electrical conductivity at loading of 5.75% but the comparison with the other machines proved difficult as the achievement of the threshold at which semi-conductivity occurred appeared independent of shear rate and mixing duration. / EPSRC / The following files are not available online: Americhem raw data; Carbon Black raw data; Videos.

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