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.

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