Dynamic state of the elastomer

The state of elastomer in the processing behaviour is assumed to be Region II of Tokita and White [24], that is, the polymer is in the elastic state. The behaviour involves a large deformation, breaking of material, and recovery of the deformation [25, 26]. This will be discussed next. 

The basic model is very simple particles of elastomer break down to smaller and smaller size of particles with the progress of the mechanical treatment. As the particle size becomes smaller, the homogenisation with carbon black is improved, and at the same time the desired degree of dispersion of the carbon black is achieved. 

The present model treats the average particle size it does not consider the particle size distribution, nor changes in the distribution during the breaking of particles. This aspect is a refinement to be made in the future, when experimental data on the particle size distribution become available. 

For simplicity, it is assumed that each particle breaks exactly in half each time it breaks and that only average particle size needs to be considered. These assumptions allow us to calculate the volume fraction of particles, V/, which break during one revolution of the rotor and the volume fraction, v, which does not break. Both and are assumed to be constants independent of the cycle. 

the average size reduction per cycle, fg, is related to the increase in the number of 

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