Carbon black agglomerates model

In this specific model, approximately the same number of chains connect the cores directly ( fixed length chains ) as they do through carbon black agglomerates, and at zero time, 2(1 /Nt) = 2.12 10-2 and m/p = 0.02. Initially, therefore, fire load is more or less equally divided between the two groups of molecules. In a relaxation experiment, when Yd reaches a value of 60 1020,2(1 /TV,-) = 0.833 10-2, and the chains of constant length can therefore be calculated as carrying about 71%... 

Once incorporation is accomplished, carbon black agglomerates break into aggregates via the onion model mechanism. When agglomerates practically disappear and disintegrate into aggregates, the mixing is considered to be complete. However, every portion of the compound must have the same composition namely distributive mixing is also important and must occur simultaneously with dispersion. 

During the dispersion process, not only the rubber particles but also the carbon black agglomerates break. Therefore, the mechanism of breaking of carbon black must be included in the dynamic model of mixing. However, this aspect is relegated to the future refinement of the model. 

Illustration Kinetics of dispersion the two-zone model. The models for agglomerate rupture when integrated with a flow model are useful for the modeling of dispersion in practical mixers, as was discussed for the case of drop dispersion. Manas-Zloczower, Nir, and Tadmor (1982), in an early study, presented a model for the dispersion of carbon black in rubber in a Banbury mixer (Fig. 34). The model is based on several simplifying assumptions Fragmentation is assumed to occur by rupture alone, and each rupture produces two equal-sized fragments. Rupture is assumed to occur... 

Two-roll mills have been analyzed in terms of the pressure distribution and velocity profiles created between the rolls [95], the shear imposed on fluid elements exposed to these conditions in the nip region [129] and their resulting efficiency as dispersive mixing devices [130,131]. An earlier mathematical model was proposed to describe the dispersive mixing process of carbon black in rubber on roll mills, through consideration of agglomerate size distribution and... 

Figure 8. Microstructurc of carbon black. The nested model is built from planar BSU stacks interconnected by covalent bonds (see top scheme). One BSU (central frame in top scheme) is resolved in high resolution TEM of a real carbon black particle (FW-1. Degussa. Phillips CM 20 FEG, 200 keV). The main image shows a projection through an agglomerate of spherical black particles The distance between the BSU is 340 pm.

Fig. 34. Top Schematic view of a Ban ry Offo/n Evolution of the agglomerate size distribution with time predicted by the two-zone model with parameter values corresponding to the dispersion of carbon black in rubber in a Banbury muter. The size of an agglomerate after j ruptures is given by Dj — DQl2 i, where Do is the initial size of the agglomerates. The size of the aggregate (primary particle) corresponds to j = 28 (Manas-Zloczower, Nir, and Tadmor, 1982).

From Fig. 1 it follows that both FW200 and FEF N550 carbon blacks revealed a high tendency to agglomerate in paraffin oil (a model of elastomer matrix). The addition of dispersing agents reduced this effect crmsiderably. 

Natural rubber was chosen as a model for study for the following reasons (i) much background information about natural rubber exists (ii) although agglomerates of natural rubber are readily incorporated into natural rubber, there is a need to improve the rate at which carbon-black can be dispersed therein. 

To investigate dispersive mixing, 2 mm spheres of fluffy carbon black were moulded into model agglomerates , densities 0.3 and 0.4 gJcrcE and a device ( 2) with 10 mm cavities in both rotor and stator compared with device 1 (deep cavities). Neither were dispersed in 1 (deep cavities), nor was 0.4 in 2 (shallow cavities). However, the 0.3 density agglomerate was dispersed in 2 by tail formation and erosion as described in Chapter 14. 

---