Dispersive Mixing during Processing

A set of empirical equations was obtained by Wu to describe the dispersed phase average particle size obtained after dispersive mixing in an extruder (13). The equations were based on the case of a Newtonian drop suspended in a Newtonian matrix, that is, Taylor s theory (16,17) with an extension to the case of a viscoelastic drop in a viscoelastic matrix. The empirical data employed were for blends containing 15 wt% dispersed phase and 85 wt% matrix phase. The particle size was found to be critically dependent on the ratio of the dispersed phase to the matrix phase melt 

In contrast and for comparison, the theoretical equation from Taylor s theory (16, 17) for a Newtonian drop suspended in a Newtonian matrix with the concentration of the dispersed phase particle assumed to be vanishingly small is 

The calculated particle diameters from Equation 12.2 may be considered a lower limit, that is, the Taylor limit, due to the assumption of Newtonian behavior of the system and vanishingly small concentration of the dispersed phase. Polymers exhibit non-Newtonian behavior, namely, the droplets elongate elastically before breaking. This behavior corresponds to an increase in interfacial tension, and therefore, particle size increases as predicted by Equation 12.1, over that predicted from Equation 12.2. (This is discussed below and can be seen in the last two columns of Table 12.3). 

Run ID T ( F) zones 1-7 Residence time (s) Shear rate (s ) Feed rate (Ibh ) 

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The most common example of dispersive mixing of particulate solid agglomerates is the dispersion and mixing of carbon black into a rubber compound. The dispersion of such a system is schematically represented in Fig. 3.22. However, the break up of particulate agglomerates is best explained using an ideal system of two small spherical particles that need to be separated and dispersed during a mixing process. 

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