Mixing, Devolatilization, and Reactions in Extruders

FIGURE 8.28 Spiral path of a fluid element in the channel of a 

As discussed in Chapter 6, the quality of mixing is related to the increase in interfacial area, which is proportional to strain. The calculation of the average strain, y, requires the residence time distribution function,/(f). We present the analysis for isothermal Newtonian flow in a single-screw extruder only, which is due to Pinto and Tadmor (1970). We give only a descriptive analysis for twin-screw extruders. 

The analysis begins with the assumption that curvature is not important, and hence, one can use the parallel plate model to describe flow in the screw channel. The axial velocity profile was given in Eq. 8.102 and is reproduced here in the following form  

it is necessary to locate the position of the particle in the lower part of the channel, fc, which had a position f in the upper portion of the channel (i.e., 2/3). Because the flow is circulatory in the x direction, the amount of fluid flowing between and 1.0 (the wall) per unit width in the upper part of the channel must be equal to the amount of fluid flowing per unit width in the opposite direction between 0 and Ic in the lower portion of the channel. Mathematically this is given by 

The average axial velocity, v (, of a fluid particle which alternates its position between and c, is given by the following equation  

---