Laminar Mixing in Simple Geometries

In this section we discuss two examples of mixing in simple geometries parallel plates and concentric cylinders. The parallel plate geometry is used as the basis of the analysis of the single-screw extruder and concentric cylinders are used as part of the design of rotational dies. The flow kinematics are calculated and mixing in terms of striation thickness reduction is evaluated. 

Example 6.6. Mixing in Plane Couette Flow (Parallel Plate Geometry PCF) 

Consider two infinite parallel plates and a polymer blend (with equal viscosity components) filling the space between them. The discussion that follows holds for the case of both Newtonian and non-Newtonian fluids. At time f = 0 the system is at rest. Then, at time r = 0+ the upper plate starts moving with velocity in the positive z direction. The move- 

FIGURE 6.11 Effect of shear strain on striation thickness of particles of the minor component represented by simple geometries, in a plane Couette flow (PCF). 

The length L, B, and the striation thickness, 5, for all the geometries except the sphere can be calculated from trigonometrical arguments as follows  

---