Shear laminar mixing

Figure 7.3. Laminar shear mixing in a coaxial cylinder arrangement...

The static mixers (SM) operate on the principle of repetitive dividing of a flow channel into at least two new channels, reorienting them by 90°, and dividing again. The flow is a pressure driven, laminar shear. Mixing by SM is related to the numbers of striations (N ) generated by a number of SM elements (n ) and the number of divisions (new channels) engendered by each element (n ) ... 

An excellent measure of mixedness is the specific interfacial area, or the interfacial area per unit volume of the mixture, A For completely separated phases, A = 1 m /1 m = 1 m As the mixing progresses, the value of increases — larger is its value, better is the blend s mixedness. In laminar shear mixing A of randomly oriented elements depends on strain, y ... 

An idealized laminar flow field, i.e. tangential flow in a coaxial cylinder arrangement, can be used to illustrate some of the principles of laminar shear mixing which are relevant to more complex flows in real mixing machinery. Consider the situation in Figure 11.2 in which a line of coloured tracer (minor component) is laid down and its motion is observed as the outer cylinder is rotated in an anti-clockwise direction. 

Furthermore, the role of the total strain, y in laminar shear mixing is again highlighted in equation (11.4). 

Whilst in-line static mixers act on the distributive mixing principle for their effectiveness in laminar blending, it has been mentioned earlier in this chapter that laminar shear mixing can be enhanced by redistribution, see Figure 11,7. Thus redistribution of the two components to be mixed between periods of laminar shear or elongation is very beneficial. 

Distribution of components in a mixture through laminar shear mixing frequently occurs in a disordered manner, although motionless mixers are designed to blend in a more regular way through a process of repeated stream splitting and material combination. 

A model used to demonstrate laminar shear mixing is Couette flow [16, 17], the principle used in the Couette Viscometer ... 

Figure 2.13 Limitations of laminar shear mixing in a single screw extrnder.

Laminar shear mixing will occur which will provide distributive mixing. 

Laminar shear mixing (slow) Laminar shear mixing (rapid but slowing)... 

Blends were prepared using 20wt% amorphous PA as the disperse phase in PS. Viscosity ratio of PArPS was about 14 well above the limit of about 4 for laminar shear mixing. Samples were mixed for times varying from 1 to 15 minutes and examined by scanning electron microscopy (SEM) following solvent extraction of the PS. 

With no elongational shear there could be limits related to viscosity ratio, particularly as there can be difficulties in laminar shear mixing of viscous fluids with widely differing viscosities. However, results by Yu and co-workers [25] for trials using a viscosity ratio of 34 at 180 °C and 45 at 160 °C indicates that this may not be a limitation for many applications. 

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