Laminar mixing striation thickness

Macromixing The phenomenon whereby residence times of clumps are distributed about a mean value. Mixing on a scale greater than the minimum eddy size or minimum striation thickness, by laminar or turbulent motion. 

Striation thickness Average distance between adjacent interfaces of materials to be mixed by a laminar mechanism. 

Figure 7.27. Twisted-blade type of static mixer operating in the laminar flow regime (a) Distributive mixing mechanism showing, in principle, the reduction in striation thickness produced (f>) Radial mixing contribution...

First and foremost, the laminar mixing flow created in the reactive processing equipment, must reduce the striation thickness to a level where the diffusion characteristic time, tD = r2/ )AB, is small compared to the reaction characteristic time. Since the molecular diffusivities of low molecular weight components in polymeric melts (see Section 8.3) are very small and of the order of 10 6 cm2/s, the striation thickness must be reduced to the micron level in order to get a characteristic time t of the order of 1 s. Shear flow can accomplish this in reasonable mixing times because the striation thickness is inversely proportional to the total shear (see Section 7.3)... 

This study (3) was done to produce an ABS type resin by dry and melt blending SAN and a nitrile rubber in a motionless mixer. In polyblends of two semicompatible polymers, the particle size of the dispersed phase is an important factor concerning final properties, particularly if a rubber is dispersed to improve impact strength. Motionless mixers should give precise control over the final particle size since for laminar flow the number of fluid layers and the striation thickness can be predicted mathematically. The hypothesis that the impact strength should peak out at a precise number of mixing elements was thus investigated. 

In simple laminar flows (e.g. one-dimensional shear or elongation) the time evolution of some mixing parameters (e.g. striation thickness or intensity of segregation) has been calculated in a number of cases (Chapter 11 for general information). In turbulent, single-phase fluids it is very difficult to model the transport phenomena in full physical detail. Qualitatively, however, the following sequence may be visualized after the feed streams have met ... 

According to the expression for the shear in a tube with laminar flow and assuming that the initial striation thickness is equal to half of the channel diameter d, the mixing time is given by the flowing expression as a function of the Peclet number Pe ... 

Polymer mixtures containing deformable components tend to contain streaky or layered structures resulting from laminar shear flow. In such cases, the striation thickness (the distance between the streaks) can be measured to provide an indication of degree of mixing. As mixing progresses, a decrease in striation thickness is accompanied by an increase in interfacial area between the components. Reductions in striation thickness will depend on the level of imposed shear strain and the orientation of the components relative to the direction of shear [38]. 

Micro-mixing is often a relatively slow process in the diffusion equation the characteristic path length is the average striation thickness 8 in the laminar flow, so that the diffusion time should be (see eq. (4.8)) ... 

The mixing process in a single-screw extruder is laminar. The materials being mixed exist as discrete layers, striations. The process of mixing involves a reduction in the striation thickness, this being related to an increase in interfacial area between the major and minor components of the mixture. 

It can be shown that the change in striation thickness on mixing, and hence in the degree of laminar mixing, is a simple function of the total shear strain imposed on the system. However, at the end of the process the components of the mixture still exist as discrete components. The total shear strain exerted on the melt is a function of the residence time of the melt in the process. As a result of the complex velocity profile of the melt in the screw channel, the residence time of the melt in the channel varies as a function of the position of the melt in the screw channel as well as the down-channel velocity of the melt. 

Most of this handbook treats spatial mixing. Suppose that a sample of fluid is collected and analyzed. One may ask Is it homogeneous Standard measures of homogeneity such as the striation thickness in laminar flow or the coefficient of variation in turbulent flow can be used to answer this question quantitatively. In this chapter we look at a different question that is important for continuous flow systems When did the particles, typically molecules but sometimes larger particles, enter the system, and how long did they stay This question... 

The real power of using stretching computations to characterize chaotic flows lies in the fact that stretching is the link between the macro- and micromixing intensities in laminar mixing flows. In this section we describe the method for computing striation thickness distribution in our 3D example, the Kenics mixer. 

STRIATION THICKNESS AND LAMINAR MIXING 165 Equations 6.40 and 6.41 can be combined to give... 

Sometimes micro mixing in the continuous phase is important. This also acts on the intermediate scale eddies or "striations" (in laminar flow) with significant concentration differences will usually have a "thickness" that is also on the order of 10 to 10 m. 

---