Mixing in Laminar Flow

Effective partition of the flow into partial flows occurs in extruders. The flow in an extruder is shown schematically in Fig. 9.3 [2]. For the sake of simplicity, the mechanism in a single screw extruder is explained. However, the processes can, in principle, be applied to a co-rotating twin screw extruder. 

The axial distance A between b and b is a measure of the mixing action The shorter the distance A, the greater is the mixing action. The distance A depends on the kinematic parameter of flow A  

A further aspect of distributive mixing in creeping flow is that the viscosity has no effect on the mixing action. The mixing efficiency depends solely on the type of flow. 

In co-rotating twin screw extruders, in addition to flow splitting at the flight, further flow splitting takes place in the intermeshing zone (see Fig. 9.5). Furthermore, a multi-flighted screw geometry increases the number of partial flows. The number of partial flows equals 

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Statie mixers, as reviewed in Chapter 7, eontain mixing elements enelosed in a tubular housing through whieh radial mixing is aehieved. They redistribute fluid aeross the flow ehannel and eonsequently rearrange temperature and eomposition distributions. They are often used to promote mixing in laminar flow systems thus having a pro-nouneed effeet on the RTD. 

L. Erwin, New Fundamental Considerations on Mixing in Laminar Flow, paper presented at the Society of Plastics Engineers 36th Annual Technical Conference, Washington, D.C., 1978, p. 488. 

Figure 9.1 Principle of distributive mixing in laminar flow...

Power coefficient for mixing in laminar flow regime... 

E.S. Szalai, J. Kukura, P.E. Arratia, and F.J. Muzzio. Effects of hydrodynamics on reactive mixing in laminar flows. AIChE J., 49 168-179, 2003. 

These interesting devices consist of a tube or duct within which static elements are installed to promote cross-channel flow. See Figure 8.5 and Section 8.7.2. Static mixers are quite effective in promoting radial mixing in laminar flow, but their geometry is too complex to allow solution of the convective diffusion equation on a routine basis. A review article by Thakur et al. (2003) provides some empirical correlations. The lack of published data prevents a priori designs that utilize static mixers, but the axial dispersion model is a reasonable way to correlate pilot plant data. Chapter 15 shows how Pe can be measured using inert tracers. 

For mixing in laminar flow, diffusion is an important mechanism. The Peclet number, Pe, indicates the relative importance of advection to diffusion and is given by... 

This is a problem of considerable importance, especially in the area of bulk and solution polymerization, where reactions with high intrinsic rates take place in media of high viscosity. But there are also a number of organic syntheses that are carried out in viscous solutions (e.g., nitrations) or in viscous suspensions, where this problem is relevant. Some physical aspects of micro- and meso-mixing in laminar flow have been discussed in section 4.2,3,2, It was argued that in laminar flow meso- and micro-mixing cannot be separated. It is more practical to denote the combined process as "micro-mixing , as is commonly done in the literature. 

Pipe reactors can be operated in laminar or turbulent flow. In laminar flow radial diffusivity is molecular only, which is very slow, particularly if the viscosity is high. In turbulent flow the radial fluctuating velocity component produces the radial turbulent diffusivity which is much faster than molecular diffusivity. Many devices have been developed to promote fast radial mixing in laminar flow, such as static mixers, which are discussed below and in Chapter 7. Besides static mixers, a number of methods exist to promote faster radial mixing in turbulent flow, since even in turbulent flow it takes 50 to 100 pipe diameters to achieve... 

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