Mixing cross-channel

Mixing in single screw extruders. Mixing caused by the cross-channel flow component can be further enhanced by introducing pins in the flow channel. These pins can either sit on the screw as shown in Fig. 3.29 [9] or on the barrel as shown in Fig. 3.30 [15]. 

Figure 1.65 CFD simulations giving 3-D mass contour plots in the cross-channel structure for a design without and one with two static mixing elements. The completeness of mixing can be judged from the cross-sectional mass distribution at the outlet [71] (by courtesy of Elsevier Ltd.).

A full analytical solution of the cross channel flow vx(x,y) and vy x, y), for an incompressible, isothermal Newtonian fluid, was presented recently by Kaufman (18), in his study of Renyi entropies (Section 7.4) for characterizing advection and mixing in screw channels. The velocity profiles are expressed in terms of infinite series similar in form to Eq. 6.3-17 below. The resulting vector field for a channel with an aspect ratio of 5 is shown... 

Fig. 6.11 Vector field of the cross-channel flow of an incompressible isothermal Newtonian fluid in a channel with an aspect ratio of 5. [Reprinted by the permission from M. Kaufman, Advection and Mixing in Single Screw Extruder—An Analytic Model, The AIChE Annu. Tech. Conf. Meeting Proc., San Francisco (2003).]...

The SSE is an important and practical LCFR. We discussed the flow fields in SSEs in Section 6.3 and showed that the helical shape of the screw channel induces a cross-channel velocity profile that leads to a rather narrow residence time distribution (RTD) with crosschannel mixing such that a small axial increment that moves down-channel can be viewed as a reasonably mixed differential batch reactor. In addition, this configuration provides self-wiping between barrel and screw flight surfaces, which reduces material holdback to an acceptable minimum, thus rendering it an almost ideal TFR. 

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. 

The numerics in Table 16.2 make two points. One is that turbulence is difficult to achieve at the mesoscale and nearly impossible to achieve in micro- and nanoscale devices. The other point is that diffusion becomes so fast at the microscale that cross-channel (e.g., radial) mixing is essentially instantaneous for all but the very fastest reactions. Thus composition and temperature will be approximately uniform in the cross-channel direction. The solutions to the convective diffusion equations in... 

Figure 16.2 Bottom grooves to promote cross-channel mixing in a mesoscale duct. See Stroock and Whitesides (2003).

The use of microscale reactors is not confined to single-phase systems. Both striated and droplet flows of two-phase liquid mixtures have been studied, as have suspensions of solid particles. It seems that almost any chemistry can be used at the microscale. Effectiveness factors in heterogeneous catalysis will be nearly 1.0 since diffusion distances are so small. As pointed out below, rapid molecular diffusion gives nearly instantaneous cross-channel mixing and may cause significant axial mixing. 

Diffusion can be slow at the mesoscale. Here is one approach to improving cross-channel mixing. See ... 

Tabeling, P., Chabert, M., Dodge, A., Jullien, C., Okkels, F. Chaotic mixing in cross-channel micromixers, Philos. Trans. R. Soc. Lond. A 362, (2004) 987-1000. 

Xia HM, Wan SYM, Shu C, Chew YT (2005) Chaotic mictomixers using two-layer crossing channels to exhibit fast mixing at low Reynolds numbers. Lab Chip 5(7) 748-755... 

Screws by themselves do not provide much mixing. In an SSE, the requirement for developing pressure to form the extrudate leads to some cross-channel mixing. 

Similar problems occur in the melt conveying zone. A polymer element at about 2/3 of the height of the channel will have no cross-channel velocity component and as a result will have a short residence time in the melt conveying section and little mixing... 

Other mixing screws have been developed in the past to disrupt the solid bed and mix unmelted with melted material. The double wave screw shown in Fig. 8.80 breaks up the solid bed and mixes the material by forcing a cross-channel flow by the cyclic variation in channel depth. The principle of the double wave screw was used by Barr in his energy transfer (ET) screw [90]. The ET section is basically a double wave section with occasional undercuts in both flights to force a cross-channel mixing between the two channels. Modeling of the ET mixer is discussed in Section 12.4.3.2 see also Figs. 12.23 to 12.25. 

Mixing in single screw extruders is determined mostly by the two main velocity components in the screw channel. These are the velocity in the direction of the channel (z-direction) and the velocity in the cross-channel direction (x-direction) (see Fig. 45). 

The velocity distribution in the extruder channel in the down channel and the cross channel direction result in the spiral path of the material. The material does not back flow even at higher back pressures, but rather moves back and forth in a spiral fashion over a relatively short distance. Due to the spiral motion, the residence time in the extruder is reasonably uniform but the mixing action is very limited. 

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