Two-channel model

For considering radial heterogeneity in a two-phase system, the pseudo-fluid model is simultaneously applied to the core dilute region and the wall dense region, resulting in the so-called two-channel model (Nakamura and Capes, 1973 Bai et al., 1988 Yang, 1988 Ishii et al., 1989 Berruti, 1989 Rhodes, 1990). 

Fig. 6. /

Figure 2.14 Transfer from state 9 to state 8 when following adiabatically the resonance issued from 9 around the exceptional point where the resonance energies from 8 to 9 are merging. The paths are as follows thin solid curve, the two-channel model thin dashed curve, four channels, with inclusion of the two lower channels of Figure 2.8 thick dashed curve, four channels, with inclusion of the two higher channels of Figure 2.8 thick solid curve, six channels, with inclusion of all channels of Figure 2.8.

G. R. North and J. J. Leventhal, Two-channel model for electron transfer in ion-molecule collisions, J. Chem. Phys. 51, 4236-4237 (1969). 

Figure 2 Bleach at 670 nm following 520 nm excitation in P, tricomutum thylakoids. Fits from both one (—) and two (—) channel models are overlaid. The transfer time from the one channel model is 0.9 .l ps the times from the two channel model are 0.5 .l and 2.0i.5 ps with relative amplitudes of 1.7 db. 7 1. The residuals for the one channel fit are shown in curve a) those for the two channel fit are shown in curve b).

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. 

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