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Prediction of the inversion velocity in the binary-solid liquid fluidized bed

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Introduction

Liquid solid fluidization of a mixture of particles is common to a number of industrial processes, with specific applications in mineral classification, elutriation, crystallization and fluidized bed leaching, to name but a few.

When particles with different densities or sizes are fluidized by liquid, generally, the particles tend to segregate. The larger or the heavier particles are segregated to the lower layer, whereas the smaller or the lighter ones are in the upper part of the beds. For two species differing in their size as well as density such that the larger particles are lighter and the smaller ones are denser, the segregation pattern is more complex and even lead to layer inversion. A given mixture, which is not at the stable equilibrium state will exhibit a driving potential to segregate into a mixed bottom layer and a pure layer of one component or another floating above it, depending on which one is excess to equilibrium, illustrated in Fig. 1.

The layer inversion phenomena have been extensively reported in the literature from quite different theoretical bases (Pruden & Epstein, 1964; Moritomi, Iwase, & Chiba, 1982; Van Duijn & Rietema, 1982; Moritomi, Yamagishi, & Chiba 1986; Gibilaro, Di Felice, Waldram, & Foscolo, 1986; Jean & Fan, 1986; Di Felice, 1993). Unfortunately, various models provide different predictions for the same process. Some of these predictions deviate significantly from experimental data. A comparative analysis of the previous studies (Rasul, Rudolph, & Wang, 2000) identified that only the model developed by Gibilaro et al. (1986) provide a good mechanics explanation and acceptable predictive agreement with the experimental results in terms of volume fractions of solids and fluid corresponding to segregation potential-free mixture conditions.

Since the layer inversion was first studied systematically by Moritomi et al. (1982), prediction of the inversion velocity is one of the most interesting and important aspects in studying the inversion phenomenon. On the basis of the complete segregation model, the present work provides a simple and precise method to predict the inversion velocity in the binary solid mixture liquid fluidization.

Section snippets

Equilibrium in the mixed layer

The layer position in the liquid fluidized bed is determined by the bulk density of each layer. In the present paper, we mainly investigate the binary system. Here we specify the larger and the lighter species as 1, and the smaller and denser one as 2. The bulk densities of the two layers formed by two species are known asρb1fε1s1(1−ε1),ρb2fε2s2(1−ε2),respectively. If the bed is completely segregated, there are two layers of pure component, whose position in the bed is determined by

Result and discussion

The inversion velocity predicted by the current work was compared with experimental data of the previous studies, illustrated in Table 1, Table 2. From Table 2, it is clear that the new model predicted the inversion velocity precisely for most cases.

This model basically corresponds with complete segregation model proposed by Gibilaro et al. (1986). According to complete segregation model, if the concentration of the solids in the bottom mixed layer is the same as the ratio of the solids charged

Conclusion

A model is proposed in the present work to predict the inversion velocity for the fluidization of the binary solid mixture. By comparison with previously reported results, it is shown that this model precisely predicted the inversion velocity for most cases. An advantage of this model is that it is easy to use, not as complicated as completely segregation model. Further work needs to be done to predict the composition of the bottom mixed layer at a given velocity by using this model.

Notation

dsparticle diameter, m
ggravitational acceleration, m/s2
Lbed length, m
mmass of the solid charged in the bed, kg
nRichard and Zaki exponent
Ppiezometric pressure, N/m2
ReReynolds number Re=ρfufdsf
usuperficial velocity, m/s
utunhindered particle setting velocity, m/s
Greek letters
αsolid volume fraction in the mixed zone
εvolume fraction
ε1evolume fraction of the layer with only component 1
ε2evolume fraction of the layer with only component 2
ρbbulk density, kg/m3
ρbeequilibrium bulk density, kg/m3
ρffluid

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References (12)

  • L.G. Gibilaro et al.

    Chemical Engineering Science

    (1986)
  • R.H. Jean et al.

    Chemical Engineering Science

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  • H. Moritomi et al.

    Chemical Engineering Science

    (1982)
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    Chemical Engineering Science

    (1986)
  • B.B. Pruden et al.

    Chemical Engineering Science

    (1964)
  • M.G. Rasul et al.

    International Journal of Mineral Processing

    (2000)
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