(281g) Noble Method for Evaluating the Distributive Mixing of Bimodal Lagrangian Particles

Mixing operation have been one of the most important process at chemical industry for a long time. Several equipment such as static mixer or twin screw extruders are developed to obtain uniformity of product. Also considerable researches have been conducted to increase the mixing efficiency. In the most researches about mixing, evaluating the degree of mixing was an issue. For evaluating the degree of mixing quantitatively, the mixing is classified with phases of mixing materials¹. Among phases, particle-particle mixing (powder mixing) takes considerable part of research, because of its discretizational characteristic.

Since Danckwerts proved that the variance among samples can represent the scale of segregation, the variance among bin counts is useful and popular index to quantify the spatial distribution of Lagrangian particles². With the domain which is divided by several bins (cells), the variance among particles number in each bin is easy to be calculated and understood. When the spatial distribution of particles appear, the variance tend to be smaller. Although the variance among bin counts is effective to quantify the spatial distribution of unimodal particle systems, it is hard to applicate the method at bimodal particles systems. However, most of the practical particle mixing processes are bi- or multimodal particles systems. In this research, using the variance among bimodal bin counts, mixing between bimodal particles was evaluated. Bimodal bin counts is defined by subtraction of number of two particles species in each cell. Therefore bimodal bin counts values represent quantitative difference between two particles species in each cell and variance among bimodal bin counts represent the degree of mixing between two particle species. When the system reach almost evenly mixed state, variance becomes to be zero. By adapting conventional and bimodal bin counting method simultaneously, utility of the variance among bimodal bin counts is acknowledged with 4 examples; systems with balanced and imbalanced number of particles with 2D mixer and fluidized bed. With variation of the form of variance, 4 examples were analyzed. And examples proved effectiveness of variance among bimodal bin counts as index to quantify the mixing between bimodal particles. Also, to estimate the effect of the number of bins, case studies were conducted with changing the total amount of bins. For 2D mixer, 6 kind of bin sizes were adopted, and for fluidized bed, 5 kind of bin sizes were adopted based on the size of domain and the number of total particles. As a result, variance among bimodal bin counts evaluate systems appropriately which have balanced number of particles, whereas variance among bimodal bin counts with sensitivity factor and variance among conventional bin counts only for minor particles evaluate systems appropriately which have imbalance number of particles. The effect of the number of bins is minor factor within reasonable region; smaller amount than total number of particles with small size enough to evaluate the mixing.

References

1. Harnby N, Edwards FM, Nienow WA. Mixing in the process industries (2^nd edition). Butterworths-Heinemann, 1997.

2. Danckwerts PV. The definition and measurement of some characteristics of mixtures. Appl Sci Res. 1952;A3;279–296.