Mixedness multi component

Until now, the quantitative evaluation of the multi-component mixedness based on the spatial distribution of each component in the vessel was discussed. It is obvious that the evaluation of the mixing capacity should be performed based on the change in the multi-component mixedness with time. However, few investigations exist on the multi-component mixing capacity based on the change in mixedness with time. 

Next, the case of m = n in Eq. (2.41), that is, the case that the number of components equals the number of imaginary equivolume partitioned regions, is considered. In this case, the denominator in Eq. (2.41) is log n and the formula coincides with the definition of the whole mixing capacity defined by Eq. (2.30). This is the point of contact between the multi-component mixedness and whole mixing capacity that is, both indices need not be discussed separately. 

This fact implies that the mixedness by using the transient response method is a special case of the multi-component mixedness12. 

It is possible to define an evaluation index for the mixing state by using the definition of multi-component mixedness in the previous section. The following discussion focuses on the mixing state of the continuous phase and the dispersed phase with a particle size distribution. 

The distribution of the dispersed particle size is divided into m - 1 groups in the order of size, and each group is considered to be individual component. Additionally, the continuous phase is treated as another component. From this consideration, the mixing can be treated as m-component mixing, and the multi-component mixedness defined by Eq. (2.43) in the previous section can be applied. The extended definition of mixedness for the mixing of the continuous phase and dispersion phase can be expressed as... 

Mixedness for multi-component mixing based on the distribution of each component in the vessel. 

Under these conditions, the uncertainty regarding the component of the element that is selected is considered. In fact, the following discussion is the same as that in the definition of the multi-component mixedness. Only the practical conditions corresponding to the maximum and minimum values of the mutual entropy are different from the case of the definition of the multi-component mixedness. According to Section 1.7, the mutual entropy 1(0, R) has the following minimum and maximum values ... 

The difference between this separation efficiency and that from the multi-component mixedness is that the correspondence of the conditions for the maximum and minimum values of the mutual entropy is reversed. Therefore, it is natural that this separation efficiency has the following clear relationship with the multi-component mixedness ... 

Ogawa, K. (1984). An expression of quality of mixedness for multi-component batch mixing. Kagaku Kogaku Ronbunshu, 10, 261-264. 

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