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Theoretical study of influence of the mixing parameters on mixing time and mixture quality of dissimilar particulate solids

V. Mizonov, A. Mitrofanov, I. Balagurov, H. Berthiaux, V. Zaitsev

Vestnik IGEU, 2018 issue 5, pp. 56—61

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Abstract in English: 

Background. Mixing of particulate solids is widely spread in many industries. Mixing can be realized as an independent  process to obtain a homogeneous mixture or half-finished product, as well as an accompanying process in particulate solids treatment, for instance, in coal energetics. Any mixing is the combination of two sub-processes: pure diffusion mining that leads to equalizing of components distribution over a mixture volume, and segregation that leads to exfoliation of the mixture. Despite the models of mixing taking into account the both components of the process are known, their separate influence on mixture quality formation is not practically investigated that makes it difficult to choose the rational parameters of a mixture mechanical agitation to reach as much homogeneity as possible. It is obvious that, at present, such analysis deserves special attention.

Materials and methods. The method of mathematical modeling and numerical experiments is used to solve the above problem. The model is based on the theory of Markov chains. The process of mixing is presented as a discrete one in space and time. The matrix of transition probabilities is presented as multiplication of two matrices: one for pure diffusion mixing, and another one for segregation mixing. The state of the mixture is presented as a column vector. Its homogeneity is characterized by the standard deviation. The recurrent calculations using the matrix equality allow estimating the evolution of the mixture state and the optimum mixing time corresponding to the maximum homogeneity of the mixture.

Results. The dependence of the maximum reachable homogeneity and the time when it can be reached on the intensity of diffusion and segregation mixing is found. It is shown that one and the same maximum homogeneity can be reached at different combination of these intensities. It is found that the rate of segregation mixing is much higher than of diffusion one. However, the maximum value of homogeneity itself in this case is much worse in comparison to the case when diffusion mixing prevails.

Conclusions. The proposed model allows finding the rational combination of diffusion and segregation intensity of mixing to reach a required mixture quality and, with orientation on them, choosing the rational way of mixture agitation to obtain it.

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Key words in Russian: 
смесь сыпучих материалов, моделирование, цепь Маркова, диффузионное перемешивание, сегрегационное перемешивание, качество смеси
Key words in English: 
mixture of particulate solid, modeling, Markov chain, diffusion mixing, segregation mixing, mixture quality
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