The probabilistic model of the process mixing of animal feed ingredients into a continuous mixer-reactor

A mathematical model of the polydisperse medium mixing process reflects its stochastic features in the form of uneven distribution of phase elements on the time of their presence in apparatus, particle size, ripple retention of the apparatus, random distribution of the material and thermal phase flows of the working volume, heterogeneity of the medium physical- and chemical properties, complicated by chemical reaction. For the mathematical description of the mixing process of animal feed ingredients in the presence of chemical reaction the system of differential equations of Academician V.V. Kafarov was used. Proposed by him hypothesis based on the theory of Markov's processes stating that "any multicomponent mixture can be considered as the result of an iterative process of mixing the two components to achieve the desired uniformity of all the ingredients in the mixture" allows us to consider a process of mixing binary composition in a paddle mixer in the form of differential equations of two ingredients concentration numerous changes until it becomes a homogenous mixture. It was found out that the mixing process of the two-component mixture is determined in a paddle mixer with a constant mixing speed and a limit (equilibrium) dispersion of the ingredients in the mixture i.e. with its uniformity. Adjustment of the model parameters was carried out according to the results of experimental studies on mixing the crushed wheat with metallomagnetic impurity, which was a key (indicator) component. According to the best values of the constant of the continuous mixing speed and the equilibrium disperse values of the ingredients contents, the mathematical model parameters identification was carried out. The results obtained are used to develop a new generation mixer design.