SYSTEMATIZATION OF MATHEMATICAL MODELS OF FEED MATERIAL MIXING

Source abstract

Mathematical description of feed material mixing requires a clear distinction between models, since the heterogeneity of the components and the complexity of their movement determine the specific nature of transport, segregation, and interparticle interactions. This limits the direct transfer of models and their parameters between different material systems. The study aims to systematize mathematical models of mixing, determine their functional interrelationships, establish the conditions for transition between different levels of description, and define their applicability limits with regard to material properties and the structural and technological parameters of mixers. The methodological basis comprised systemic, structural-functional, and comparative approaches. Statistical, kinetic, RTD, zonal, Markov, continuum, and particle-based models were analysed. The models were compared according to the mathematical object, spatial and temporal scale, state variables, evolution law, observation procedure, parameters, and output indicators. An operator architecture was proposed to distinguish the physical state of the mixture, its model representation, evolution, formation of observable quantities, and quantitative evaluation. It was shown that the coefficient of variation, mixing indices, and RTD moments are primarily results of observation and data reduction rather than universal state variables. The transition from DEM to a continuum description was found to be achieved through spatial averaging, whereas the transition to a zonal model is based on the integration of balances over defined volumes. Markov and RTD representations are formed through the description of interzonal exchange and observation of the output signal. The information preserved and lost during model reduction was identified. It was substantiated that the choice of mathematical representation should be determined by the purpose of the calculation, the required level of detail, material properties, mixer design, and available experimental data. The formulated provisions provide a basis for developing zonal-balance models of feed material mixing.