SIMULATION MODELING OF THE PROCESS OF MIXING FRACTURED MIXTURES IN A PERIODICALLY ACTIVE VIBRATING APPARATUS

The quality of dry construction mixtures is determined by their homogeneity, which directly depends on the efficiency of the mixers, among which vibration mixers are used for gentle and intensive mixing of loose materials of various density and dispersion. However, the process is complicated by the phenomenon of particle segregation and the need to take into account the random characteristics of the materials and the parameters of the vibration effect. To describe the mixing process, the authors of the article propose a probabilistic approach using the convective diffusion equation. An effective way to solve this equation is to use the mathematical framework of Markov chain theory, which implements stochastic modeling. The mixing vessel is represented as an array of ideal mixing cells, and the movement of components is governed by a transition probability matrix. The model allows for the prediction of the distribution of components in the mixture, taking into account random factors. Simulation modeling has confirmed the adequacy of the description of the processes of vibro-liquefaction and mixing, including the diffusion and segregation mechanisms. The method for determining the stochastic coefficients of the model has been tested on a virtual simulation setup, a digital computer model of a periodic-action vibrating apparatus. The proposed approach allows for the quantification of the effectiveness of vibratory mixing. The model can be used for the design of technological lines and the control of the quality of construction mixtures. Further research should focus on the consideration of the actual rheological properties of materials.