(70ai) Experimental investigation and mathematical modelling of evolution of the axial non homogeneity of mixtures in static mixers

The objective of the study is to investigate experimentally and describe mathematically how an initial axial non-homogeneity of a mixture of two granular materials changes from one passage through a static mixer to another. The two static mixers were chosen for the study: the laboratory revolving static mixer with changeable mixing zone, and the industrial static mixer of Sulzer type, which also allows changing the number of mixing elements in the zone. The following granular materials of different density and mean particle size were used in the experiments: carborundum, aluminum oxide, sugar, semolina, couscous, millet. Artificial compositions of couples of the materials (including the case of colored particles of couscous and pure couscous to examine the process without any segregation) were fed into a mixer at the top and then collected at the bottom. After analysis of their concentration distribution the mixture was removed to the top again for the next passage, etc. The sample was removed to the top at the same position for Sulzer mixer, and at the turned upside-down position for the laboratory mixer imitating a revolving mixer. A mathematical model of such processes based on the theory of Markov chains is proposed. The state of the mixture is presented as several macrostates corresponding to the scale of its quality control. After passing through the mixing zone these states are transforming into microstates ? parts of every component falling down on the bottom after every transition. This transformation occurs according to the matrix of transition probabilities for every component in the mixing zone. After the fall is finished these microstates are to be recollected into the macrostates of the same scale as before, as it was done in the experimental study. Then, for the revolving mixer, the new macrostate vector is to be turned upside down, again transformed by the matrix, and so on. For Sulzer mixer turning upside-down was not being done. The model parameters, i.e., the transition probabilities of the matrix, were defined from results of experiments by comparison of experimental and calculated distributions of concentrations at the bottom. It was shown that with a reasonable accuracy the transition probabilities could be expressed as an experimental function of the only parameter of a material ? its settling velocity. The model allows calculating the necessary number of passages giving a required quality of the mixture, and predicting the asymptotic distribution of components, which is not homogeneous if the transition matrices for components are different. Calculated parameters of the processes are in good correlation with the experimental data.