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The technological features of the production and transportation of some solid finely dispersed products of the chemical industry require the use of an additional deaeration operation (compaction). This processing of powders affects the quality of the product, delivery conditions. The production of deaerated granules-spheres from mineral components and bitumen for the preparation of asphalt concrete mixture or from powders for the production of dry dyes is relevant. The aim of this work is the mathematical modeling of the deaeration (compaction) process of solid finely dispersed media in a gap with perforated hemispherical shapes on the surfaces of the shaft and conveyor belt within the framework of the mechanics of heterogeneous systems. The distinctive features of the proposed method for modeling mechanical deaeration, as a technological process, from the known classical models are as follows. First, the plane-deformation model is described neglecting the forces of interphase interaction. The model assumes consideration of the movement of: a) the components of the solid skeleton of the dispersed medium together with the carrying phase as a whole; b) gas in an isothermal state through the pores of a finely dispersed material. This work is devoted to the study of part (a), i.e. behavior of the solid particle-gas system as a whole. Second, the compressibility of the solid particle-gas mixture is taken into account in the absence of elastoplastic deformations of the particles themselves. The efficiency of the seal-deaerator for solid finely dispersed media is estimated using the obtained analytical dependencies for the main strength and speed indicators of the process under study. Using the example of the deaeration of kaolin, the change in the degree of compaction of the resulting sample of a spherical granule with specified strength characteristics is investigated. It is shown that for the initial time interval up to 3.7⨯10-2 s, the growth of the porosity value relative to the horizontal coordinate along the conveyor belt is exponential and increases by a factor of 1.1. After eight such time intervals, the porosity values stabilize along the indicated coordinate with an increase of more than 1.4 times from the initial value.

The aim of this work is to develop a stochastic method for calculating the average value of the volume fraction of a key bulk component at an intermediate stage of mixing with an inclined bump based on the energy method. The specified characteristic is used to assess the quality of the granular mixture when choosing a criterion in the form of a heterogeneity coefficient of the product obtained at the corresponding stage of operation of the gravitational apparatus. This equipment is designed to produce a mixture of solid dispersed components in a ratio of 1/10 or more. At the same time, at each stage of mixing, two types of mixing devices (brush elements and inclined bump surfaces) work. A distinctive feature of the application of the energy method is to obtain an analytical relationship for the desired characteristics of the process of mixing bulk materials, taking into account their physical and mechanical properties and a set of structural and operational parameters of the apparatus. The calculation of the increment angles of reflection of rarefied flows of bulk components after interaction with the bump surface is proposed. The differential distribution functions of the number of particles of these components over the states of macrosystems are taken into account. The basis is the results of stochastic modeling of mixing of flowing media with brushes. The effectiveness of the intermediate stage of mixing with the bump using the coefficient of heterogeneity of the granular mixture is analyzed. The influence of the most significant design parameters of the gravitational apparatus and its operating modes on the quality of the intermediate mixture in comparison with the results for the initial and final steps is investigated. It has been established that this class of parameters includes the angular velocity of rotation of the drum, the angle of inclination of the bump to the horizontal, the pitch of screw winding, and a comprehensive indicator of the deformation of the brush elements. For example, an increase in the last complex indicator by 0.05 units leads to a decrease in the inhomogeneity coefficient by (0.15–0.80%) in the studied range of the angular velocity of rotation of the drums. In addition, the consequence of this is a decrease of 0.5 s−1 for the value of the angular velocity of the mixing drum, which corresponds to the minimum value for the specified quality criterion of the mixture. The latter fact allows under the selected conditions ensuring a reduction in energy costs for the expended power drives of the mixing drums. The results of the work, confirmed by experimental studies, predict rational ranges of change of significant process parameters using the criteria for the best mixing of components proposed by the authors earlier.