Stochastic analysis of impact mixing of bulk materials in a rotary apparatus

The purpose of this work is to analyze the distribution of bulk materials according to the characteristic parameters of the mixing process at the second stage of processing in a rotary apparatus. The design of the rotary device has a wide range, including for the needs of agriculture, for example, when forming mixtures of mineral fertilizers and multifunctional pyrethroid drugs. At this mixing stage, impact interaction with the bump surface of rarefied flows of bulk components occurs, obtained by scattering the rotating drum by elastic blades at the previous stage of the technological chain. The obtained dependencies between the characteristic angle of dispersion of bulk materials by the specified mixing drum (at the first stage) and the angle of reflection of the corresponding flows from the baffle surface (at the second stage) are used in the stochastic analysis of impact mixing. Modeling of the differential functions of the distribution of the number of particles of mixed bulk components by the angle of reflection from the baffle surface is carried out taking into account the physical and mechanical characteristics of the working materials, design parameters, and operating parameters of the rotary apparatus. The calculation results made it possible to reveal the effective ranges of variation of the characteristic parameters for the shock mixing of bulk materials in a rotary apparatus.

The Knudsen Paradox in Micro-Channel Poiseuille Flows with a Symmetric Particle

The Knudsen paradox—the non-monotonous variation of mass-flow rate with the Knudsen number—is a unique and well-established signature of micro-channel rarefied flows. A particle which is not of insignificant size in relation to the duct geometry can significantly alter the flow behavior when introduced in such a system. In this work, we investigate the effects of a stationary particle on a micro-channel Poiseuille flow, from continuum to free-molecular conditions, using the direct simulation Monte-Carlo (DSMC) method. We establish a hydrodynamic basis for such an investigation by evaluating the flow around the particle and study the blockage effect on the Knudsen paradox. Our results show that with the presence of a particle this paradoxical behavior is altered. The effect is more significant as the particle becomes large and results from a shift towards relatively more ballistic molecular motion at shorter geometrical distances. The need to account for combinations of local and non-local transport effects in modeling reactive gas–solid flows in confined geometries at the nano-scale and in nanofabrication of model pore systems is discussed in relation to these results.

Methods of Nonequilibrium Statistical Mechanics in Models for Mixing Bulk Components

When describing the mechanics of the behavior of bulk materials during their mixing, a theoretical basis for the design of the specified equipment is formed. In recent years, the most well-known methods of modeling this process include the stochastic approach, in the framework of which models of the following types are actively developing: cell, managerial, with time series, energy, etc. Moreover, as a rule, predicting the quality of the finished mixture according to the selected criterion is achieved by using numerical calculation methods based on the generated cyber system. Of particular interest is the use of the energy method from the statistical mechanics of nonequilibrium processes due to the possibility of obtaining analytical simulation results. The paper describes the motion models of bulk components in rarefied flows, which are built on the basis of the energy method and take into account the main characteristics of the studied mixing process.