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The article presents the results of a study of the danger of copper (I) oxide nanoparticles for the health of living organisms and ecological systems. A sol containing Cu2O nanoparticles was obtained by reducing metal ions in the presence of a polymer protector. The sol was then further processed to purify and separate it into its components. The products of synthesis and processing were examined using transmission electron microscopy, scanning electron microscopy, and X-ray diffraction. It has been established that as a result of processing Cu2O nanoparticles of spherical shape and a diameter of 34-149 nm (average diameter = 62 nm) were obtained. Factors affecting the hazard of this nanomaterial were identified. Using mathematical modeling methods, it was determined that the obtained nanoparticles have a hazard coefficient D= 1.773 in the case of laboratory production (medium level of potential hazard), D= 1.874 in the industrial production case (high level of potential hazard).

The Couette-Taylor flow is considered in a wide gap between coaxial cylinders in the case when the outer cylinder is at rest and the inner one rotates at a constant speed. Unsteady motion of a viscous fluid is described by the system of Navier-Stokes equations. The problem is solved by the control volume method in the OpenFOAM software. Two stable states were obtained depending on the surface rotation speed: the cylindrical Couette flow and the Taylor vortex flow. The calculation results are compared with the known data of other authors. The dependence of the dimensionless shear rate on the Taylor number is obtained.

The problem of the collapse of a spherical gas cavity in a fluid under non-isothermal conditions is considered. Numerical simulation of the motion of a two-phase medium is based on the volume of fluid method (VOF). The numerical results of fluid pressure history at control points located at different distances from the center of the cavity during the process are obtained.

The process of underwater implosion of the air sphere in the cylindrical reservoir is considered. Numerical simulation of the two-phase flow is based on the volume of fluid approach. Both air and water are considered compressible. Menter's Shear Stress Transport turbulence model is chosen for the closure of Unsteady Reynolds-averaged Navier-Stokes equations. The solution of the problem is carried out by the finite volume method. The implosion event is on the order of milliseconds. The simulation results demonstrate that the pressure wave with high peak pressure moves from centre of the gas volume to reservoir wall. A comparison of pressure time histories were made between experimental data and numerical simulation results.

Gas-thermodynamic processes taking place during spraying of polymer powder materials are considered. Numerical and analytical models describing these processes are proposed. For the case of circular cylinder rotating with a constant angular velocity results of calculations and engineering formulas for estimating the thickness of powder particles layer deposited on the processed surface are present.

The influence of mechanical impurities in the fluid on the structure of the flow near a stationary, rotating cylinder, on its hydrodynamic characteristics and the heat exchange with the stream was investigated numerically. It was shown that the presence of impurities in the liquid leads to a significant change in the pattern of the flow, to increase in the resistance and heat transfer of a stationary cylinder, reducing the lifting force. The emissivity of the rotating cylinder in a fluid flow with an admixture of substantially depends on the dimensionless velocity of the surface. If the speed is less critical, equal to 3.0, the heat is intensified. At higher values, on the contrary, the heat transfer deteriorates. The necessity of considering these circumstances when developing technologies for deposition of functional coatings is evidential.