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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 processes of copper reduction on the steel surface in the presence of a polymer protector were researched to determine the effect of the polymer pseudo-matrix on the characteristics of the resulting nanoparticles. Poly(N-vinylpyrrolidone) with different molecular mass, poly(ethylene glycol) and poly(ethylene glycol monolaurate) were used as a polymer pseudo-matrix. Transmission electron microscopy, scanning electron microscopy, electron spectroscopy, and thermogravimetric analysis were used to characterize the synthesis products. It was found that in the presence of a polymer protector, nanocomposite particles are formed, including copper-containing particles and a polymer. It is shown that the nature of the polymer affects the morphological structure of nanocomposites formed on the surface of steel. In the presence of poly(N-vinylpyrrolidone), spherical agglomerates consisting of smaller copper particles are formed. In the presence of poly(ethylene glycol monolaurate), needle-like structures are formed. In the presence of poly(ethylene glycol), dendritic structures are formed. In this case, copper nanoparticles of 3-10 nm size are formed directly on the steel surface in the presence of poly(N-vinylpyrrolidone) or poly(ethylene glycol monolaurate).

The possibility of using amphiphilic polymers of N-vinylpyrrolidone as polymer protectors of metal nanoparticles is researched. When metal ions are reduced in aqueous solutions of the corresponding salts in the presence of amphiphilic polymers, copper nanoparticles with a diameter of 4-12 nm or palladium particles with a diameter of 3-5 nm are formed. Nanoparticles are included in rather large aggregates of micelles of amphiphilic polymers. It was found that extremely stable sols are formed in the presence of amphiphilic polymers. In this case, the stability of sols to irreversible aggregation and oxidation of metal nanoparticles increases both with increasing length of the polymer’s hydrophilic chains and with increasing length of hydrophobic fragments. In the presence of a low-molecular-weight electrolyte, particles with a smaller diameter are formed. However, the resistance of metal nanoparticles to oxidation is reduced by 6-10 times.

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 results of the study of the possibilities of using copper-containing nanoparticles obtained by pseudomatrix synthesis as a catalyst for cyclic gas nitriding of steel products were presented in this paper. It was shown by the example of steel 08Yu (corresponding to the European standard of steel DC04/DC03 EN 10139) that the preliminary application of nanocomposite-catalyst including copper-containing nanoparticles and macromolecules of poly-(N-vinylpyrrolidone) polymer pseudomatrix to the product significantly intensified the chemical heat treatment process. It was found that under identical treatment process conditions the thickness of the diffusion layer for a sample with a pre-applied nanocomposite was 90 urn, and without such pretreatment — 42 urn It is noted that the achievement of this effect is due to the catalyst synthesis peculiarities, which allows to obtain a copper sol with a narrow size distribution of particles resistant to aggregation.

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.

The motion and heat transfer of water droplets with a swirling air flow is investigated. Flow was considered in a cylindrical chamber in the absence of gravity. We created a mathematical model of this problem and made appropriate calculations. The features of the air flow at a tangential feeding it into the chamber, and the motion of the drops, their thermal behaviour are founded. We presented the recommendations for the rational choice of parameters of the apparatus and rational operation regime.

Mathematical modeling of processes occurring during the spraying of polymer powder compositions on the surface of parts and products is considered. Relations describing the flow around processed bodies, movement of the powder particles in a stream of the carrying medium, dynamics of their deposition on the body surface are presented.

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.

Non-isothermal flow around the porous permeable cylinder of square cross section by a viscous incompressible fluid is considered. The motion and energy equations is solved numerically using the finite volume method. The character of the fluid flow, change of the cylinder drag coefficient and Nusselt number as a function of Reynolds and Darcy numbers is analyzed.

Heating and melting of particles of polymeric powder in the central flow channel of spraying gun is investigated. Mathematical models of these processes taking into account convective and radiative-convective heat interaction of particles with environment is represented. Relations for calculating the temperature of the particles depending on the longitudinal coordinate, time of flight, operating and design parameters as well as thermophysical characteristics of the particles material and environment are given.

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.