№ 2 (2025)

The known approaches to the mathematical modeling of the processes of targeted atomization of medical drugs into the airways are presented. The testified and promising solutions are distinguished. The governing physical laws, the important effects, and the factors that have the significant influence are analyzed. The problems, which have not been solved to the full extent are formulated. The promising directions of the development of the systems of drug atomization in anatomical airways are determined.

The system of maintenance of the formation pressure is associated with the appearance of technogenic fractures near injection wells, which leads to sharp watering of the extracted oil. Geomechanic simulators also leave out variations in the hydrodynamic fluxes due to adsorption and keeping of disperse particles in the porous medium. The quasi-one-dimensional model of the fracture development dynamics developed on the basis of mechanics of multiphase media allows one to take account of these effects. The numerical solution of these equations makes it possible to predict to a high precision the geometric parameters of a fracture at different moments of time.

The unsteady problem of oil spill from a damaged tank into water is considered. The mathematical model of the joint motion of three immiscible phases (water, oil and air) includes the continuity equations, Navier-Stokes equation and the equation for determining of the interphase position. The problem is solved by the finite volume method. The oil leakage rate from the tank, the fluid velocity profile in the hole section, and the effect of the hole size on lowering the oil level are determined. Various options for filling the ballast tank are accessed from the point of view of minimizing the negative impact of oil spills on the nature. It is shown that in the event of an accident, the presence of a ballast tank filled with water significantly reduces the volume of oil leakage into water.

The mechanisms of the bending flow of a viscous jet (Ohnesorge number greater than 0.05) flowing out of a capillary channel at a low velocity (Weber number is about unity) are experimentally investigated. The bending is due to the effect of internal forces and is not related with the interaction between the liquid and the atmosphere, which is confirmed by experiments performed in a vacuum chamber. A region of intense jet bending amounting to fifteen degrees is formed near the channel end section, at a distance of the jet diameter. Further downstream the jet is “straightened”, the angle of bending being reduced. The dependences of the greatest and overall bending angles on the jet velocity are obtained for different Ohnesorge numbers. The velocities, at which the deflection is maximum, are revealed. The deviation angle values corresponding to large velocities are determined.

The impacts of water and ethyl alcohol drops on a small metal disk whose diameter (4 mm) is only slightly greater than the drop diameter (2.8 mm) are studied. The drops fell from a height of 0.10–0.65 m and reached a velocity of 1.40–3.57 m/s before impact. Using high-speed video recording, various stages of the drop collisions with the obstacle were recorded. It is found that when going over from water to ethyl alcohol under the same impact conditions, a noticeable increase in the maximum splash diameter and the time it takes to reach it is observed. Observations also show that transition from a continuous splash to a splash with fragmentation is determined exclusively by the impact Weber number, whose critical value is of the order of 100. The previously established power-law dependence of the maximum splash diameter on the impact Weber number is confirmed.

The effect of instantaneous energy release (explosion) in the gas bubble region on supersonic flow past blunt bodies (sphere) and pointed bodies (ogival body and cone-cylinder combination) is considered when the explosion occurs in unperturbed freestream flow in the immediate neighborhood of the bow shock. Physically, such an effect on the flow can occur with energy input in the region of electric gas discharge or with detonation of a combustible gas mixture inside the bubble. It is found that, in addition to the direct effect of the explosive shock wave on the surface of the body, significant non-stationary changes in the gas-dynamic flow regimes past the bodies occur during the interaction of the bow shock with the dynamically varying explosion region (shockcompressed layer and cavity). In particular, focusing and cumulation effects, which can lead to secondary effects, are noted. The momentum of the latter is comparable to or even greater than the momentum of the direct impact of the blast wave.

The analysis of the results of numerical experiments on the calculation of hydrophysical fields in the north-eastern part of the Black Sea was carried out based on the Marine Hydrophysical Institute (MHI) three-dimensional ocean dynamics model.The fundamental novelty of the simulations presented is the use of vertical turbulent exchange coefficients, obtained from the experimental data based on the velocity and temperature fluctuations microstructural profiles obtained from “Sigma-1.5” sounding complex field observations. The measurements were carried out in the upper stratified sea layers during expeditionary research on the R/V Professor Vodyanitsky. A comparison of some simulations with the MHI model and the hydrological data obtained using SeaBird SBE-911plus CTD complex synchronously with the microstructural measurements shows greater reliability in the temperature and salinity fields simulated using the experimentally determined coefficients compared to simulations carried out with the use of Pacanowski-Philander turbulence parameterization. The presented results show the prospects of the proposed approach with the use of experimentally determined turbulent exchange coefficients for the stratified sea layers in the model.