External vibrations are known to be one of the promising ways to control the behavior of multiphase systems. The computational modeling of the behavior of a gas bubble in a viscous liquid in a horizontal cylinder of square cross-section, which undergoes linearly polarized translational oscillations in weightless conditions, has been carried out. Under vibrations, the bubble moves towards the wall of the vessel with acceleration determined by the amplitudes and frequency of vibrations. Near the wall, at a distance of the order of the thickness of the viscous Stokes boundary layer, the effects of viscosity become more important and, as a result, the bubble is repelled from the wall. After some oscillations, equilibrium conditions are attained where the attractive force balances the repulsive force; accordingly, the average position of the bubble ceases to change. The numerical modelling shows that the average behaviors of a deformable bubble near a wall under normal and tangential vibration are similar.

The article presents the results of in-kind measurements and numerical modeling of the formation of water characteristics in the Kama River, which is used for technical water supply in the production of potash fertilizers. In the warm season, risks arise that threaten the sustainability of the water supply. It was found that in the summer, when the studied section of the Kama River is backed up by the Kama Hydroelectric Power Station, there is a significant decrease in flow rates, which leads to vertical stratification of water properties. This, in turn, significantly limits the possibilities of using water from the bottom zone. Under conditions of significant water discharge from the reservoir, this section has river conditions with significantly higher flow rates. Under such conditions, intense vertical mixing of water masses occurs, which improves the consumer properties of water necessary for sustainable water supply. The results of numerical modeling carried out within the framework of the three-dimensional approach confirmed this conclusion. It is shown that with an increase in the flow rate in the channel near the water intake, the concentration of salts decreases, which is an important factor in ensuring high-quality water supply.