Numerical study of the effect of vibrations on the interaction in an ensemble of gas bubbles and solid particles in a liquid

Abstract

It is known that linearly polarized translational vibrations can lead to a multiple increase in the capture cross section of deposited solid particles by a single gas bubble suspended in a liquid. This fact is of great theoretical and practical importance in the use of vibrations to intensify the flotation process, in which, however, many pop-up bubbles are involved. In the present work, in the framework of a two-dimensional formulation of the problem, the capture of solid particles by an ensemble of gas bubbles in a liquid that is exposed to high-frequency vibrations of small amplitude is numerically investigated. The ANSYS Fluent package was used as a numerical solution tool. The fields of the averaged and pulsation components of the flow velocity obtained in it were then processed with the own code in order to calculate trajectories of the movement of small particles from some “cloud” located in the calculation domain. Of the forces acting on the particle, the added mass of the fluid, the force of gravity with the Archimedean force, the Stokes force, the hereditary Basse force, and alse the vibration force due to the inhomogeneity of the pulsation field were taken into account. The calculations were carried out for millimeter bubbles of air in water and the characteristics of the particles important for the flotation process. It is shown that the effect of vibrations is significantly weakened inside the arrangement of the ensemble of bubbles as a result of the “shielding” effect, which is fully manifested in the limit of a very high frequency of vibrations and weakly depends on the distance between the bubbles. However, vibrations of a not too high frequency, for which the effect of compressibility of a gas in a bubble is manifested, are capable of penetrating into the bulk of the liquid at a sufficient intensity, thereby increasing the area of capture of particles.