Hydrodynamic interaction of weakly nonspherical gas bubbles in a liquid in the three-dimensional problem statement

The influence of the relative location of weakly nonspherical gas (air) bubbles in liquid (water) on their hydrodynamic interaction at the pressure antinode of an ultrasonic standing wave is studied. Three essentially different configurations of the mutual arrangement of the bubbles are considered: the linear, planar, and spatial ones. In the linear configuration, three bubbles are located on one straight line. In the planar configuration, five bubbles are situated on two mutually orthogonal straight lines. In the spatial configuration, seven bubbles are located on three mutually orthogonal straight lines. In all the cases, one of the bubbles is central, the others are equally-spaced from it on those lines. All the bubbles are initially spherical with a radius of 3 $\mu$m. Room conditions are considered, the frequency of the wave is 20 kHz, its amplitude is 1.2 times the static liquid pressure. A mathematical model is used, in which the liquid is assumed weakly compressible, the bubbles being homobaric. It is shown that in each configuration of the bubbles the influence of their interaction on their radial dynamics is insignificant. In each configuration, the central bubble remains stationary, while the others move to it at a speed equal for a fixed configuration. At transition from a linear configuration to a planar one and from a planar configuration to a spatial one, the bubble motion speed increases. In all the cases, the deformations of the central stationary bubbles are smaller than those of the rest. Among the central bubbles, the bubble in a planar configuration is deformed most.