Motions of deformable inclusions in a horizontally oscillating vessel with a compressible fluid

The paper is concerned with the analysis of rigid particle and compressible gas bubble motion in a horizontally oscillating vessel with a compressible fluid. A nonlinear differential equation describing motion of inclusions with respect to the vessel is derived and solved by the method of direct separation of motions. It is shown that rigid particles and gas bubbles can move both in nodes and antinodes of the pressure, depending on their size, density, and vibration parameters. The conditions under which different kinds of motion can incur have been determined. An expression for the critical radius of the bubbles which are affected by the negligible vibrational force is found. Also an approximate expression has been obtained for the average velocity of bubble׳s motion in the fluid; relationship between this velocity and bubble radius and vibration parameters has been revealed. A simple physical explanation of the noticed effects is proposed. Series of numerical experiments has been conducted, their results confirming those obtained theoretically. These results may be of interest for development of the flotation theory and other technological processes.