Motion of finely disperse inclusions in an oscillating vessel with liquid containing a compressible sphere

Abstract

The results of the present investigation may be summarized as follows: 1. Introducing a gas cavity in a liquid which occupies an oscillating vessel leads to the formation of a new vibrational system. In this system the elastic element is the gas cavity and the inertial element is the liquid. At resonance, when the excitation frequency is the intrinsic frequency of the pulsational oscillations, there is a redistribution of dynamic pressure in the liquid. In the vicinity of the gas cavity, its amplitude considerably exceeds the amplitude of the external excitation. 2. In the region of the pulsating sphere, there is an attractive manifold in the form of spherical surfaces to which small gas bubbles move, tending to occupy a stable position on these surfaces. This process depends mainly on the bubble diameter, the vibration frequency, and the amplitude of the oscillations. 3. The dynamic behavior of solid inclusions has a peculiarity in that particles move to the surface of the pulsating sphere and then are retained there. This process depends on the particle density and the amplitude of the excited oscillations. 4. The features observed in the dynamic behavior of small gas gubbles and solid particles in a sphere dynamically excited as here described are of resonant type, are specific for vibrational technology, and must be taken into account, in particular, in developing and designing equipment for flotational processes of mineral enrichment and the purification of industrial water.