Dynamics of Gas Bubbles Inside a Ball-like Area at the Nodes of a Uniform Cubic Mesh Under Sudden Liquid Pressure Rise

Abstract

The influence of hydrodynamic interaction between spherical gas bubbles inside a ball-like area at the nodes of a uniform cubic mesh on their dynamics under sudden liquid pressure rise has been investigated. Main attention is payed to the dynamics of a bubble located in the center of such a cluster of cubic structure. Prior to the pressure rise, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the radii of the bubbles are 0.25 mm, the size of the cubic mesh cells is 5 mm. The increase in the liquid pressure is 3 bar. For the sake of comparison, ball-like clusters with spherical and stochastic structures are also considered, with similar position of the central bubble and with initial minimum distance between the centers of bubbles not exceeding 5 mm. In the clusters of spherical structure, the non-central bubbles are located on concentric spheres with radii of 5 and 10 mm at the nodes of equally-oriented regular polyhedra (icosahedra and dodecahedra). In the clusters of stochastic structure, the non-central bubbles are distributed stochastically in a sphere with radius of 10 mm. A mathematical model is applied, in which the dynamics of bubbles is governed by the ordinary differential equations in the radii of bubbles and the position-vectors of their centers. It is shown that in the case of a cluster with cubic structure, the interaction between the bubbles leads to strengthening the collapse rate of the central bubble and to non-monotonic decay of oscillations of their pressure. Similar features are characteristic of the clusters with spherical and stochastic structures.