Phenomena in bubbles cluster

TL;DR

This paper explores the analogy between acoustic and electromagnetic phenomena in bubble clusters, deriving forces and energy densities, and demonstrating that gravito-acoustic forces at resonance are proportional to the bubbles' virtual masses.

Contribution

It provides a detailed theoretical derivation of acoustic forces and energy densities in bubble clusters, extending previous work on acoustic-electromagnetic analogy.

Findings

The average pressure of acoustic radiation equals the energy density of the electro-acoustic field.

Gravito-acoustic forces at resonance are proportional to the square of the bubbles' virtual masses.

The paper establishes a quantitative link between acoustic forces and bubble oscillation energies.

Abstract

Following some previous papers, we continue in this paper to give proof of the analogy between the acoustic world and the electromagnetic world. Hence we derive the expressions for: the scattering-scattering force (the electro-acoustic force) between the bubbles found in the inner cluster and the bubble found out of the cluster, the scattering-absorption force (the gravito-acoustic forces) between the bubbles found in the inner cluster, the gravito-acoustic forces between the cluster as a whole and an outer bubble, the temperature corresponding to the translational motion of the bubbles in the inner cluster and the average pressure of the acoustic radiation. The results of our calculus led us to find out that the absolute value of the average pressure of the acoustic radiation around a bubble is equal to the density of the energy of the electro-acoustic field, Eq. (10). This is the most important result of this paper. These densities are the densities of the energy corresponding to the oscillation of the bubble (the liquid around the bubble) that are involved in the interaction phenomenon between two oscillating bubbles. We have also demonstrated that the gravito-acoustic forces, at resonance, between the bubbles inside the cluster, generated by the absorption of energy in the bubbles, are proportional to the square of the virtual masses of the bubbles, Eqs. (29) and (30).