Dynamic behavior of double-cube multi-bubble system driven by square waves

This study investigates the radial dynamics of a hierarchically arranged 17-bubble system consisting of eight outer-cube bubbles, eight inner-cube bubbles, and one central bubble under finite-bandwidth square-wave excitation. The bubble positions are defined by a Cartesian coordinate model, from which the complete pairwise distance matrix is incorporated to evaluate collapse temperature, rebound, and wall velocity without relying solely on a polytropic approximation, with coupling terms fully introduced into a compressible multi-bubble equation. Non-equilibrium acoustic pressure, frequency, geometric scale ratio, bubble-size ratio, viscosity, surface tension, evaporation/condensation and interfacial thermal diffusion are characterized via dimensionless parameters to quantify coupling effects. The results identify normal expansion, complete suppression, and delayed expansion regimes of the central bubble and show that these regimes are governed by the competition between the externally imposed tensile pressure and the radiation pressure generated by the surrounding bubbles. Square-wave and sinusoidal forcing are compared under both equal-peak-pressure and equal-RMS-pressure conditions. The maximum wall Mach number and rebound amplitude are reported to delimit the validity of the spherical Keller-Miksis-based formulation. The calculated collapse temperature is interpreted as a thermodynamic severity metric rather than a direct measure of oxidant yield, because sonochemical radical production may decrease above an optimum bubble temperature. The model clarifies the parameter ranges in which a fixed-centre radial description is appropriate and the ranges in which migration- and deformation-resolving models are required.