Mechanisms of nuclei growth in ultrasound bubble nucleation

Abstract

This paper interrogates the intersections between bubble dynamics and classical nucleation theory (CNT) towards constructing a model that describes intermediary nucleation events between the extrema of cavitation and boiling. We employ Zeldovich's hydrodynamic approach to obtain a description of bubble nuclei that grow simultaneously via hydrodynamic excitation by the acoustic field and vapour transport. By quantifying the relative dominance of both mechanisms, it is then possible to discern the extent to which viscosity, inertia, surface tension and vapour transport shape the growth of bubble nuclei through non-dimensional numbers that naturally arise within the theory. The first non-dimensional number Φ₁²/Φ₂ is analogous to the Laplace number, representing the balance between surface tension and inertial constraints to viscous effects. The second non-dimensional number δ represents how enthalpy transport into the bubble can reduce nucleation rates by cooling the surrounding liquid. This formulation adds to the current understanding of ultrasound bubble nucleation by accounting for bubble dynamics during nucleation, quantifying the physical distinctions between "boiling" and "cavitation" bubbles through non-dimensional parameters, and outlining the characteristic timescales of nucleation according to the growth mechanism of bubbles throughout the histotripsy temperature range. We observed in our simulations that viscous effects control the process of ultrasound nucleation in water-like media throughout the 0-120 °C temperature range, although this dominance decreases with increasing temperatures. Enthalpy transport was found to reduce nucleation rates for increasing temperatures. This effect becomes significant at temperatures above 30 °C and favours the creation of fewer nuclei that are larger in size. Conversely, negligible enthalpy transport at lower temperatures can enable the nucleation of dense clusters of small nuclei, such as cavitation clouds. We find that nuclei growth as modelled by the Rayleigh-Plesset equation occurs over shorter timescales than as modelled by vapour-dominated growth. This suggests that the first stage of bubble nuclei growth is hydrodynamic, and vapour transport effects can only be observed over longer timescales. Finally, we propose that this framework can be used for comparison between different experiments in bubble nucleation, towards standardisation and dosimetry of protocols.

Keywords: Boiling; Bubble nuclei dynamics; CNT; Cavitation; Histotripsy; Nucleation; Ultrasound.