Unravelling the dynamics of coated nanobubbles and low frequency ultrasound using the Blake threshold and modified surface tension model

<i>Objective.</i>To develop a model that accurately describes the behavior of nanobubbles (NBs) under low-frequency ultrasound (US) insonation (<250 kHz), addressing the limitations of existing numerical models, such as the Marmottant model and Blake's Threshold model, in predicting NB behavior.<i>Approach.</i>A modified surface tension model, derived from empirical data, was introduced to capture the surface tension behavior of NBs as a function of bubble radius. This model was integrated into the Marmottant framework and combined with the Blake threshold to predict cavitation thresholds at low pressures, providing a comprehensive approach to understanding NB dynamics.<i>Main results.</i>Experimentally, inertial cavitation for NBs with a radius of 85 nm was observed at peak negative pressures of 200 kPa at 80 kHz and 1000 kPa at 250 kHz. The Marmottant model significantly overestimated these thresholds (1600 kPa). The modified surface tension model improved predictions at 250 kHz, while combining it with the Blake threshold accurately aligned cavitation thresholds at both frequencies (∼150 kPa at low pressures) with experimental results.<i>Significance.</i>This work bridges a critical gap in understanding the acoustic behavior of NBs at low US frequencies and offers a new theoretical framework for predicting cavitation thresholds of NBs at low US frequencies, advancing their application in biomedical US technologies.