The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

Abstract

A phenomenological implementation of Classical Nucleation Theory (CNT) is employed to investigate the connection between high intensity focused ultrasound (HIFU) pressure and temperature fields with the energetic requirements of bubble nucleation. As a case study, boiling histotripsy in tissue-mimicking phantoms is modelled. The physics of key components in the implementation of CNT in HIFU conditions such as the derivation of nucleation pressure thresholds and approximations regarding the surface tension of the liquid are reviewed and discussed. Simulations show that the acoustic pressure is the ultimate trigger for millisecond bubble nucleation in boiling histotripsy, however, HIFU heat deposition facilitates nucleation by lowering nucleation pressure thresholds. Nucleation thus occurs preferentially at the regions of highest heat deposition within the HIFU field. This implies that bubble nucleation subsequent to millisecond HIFU heat deposition can take place at temperatures below 100 °C as long as the focal HIFU peak negative pressure exceeds the temperature-dependent nucleation threshold. It is also found that the magnitude of nucleation pressure thresholds decreases with decreasing frequencies. Overall, results indicate that it is not possible to separate thermal and mechanical effects of HIFU in the nucleation of bubbles for timescales of a few milliseconds. This

Predicting initial nucleation events occurred in a metastable nanodroplet during acoustic droplet vaporization

“…However, the closer to the spinodal point ( ξ = 1) the thermodynamic condition is, the larger difference between the CNT and the modified CNT will be. Near saturation condition ( ξ = 0), the CNT is expected to provide accurate results, whereas its predictions become increasingly inaccurate as the thermodynamic condition is approaching to the spinodal point [33] . At the spinodal, the critical work and critical radius predicted by the CNT are larger than zero, as an indication of the intrinsic limitations of the CNT.…”

“…Nucleation is an activated process, in which an energy barrier must be surmounted to transform the metastable liquid phase to the stable vapor phase. The work W required for the formation of a vapor bubble nucleus with a radius r in the metastable liquid is given by [33] where σ is the surface tension at the PFC liquid–vapor interface, P v is the vapor pressure in a newly formed vapor bubble nucleus, N is the number of molecules inside the bubble nucleus, and are the chemical potentials of the gas phase and the liquid phase, respectively.…”

“…It is well-known that the work W exhibits a maximum W * at the critical bubble radius r * given by , where superscript * denotes conditions at the critical size [33] . The probability of growth is greater than the probability of shrinking for vapor bubble nuclei whose radii are greater than the critical radius, whereas the probability of shrinking prevails for smaller bubble nuclei.…”

“…In the CNT, for a sample of volume V , the probability of bubble nucleation Σ within a time τ is [40] where V represents the nanodroplet volume, τ is modelled as a fraction of the ultrasound wave where acoustic pressure values are the lowest and remain reasonably constant. Thus, τ is approximated as 1/10 f to ensure that P l variations within this time interval are negligible, similar to that used previously [33] . The ADV nucleation threshold P th is defined as the absolute value of the acoustic pressure P a at which Σ reaches 50%, thus the P th is given by …”

“…Consequently, it leads to large errors in the nucleation rate at a higher degree of metastability, and fails to predict the loss of stability at the spinodal. These intrinsic limitations have caused an obvious overestimation of nucleation threshold [32] , [33] . Therefore, accurately estimating the σ r with experimentally controllable parameters is crucial to overcome the current limitations.…”