Bubbles nucleation in spherical liquid cavity wrapped by elastic medium


 According to classical nucleation theory, gas nuclei can generate and grow into a cavitation bubble when the liquid pressure exceeds a threshold. However, classical nucleation theory is not including boundary effects. An enclosed spherical liquid cavity surrounding by elastic medium is introduced to model the nucleus process in tissue. Based on the equilibrium pressure relationship of a quasi-static process, the expressions of the threshold and the modified nucleation rate is derived by considering of the tissue elasticity. It is shown that the constrains plays an important role in the nucleus process. There is a positive correlation between that nucleation threshold pressure and constrains, which can be enhanced by an increasing tissue elasticity and decreasing size of the cavity. Meanwhile, temperature is found to be a key parameter of nucleus process, and cavitation is more likely to occur in confined liquids with temperature T > 100℃. In contrast, less impacts are induced by these factors, such as bulk modulus, liquid cavity size and acoustic frequency. Although these theoretical predictions of the thresholds have been demonstrated by many previous literatures, much lower thresholds can be obtained in liquids containing dissolved gases, e, g. the nucleation threshold is about -21 MPa in a liquid of 0.8 nm gas nuclei at room temperature. Moreover, when there is a gas nucleus of 20 nm, the theoretical threshold pressure might be less than 1 MPa.