Focused pulsed laser has been widely used in a wide range of applications such as element composition analysis, microsurgeries, microfluidic operations, and in clinical laser surgery for the disintegration of kidney stones and intravascular plaque treatment, among other procedures. In many of these scenarios, cavitation bubbles are generated in semi- or fully confined liquids and play a dominant role. The strong interactions of bubbles with the surrounding confined environment lead to complex dynamics of both the bubbles and elastic boundaries, which can contribute to the desired effect but can also generate undesired side effects. Therefore, it is of practical importance to explore the influence of the confinement effect on bubble dynamics. In recent years, intensive research has been conducted on the laser-induced bubble dynamics in confined liquids. The additional increase in pressure during bubble oscillations can significantly compress the bubble dynamics, resulting in a reduction in the bubble size and oscillation time. However, to the best of our knowledge, there is a lack of studies on the influence of confinement-related parameters on confined bubble dynamics and the accompanying pressure changes in liquids, as well as the change in the relationship between bubble size and oscillation time. Therefore, in this study, based on the confined Rayleigh?Plesset model, we numerically investigate the laser bubble dynamics in a spherical confined geometry. Here, the effects of the liquid size and degree of confinement on the bubble dynamics, especially on the cut-off period, are mainly studied.
A simple physical model was constructed assuming that a laser-induced spherical bubble was formed at the center of a fully sealed spherical geometry with a rigid boundary. Bubble oscillation squeezes the liquid and reduces the liquid volume, leading to pressure increase in the liquid. The relationship between the pressure increase in the liquid?solid boundary and the reduced liquid volume was assumed to be linear and linked to the bulk modulus of the liquid. The compressibility effects of the liquid were neglected, and the degree of confinement was assumed to be constant. Based on these results, a confined Rayleigh?Plesset equation was derived by introducing the confinement effect into the Rayleigh model. For the laser-induced bubbles, the ratio of the equilibrium radius to the initial radius was set at a constant value of 10.4. The radius?time curves for various bubble sizes were obtained by tuning the initial bubble radius. Using this confined Rayleigh?Plesset equation, the influence of liquid size and confinement degree on bubble dynamics was investigated.
For a laser-induced spherical bubble with Rayleigh size of 300 μm in the fully confined spherical geometry with a radius of 3 mm, the bubble size and oscillation period are highly reduced (Fig.2). The oscillation period is more vulnerable to confinement than the bubble size [Fig.3 (a)]. With increasing bubble size, the oscillation period first increases and then decreases, reaching a maximum value of 15.3 μs when the bubble size increases to 154.1 μm (corresponding to a Rayleigh radius of 209.9 μm and a Rayleigh time of 39.1 μs) [Fig.3 (b)]. The maximum period that a bubble reaches in a confined liquid is called the cut-off period. Figure 5 shows the bubble dynamics in a fully confined liquid with different liquid sizes. It shows that the cut-off period is linearly related to the corresponding maximum radius, with a coefficient of 0.1 s/m, which still holds under various degrees of confinement. Moreover, it is found that the cut-off period is reached in the fully confined condition when the Rayleigh radius is 0.06 times the liquid radius. When the cut-off period is reached, the maximum bubble size is 0.05 times the liquid radius. We also demonstrate the effects of the confinement degree on the bubble dynamics and show that the cutoff period rapidly decreases with increasing confinement degree (Fig.6).
In this study, based on the confined Rayleigh?Plesset model, we simulate the laser-induced spherical bubble dynamics in a spherical confined geometry with different liquid sizes and confinements. Owing to the prominent additional pressure increase in the liquid during the bubble oscillations, the bubble dynamics are remarkably compressed with a reduced oscillation period and maximum bubble radius, and the oscillation period is more vulnerable to confinement than the bubble radius. The confinement effect leads to a cut-off period linearly related to the corresponding maximum bubble size. It is strongly affected by the liquid size and degree of confinement. This study provides a better understanding of the principles of cardiovascular laser plaque treatment.