# Morphological Analysis of a Collapsing Cavitation Bubble near a Solid Wall with Complex Geometry
## 5 Conclusions  
The interaction mechanism between a cavitation bubble and a solid wall with a complex geometry is investigated using the pseudopotential MRT-LBM. In this study, we introduce an arbitrarily complex geometry and propose an effective boundary processing method. A model of gas-liquid-solid three-phase coupling with adjustable solid boundary characteristics is established. The dynamics of the collapsing bubble are investigated using the evolution of the density, pressure, and velocity fields. The Min-MAM is used to quantitatively describe the evolution of the bubble profiles. Several representative moments of bubble collapse can be clearly distinguished from the morphological metric curves of the Minkowski functionals. Furthermore, the effect of different surface conditions of the solid walls on the dynamic characteristics of the collapsing bubble is systematically analyzed. The results indicate that the shift in the bubble profiles is inseparable from the surface geometry of the solid wall. The conclusions of this study are summarized below. (1) The validity and feasibility of the numerical model to simulate the bubble collapse process are verified by comparing the LBM simulation with experimental results. The collapse process of a vapor bubble close to a solid wall with an arbitrarily complex geometry is accurately simulated. This provides theoretical support for investigating the dynamics of collapsing bubbles in fractal cracks. (2) The Min-MAM is adopted to quantitatively describe the evolution of the bubble profiles and acquire effective information from the collapse process. The morphological metric curves of the Minkowski functionals can characterize several typical moments, including the top depression, first collapse, and second collapse of the bubble. (3) The inherent properties of the solid wall, such as its complexity and surface geometry, should be considered when the solid wall is generalized from a plane solid wall to a solid wall with a complex geometry. Specifically, the influence of the solid wall on collaps  
Figure 15: Morphological analysis of the collapsing bubble under different offset parameters (**(I)**: \(D=1.03325\) and **(II)**: \(D=1.03476\); **(a)** fractional area \(F\), **(b)** boundary length \(U\), and **(c)** Euler characteristic \(X\)). ing bubble profiles can be analyzed by tuning different parameters, e.g., the complexity of solid walls, geometric features of solid walls, and the position offset parameter. The results demonstrate that the bubble collapse becomes slower as the complexity of the solid wall increases. The geometric features of the solid wall can influence its retarding effect on the collapsing bubble, making the bubble collapse process more varied. The effect of the geometric features of the solid wall on the collapsing bubble is stronger than that of the surface complexity. In addition, the length of the collapse time is affected by the position offset parameter. Bubble collapse becomes faster as the offset parameter increases. However, the effect of the position offset parameter on the collapsing bubble is also associated with the geometric features of the solid wall, which influences the length of the collapse time and the occurrence of the second collapse. Last but not least, based on the advantages of the pseudopotential MRT-LBM, the model in this paper can simulate the bubble dynamics near a solid wall with arbitrarily complex geometry. Several typical solid walls are introduced in this study to investigate the effect of fractal walls on the bubble collapse process, and general conclusions can be drawn. In the future, we will further study the temporal evolution of the collapsing bubble profiles near more solid walls with complex geometry or in a fractal crack. Moreover, the effect of the viscosity and surface tension on the bubble collapse model will be discussed in the subsequent study.