Vibration of a bubble close to a curved solid surface

This paper presents a theoretical and numerical investigation of microbubble vibration near curved solid boundaries. Most existing theoretical studies focus on flat boundaries, although curved surfaces are widely encountered in practical cavitation processes. The novelty of this work is the development of a curvature-dependent model based on the fluid velocity potential and the method of images. A small-amplitude vibration equation is derived that includes the effects of boundary curvature and bubble-boundary distance, while the flat-boundary case is recovered as a limiting result. The model also enables a direct comparison between convex and concave boundaries. The results show that concave surfaces produce a stronger boundary effect than convex surfaces and are more favorable for nonspherical deformation and possible microjet formation. Numerical results further demonstrate that increasing the external pressure suppresses sustained oscillations and leads to rapid collapse, while changing the boundary curvature modifies the vibration and deformation of the bubble. These findings provide a theoretical basis for understanding bubble dynamics near curved solid surfaces, with potential applications in cavitation erosion and fluid engineering.