Collapse of a bubble close to a solid boundary

A bubble equation of motion close to the solid plane is obtained by using the perturbation method. This bubble equation can explain the phenomena of the reentrant microjet penetrating the bubble produced by the external disturbances if the distance between the bubble center to the solid boundary is small enough as well as the external pressure is large enough. Furthermore, two critical points are found. One critical point is the distance between the bubble center to the solid boundary. The other is external pressure. The critical boundary at which the reentrant microjet can just be produced is given. The critical boundary depends on both the distance between the bubble center to the solid boundary and the ratio of external pressure to the initial pressure of the liquid.