Two-dimensional Rayleigh model of vapor bubble evolution

The understanding of vapor bubble generation in an aqueous tissue near a fiber tip has required advanced two dimensional (2D) hydrodynamic simulations. For 1D spherical bubble expansion a simplified and useful Rayleigh-type model can be applied. For 2D bubble evolution, such a model does not exist. The present work proposes a Rayleigh-type model for 2D bubble expansion that is faster and simpler than the 2D hydrodynamic simulations. The model is based on a flow potential representation of the hydrodynamic motion controlled by a Laplace equation and a moving boundary condition. We show that the 1D Rayleigh equation is a specific case of our model. The Laplace equation is solved for each time step by a finite element solver using a triangulation of the outside bubble region by a fast unstructured mesh generator. Two problems of vapor bubbles generated by short-pulse lasers near a fiber tip are considered: (1) the outside region has no boundaries except the fiber, (2) the fiber and the bubble are confined in a long channel, which simulates a fiber in a vessel wall. Our simulations for problems of type (1) include features of bubble evolution as seen in experiments, including a collapse away from the fiber tip. A different behavior was obtained for problems of type (2) when the channel boundary is close to the fiber. In this case the bubble's expansion and collapse are both extremely slow in the direction normal to this boundary and distortion of the bubble is observed.