Two-dimensional Rayleigh model for bubble evolution in soft tissue

The understanding of vapor bubble generation in a soft tissue near a fiber-optic tip has in the past required two-dimensional (2D) hydrodynamic simulations. For 1D spherical bubble expansions a simplified and useful Rayleigh-type model can be applied. For 2D bubble evolution, such a model has not been developed. In this work we develop a Rayleigh-type model for 2D bubble expansion that is much faster and simpler than 2D hydrodynamic simulations and can be applied toward the design and understanding of fiber-based medical therapies. The model is based on a flow potential representation of the hydrodynamic motion and is described by a Laplace equation with a moving boundary condition at the bubble surface. In order for the Rayleigh-type 2D model to approximate bubble evolution in soft tissue, we include viscosity and surface tension in the fluid description. We show that the 1D Rayleigh equation is a special case of our model. The Laplace equation is solved for each time step by a finite-element solver using a fast triangular unstructured mesh generator. Our simulations include features of bubble evolution as seen in experiments and are in good agreement with 2D hydrodynamic simulations.