An oscillating bubble near an elastic material

A method is presented to describe the behavior of an oscillating bubble in a fluid near a second elastic (biological) fluid. The elasticity of the second fluid is modeled through a pressure term at the interface between the two fluids. The Laplace equation is assumed to be valid in each of the fluids, and a difference in the respective densities is allowed. A relationship between the two velocity potentials just above and below the fluid-fluid interface can be found. The boundary integral method is then used to solve for the unknown normal velocities at both the bubble interface and fluid-fluid interface. These said normal velocities are subsequently utilized to update the position of the interface(s) for the next time step. For bubbles oscillating near a second nonelastic fluid, the bubbles can develop a jet towards or away from the fluid-fluid interface (depending on the distance of the bubble from the fluid-fluid interface and the density ratios of the two fluids). This behavior can be greatly modified when the second fluid possesses some elastic properties. The elasticity causes a small perturbation to travel along the surface of the bubble. A complex interaction between this growing perturbation and the bubble in its collapse phase can lead to the bubble assuming a “mushroom” shape and/or even breakup into two smaller bubbles. These phenomena have not been observed when the elasticity is absent in the second fluid. Excellent agreement with experimental data was obtained for a wide range of parameters.