In this paper, the bubble dynamics in a narrow vertical rigid cylinder with a compliant coating filled with water is studied numerically. Considering the surface tension and the coincidence of bubble and cylinder centers, an adopted axisymmetric boundary integral equation approach besides a finite difference method is used for numerical simulation of bubble evolution accompanying with computing the pressure and velocity fields of fluid around it. The compliant boundary is modeled as a membrane with a spring foundation. It is found that the confinement of bubble by the cylinder increases greatly its lifetime and influences its behavior. The first stage of bubble contraction depicts the flattening of its top and bottom parts. A liquid counter-jet is then initiated and develops itself toward the bubble center; the bubble becomes biconcave at the end of the contraction phase. The bubble dynamics is affected by the ratio of cylinder radius to the maximum radius of the bubble. The results also represent the effects of two compliant coating characteristics including its mass per unit area and the spring constant on the bubble behavior. This investigation is motivated by the possibility of utilizing bubbles in the therapeutic cardiovascular applications.
