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.