In this paper, the ring bubble contraction inside a narrow vertical rigid cylinder
with a compliant coating filled with water is studied numerically. To simulate
ring bubble dynamics numerically, in addition to computing the pressure and
velocity fields of the surrounding fluid, an axisymmetric boundary integral
equation approach is adopted alongside a finite difference method. The
compliant boundary is modeled as a membrane with a spring foundation.
During the ring bubble contraction and under the attraction of the cylinder wall
due to the Bjerknes force, a horizontal ring jet is initiated and develops
towards the cylinder wall. The numerical results represent the effects of the
cylinder radius and two compliant coating characteristics, including its mass
per unit area and the spring constant, on the ring bubble behavior. This
investigation is motivated by the possibility of utilizing the ring jet in therapeutic cardiovascular applications.