Numerical study on ring bubble dynamics in a narrow cylinder with a compliant coating

Abstract

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.