Numerical analysis of a gas bubble near a rigid boundary in an oscillatory pressure field

Abstract

The behavior of a gas bubble near a rigid boundary in an oscillatory pressure field is numerically investigated by means of two kinds of methods. The boundary integral method is utilized to simulate the bubble profiles at various times, and the image theory is also applied for solving the differential equations describing the nonlinear oscillations and migrations of a spherical gas bubble. Both calculations are performed, assuming that the liquid around a bubble is inviscid, incompressible, and irrotational and that the gas inside the bubble follows a polytropic gas law. The influence of the boundary proximity on the bubble motion is characterized by the bubble migration and the deformation of the bubble shape, especially by the liquid microjet formation. It is found that the period and the amplitude of the bubble oscillation are related not only to the nature of the time-dependent pressure in the liquid but also to the bubble location from a rigid wall. Furthermore, the influence of the boundary proximity on the frequency response curve associated with the bubble oscillation is examined on the supposition that the surrounding pressure oscillates with small amplitude and a rigid boundary is relatively far from a bubble.