Boundary integral equations as applied to an oscillating bubble near a fluid-fluid interface

Abstract

A new method is presented to describe the behaviour of an oscillating bubble near a fluid-fluid interface. Such a situation can be found for example in underwater explosions (near muddy bottoms) or in bubbles generated near two (biological) fluids separated by a membrane. The Laplace equation is assumed to be valid in both fluids. The fluids can have different density ratios. A relationship between the two velocity potentials just above and below the fluid-fluid interface can be used to update the co-ordinates of the new interface at the next time step. The boundary integral method is then used for both fluids. With the resulting equations the normal velocities on the interface and the bubble are obtained. Depending on initial distances of the bubble from the fluid-fluid interface and density ratios, the bubbles can develop jets towards or away from this interface. Gravity can be important for bubbles with larger dimensions.

Dynamic behaviour of a bubble near an elastic infinite interface

“…Buoyancy effects will not have enough time to respond compared to the oscillation time of the bubble, and thus the effect of gravity is negligible. This is verified by calculating the buoyancy parameter given in Klaseboer and Khoo (2004a). On the other hand, the bubbles are sufficiently large for surface tension effects to be negligible as well.…”

Cavitation and bubble dynamics: the Kelvin impulse and its applications

“…If the wave is strong enough, a high-speed liquid jet forms towards the end of collapse. Axisymmetric jetting for acoustic bubbles in an infinite liquid was studied by Calvisi et al [29], Wang & Blake [30,31], and near a boundary subjected to ultrasound propagating in the direction perpendicular to the boundary by Klaseboer & Khoo [32,33], Fong et al [34,35], Calvisi et al [29,36] and Curtiss et al [17]. Wang & Manmi [37] implemented the three-dimensional boundary integral method (BIM) model for microbubble dynamics subjected to ultrasound propagated parallel to the boundary (figure 11).…”

Experimental study on the dynamics of an oscillating bubble in a vertical rigid tube

“…In the experiments, for the same maximum radius of the bubble with R max % 2.6 mm (dashed line), the bubble lifetime in the tube (bubble is at the center of the tube and k = 1.53) is 4.68 ms which is about 7 times more than the one in the free field (0.67 ms). Klaseboer and Khoo [17] showed numerically that near a rigid boundary the bubble lifetime increases. In this work, the bubble is entirely confined by the tube radially and thus the all surrounding presence of the cylindrical wall could have greatly increased the bubble lifetime and the buoyancy plays an additional role.…”

“…While the dynamic evolution of a bubble in an infinite fluid domain in the vicinity of rigid, free, and flexible surfaces has been widely studied numerically and experimentally [17,31,32,16,11,12], the dynamic behavior of a bubble in the bounded fluid domain, for example, a tube is comparatively less investigated in the literature [20,21,23]. The dynamics of a laser-generated vapor bubble inside microtubes was studied both experimentally using a high-speed image recording technique, and theoretically via comparison of two theoretical models (one pure inertia-driven model neglecting the thermal effects based on a discontinuous time dependence of vapor pressure inside the bubble and another based on heat transfer in addition to inertia and viscous friction) by Sun et al [29].…”