![]() modified the BIM model by removing empirically a part of the bubble potential energy at the end of the first cycle of oscillation. The BIM model is suitable for an incompressible flow and does not account for the significant energy loss due to emission of shock waves associated with bubble dynamics. It has been applied for an axisymmetric configuration for a bubble near a rigid wall, a free surface or compliant surface and for three-dimensional configurations. The boundary integral method (BIM) is grid-free in the flow domain and computationally efficient, and is thus widely used in the field of bubble dynamics. It is, therefore, very important to study bubble dynamics in near contact with a rigid boundary. We believe that these phenomena have clear potential to damage the boundary. ![]() This leads to the direct impact of a liquid jet on the boundary once it penetrates through the bubble, the direct contact of the bubble at minimum volume at high pressure and high temperature with the boundary, and the direct impingement of shock waves on the boundary once emitted. Ī bubble initiated near a rigid boundary can be almost in contact with the boundary because of its expansion and migration to the boundary as a result of the attraction by the second Bjerknes force. These mechanisms are also associated with sonochemistry and ultrasound cavitation cleaning-one of the most effective cleaning processes for electrical and medical micro-devices. In these applications, cavitation microbubbles absorb and concentrate a significant amount of energy from ultrasound, leading to shape oscillation, violent collapsing, shock waves and bubble jetting. Recent research on ultrasound cavitation bubbles is associated with several important medical applications, including extracorporeal shock wave lithotripsy, tissue ablation (histotripsy), and oncology and cardiology. Similarly, the damage mechanism of an underwater explosion is associated with a shock wave emitted at the inception of an underwater explosion bubble and bubble jetting formed at the end of collapse. The cavitation damage mechanism is believed to be associated with shock waves and bubble jetting, both of which are formed at the end of collapse. The study of bubble dynamics in the neighbourhood of a rigid boundary is associated with cavitation erosion to propellers, turbines and pumps. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s/ R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. Our computations correlate well with experiments for both the first and second cycles of oscillation. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. The wall effects are modelled using the imaging method. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. ![]()
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