Computational modelling of weak shockwave-gas bubble interactions in water

The interaction of a shock wave with a gas bubble in a liquid medium is central to engineering applications such as shockwave lithotripsy and microbubble-mediated drug delivery. Numerical simulations and experimental observations have found that the interaction of a shock wave with a bubble leads to the formation of a re-entrant jet for amplitudes above approximately 10 MPa. However, the interaction with waves of lower amplitude remains less well-studied. In this study, the response of a single bubble to low-amplitude, infinite-width shock waves is investigated through numerical simulations. Three distinct regimes are identified: (i) The formation of a re-entrant jet before the first bubble collapse, (ii) The formation of a re-entrant jet whilst the bubble rebounds, (iii) No formation of a re-entrant jet whilst the bubble undergoes linear oscillations instead. For each regime, we characterise the collapse through the jet impact time, interfacial velocities, associated pressure and velocity fields along with visualisations of the re-entrant jet. Additionally, we explore the influence of surface tension and viscosity on the formation of the re-entrant jet for bubbles of different diameters. Our simulations suggest that single bubbles impacted by shock waves of infinite width form a re-entrant jet at much lower amplitudes than previously reported.