Bubble Dynamics in a Compressible Liquid
Qian Xi Wang (University of Birmingham)
Thursday 19th May, 2011 14:00-15:00 Maths 325
Bubble dynamics has been studied extensively for about a century. It has traditionally been associated with cavitation on ship propellers, fluid machinery and piping systems, as well as underwater explosions. Recent research on micro-cavitation bubbles subjected to ultrasound plays a key role in numerous medical procedures, including sonoporation, ultrasound lithotripsy. As illustrations, injected bubbles in blood are used to carry reagents to the site of tumor tissue or a blood clot. Once they reach their target, the bubbles are acoustically excited to a violent collapse, releasing reagents transported within the bubble that can combat the tumor or clot. The theoretical and computational studies on bubble dynamics have been largely based on incompressible fluid model, which yields undamped oscillations of constant periods. In practice, the bubble undergoes oscillations with the amplitude and period reducing significantly with time. The compressible effects of the liquid are significant and not negligible. In this work, a new BIM model is developed for non-spherical bubble dynamics in a compressible liquid using the method of matched asymptotic expansions. The numerical model agrees well with the general Keller-Herring equation (GKHE) (Keller & Kolodner 1956) for spherical bubbles and the experiment (Hung & Hwangfu 2010). Our theory predicts damped oscillations of diminishing period. References Hung, C. F. & Hwangfu, J. J. 2010 To be published in J. Fluid Mech. Keller, J. B. & Kolodner, I. I. 1956 J. Applied Phys. 27(10), 1152-1161. Wang, Q X 2004 Phys. Fluids 16 (5), 1610-1619. Wang, Q. X. & Blake, J. R. 2010 To be published in J. Fluid Mech.