Scaling laws for jets of single cavitation bubbles

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter zeta >= 0, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets (zeta < 10(-3)) hardly pierce the bubble, but remain within it throughout the collapse and rebound. Intermediate jets (10(-3) < zeta < 0.1) pierce the opposite bubble wall close to the last collapse phase and clearly emerge during the rebound. Strong jets (zeta > 0.1) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of zeta, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets (zeta < 0.1) depend only on zeta, not on the jet driver (i.e. gravity or boundaries). In the same regime, the jet parameters are found to be well approximated by power laws of zeta, which we explain through analytical arguments.

Shock waves from nonspherical cavitation bubbles

Nicolas Dorsaz, Mohamed Farhat, Philipp Kobel, Danail Obreschkow, Outi Supponen, Marc Tinguely

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical to very nonspherical by decreasing their distance to a free or rigid surface or by modulating the gravity-induced pressure gradient aboard parabolic flights. The nonspherical collapse produces multiple shocks that are clearly associated with different processes, such as the jet impact and the individual collapses of the distinct bubble segments. For bubbles collapsing near a free surface, the energy and timing of each shock are measured separately as a function of the anisotropy parameter zeta, which represents the dimensionless equivalent of the Kelvin impulse. For a given source of bubble deformation (free surface, rigid surface, or gravity), the normalized shock energy depends only on zeta, irrespective of the bubble radius R-0 and driving pressure Delta p. Based on this finding, we develop a predictive framework for the peak pressure and energy of shock waves from nonspherical bubble collapses. Combining statistical analysis of the experimental data with theoretical derivations, we find that the shock peak pressures can be estimated as jet impact-induced hammer pressures, expressed as p(h) = 0.45(rho c(2) Delta p)(1/2) zeta(-1) at zeta > 10(-3). The same approach is found to explain the shock energy decreasing as a function of zeta(-2/3).

Amer Physical Soc2017

Collapse phenomena of deformed cavitation bubbles

Outi Supponen

Cavitation bubbles are a topic of long-standing interest owing to the powerful phenomena associated with their collapse. Their unique ability to focus energy typically causes damage in hydraulic machinery (turbines, pumps, propellers, ...) but, if managed correctly, can also be beneficial in numerous applications such as cleaning practices and biomedical sciences. Here the complex problem of cavitation, often multi-scale both in time and space, is reduced to a simplified case study of the collapse of a single, initially spherical bubble. We study the bubble's energy distribution into its distinct collapse phenomena, namely the micro-jets, shock waves and luminescence, and aim to quantify and predict how such a distribution is affected by the bubble's deformation. Combining experiments with statistical analysis, numerical simulations and theoretical models, we seek to quantify and predict the key properties characterising each of the collapse phenomena. The deformation of bubbles is characterised by the liquid micro-jets formed during their non-spherical collapse. A unified framework is proposed to describe the dynamics of such jets, driven by different external sources, through an anisotropy parameter

\zeta

, which represents a dimensionless quantity of the liquid momentum at the bubble collapse (Kelvin impulse). The bubbles are carefully deformed in variable gravity aboard European Space Agency parabolic flights or by introducing surfaces nearby. Through high-speed visualisation, we measure key quantities associated with the micro-jet dynamics (e.g. jet speed, impact timing), which, upon normalisation, reduce to straightforward functions of

\zeta

. This is verified by numerical simulations based on potential flow theory. Below a certain threshold, all of these functions can be approximated by useful power laws of

\zeta

that are independent of the micro-jet driver. For bubbles collapsing near a free surface, we identify and measure the shock waves generated through distinct mechanisms, such as the jet impact onto the opposite bubble wall and the individual collapses of the remaining bubble segments. The energy carried by each of these shocks is found to vary with

\zeta

. We find that for bubbles that produce jets, the shock wave peak pressure may be approximated by the jet-induced water hammer pressure as a function of

\zeta

. Following such an approximation, we also develop a semi-empirical model to explain the shock energy variation with

\zeta

. Finally, an innovative luminescence detection system is built to overcome the challenge of measuring the spectra (300-900nm) of the weak, small, rapid and migrating flash light from individual bubble collapses. We find an approximately exponential quenching of the luminescence energy as a function of

\zeta

. Surprisingly, the blackbody temperature of luminescence does not vary with

\zeta

. Multiple peaks are measured within a time frame of approximately 200ns, implying non-uniform gas compression during the collapse. Overall, these results help in predicting bubble collapse characteristics in known pressure fields and can be useful for numerical benchmarking.

EPFL2017