Shock Wave Formation in the Collapse of a Vapor Nanobubble

Abstract

In this Letter a diffuse-interface model featuring phase change, transition to supercritical conditions, thermal conduction, compressibility effects and shock wave propagation is exploited to deal with the dynamics of a cavitation bubble. At variance with previous descriptions, the model is uniformly valid for all phases (liquid, vapor and supercritical) and phase transitions involved, allowing to describe the non-equilibrium processes ongoing during the collapse. As consequence of this unitary description, rather unexpectedly for pure vapor bubbles, the numerical experiments show that the collapse is accompanied by the emission of a strong shock wave in the liquid and by the oscillation of the bubble that periodically disappears and reappears, due to transition to super/sub critical conditions. The mechanism of shock wave formation is strongly related to the transition of the vapor to supercritical state, with a progressive steepening of the compression wave to form the shock which is eventually reflected as an outward propagating wave in the liquid.Vapor bubble collapse is a fascinating classical problem [1] involving vapor-liquid phase transition and extreme pressures and temperatures [2,3]. Typical experiments concern ultra-fast imaging and the analysis of light and sound emitted after the collapse [4][5][6], see also the review [7]. Both free cavitation bubbles and nano bubbles at solid walls are increasingly investigated [8][9][10]. In ordinary conditions, gas bubble nucleation is associated with the metastability of the mixture of liquid and dissolved gas which, once the free energy barrier between the two states is overcome and the critical nucleus is formed, evolves toward a finite size bubble. The same mechanism is at work in forming pure vapor bubbles when the (ultra pure) liquid is kept in metastable conditions [11], i.e. its pressure is below the equilibrium vapor pressure at the given temperature. In these conditions, away from solid walls (see e.g. [12] for the role of asperities on solid surfaces as a catalyst of bubble nucleation), local density fluctuations can generate the critical vapor nucleus from which the eventual bubble is formed.Intermingled phenomenologies, [13,14], such as interface dynamics [15,16], thermodynamics of phase change [17], and dissolved gas diffusion [18], are a challenge to theoretical modeling of cavitation. The available descriptions combine two distinct adjoining regions, liquid and vapor phase, respectively, with vapor pressure taken to be the saturation pressure [19] and phase transition accounted for through suitable kinetic equations and latent heat release [18].Contrary to available models, the diffuse interface approach discussed in the present Letter encompasses all phases (liquid, vapor and supercritical) and phase transitions involved, embedding capillary forces, compressibility effects and shock wave propagation. The approach enables an unprecedented analysis of collapse, where the bubble interface speed may exceed the speed of sound. This leads to the form...

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