Rayleigh–Taylor instability of cylindrical water droplet induced by laser-produced cavitation bubble. (3rd June 2021) - Wang, Jingzhu; Li, Hongchen; Guo, Wenlu; Wang, Zhan; Du, Tezhuan; Wang, Yiwei; Abe, Akihisa; Huang, Chenguang
Abstract: Abstract : This study gives insights into the interfacial instability of water droplets through a combination of laboratory experiments, numerical simulations and analytical modelling. An experiment is conducted in a narrow gap between two plates to model the two-dimensional cylindrical geometry, and a pulsed laser beam is focused inside a water droplet to generate a cavitation bubble. Three distinct characteristics of droplet deformation can be observed: (i) splashing; (ii) ventilating; and (iii) a stable state. In addition, an analytical model considering the Rayleigh–Taylor instability and bubble oscillation is developed based on the assumption that fluid is inviscid and incompressible. The analytical model is solved to obtain a phase diagram describing three distinct phenomena. Two dimensionless parameters, $\hat {η }_{ins}$ and $\hat {η }_{sta}$, are used to determine the boundaries between different regimes. The parameter $\hat {η }_{ins}$ is defined by the ratio of the perturbation amplitude to the difference between the droplet and bubble radii, whereas the other parameter $\hat {η }_{sta}$ is defined by the ratio of the perturbation amplitude to the initial droplet radius. Interfacial instability is induced when the perturbed droplet surface penetrates the bubble boundary, namely, $\rvert \hat {η }_{ins} \rvert ≥ 1$ . Splashing and ventilating phenomena occur for $\hat {η }_{ins}≥ 1$ and $\hat {η }_{ins}≤ -1$, respectively. A stable state occurs when droplet fragmentation does not appear despite small-amplitude perturbations for $\hat {η }_{sta}≤ 0.1$ . There is a transition zone between the ventilating and stable state, which is bounded by $\hat {η }_{ins} = -1$ and $\hat {η }_{sta} = 0.1$ . Finally, the phase diagram is verified by the experimental and numerical results.