Mass log-stable distribution of fragments in liquid-liquid jet fragmentation based on a two-step cascade between viscous shear instability and Rayleigh-Taylor instability

This work is devoted to the study of liquid-liquid fragmentation. It contains both an experimental part and a theoretical part. In the experimental part, a low-melting point liquid metal jet is injected into a water pool. High-speed shadowgraph method is used to measure the jet velocity and to observe the dynamics of the fragmentation. Thereafter, the solidified fragments are sieved and weighted allowing to measure their mass distribution according to their size. The mass Probability Density Function (PDF) is then fitted using log-stable laws, generalization of log-normal laws. In the theoretical part, it is shown how it is possible to compute the shift parameter of the stable law considering that the droplets are mainly generated by a boundary layer stripping mechanism. Actually the computation relies on a viscous shear instability mechanism (different from classical Kelvin-Helmholtz instability) sometime called "gradient instability". The width of the distribution (or more precisely its scale parameter) is computed assuming a cascade mechanism between this first wave instability and a secondary Rayleigh-Taylor mechanism applied on the generated wave. The model is then compared to present experimental results and previously published results obtained in the field of nuclear safety studies (Fuel-Coolant Interaction or FCI). Two fitting parameters are then identified. The agreement is good when phase change and solidification effects can be neglected and qualitatively good (i.e. fitting parameters need to be modified) when these effects cannot be neglected.