Growth and instability of the liquid rim in the crown splash regime

Abstract

AbstractWe study the formation, growth and disintegration of jets following the impact of a drop on a thin film of the same liquid for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{We}<1000$ and $\mathit{Re}<2000$ using a combination of numerical simulations and linear stability theory (Agbaglah, Josserand & Zaleski, Phys. Fluids, vol. 25, 2013, 022103). Our simulations faithfully capture this phenomena and are in good agreement with experimental profiles obtained from high-speed X-ray imaging. We obtain scaling relations from our simulations and use these as inputs to our stability analysis. The resulting predictions for the most unstable wavelength are in excellent agreement with experimental data. Our calculations show that the dominant destabilizing mechanism is a competition between capillarity and inertia but that deceleration of the rim provides an additional boost to growth. We also predict over the entire parameter range of our study the number and timescale for formation of secondary droplets formed during a splash, based on the assumption that the most unstable mode sets the droplet number.