In this paper, drop impact onto a sphere is numerically investigated at moderate Reynolds and Weber numbers. It is naturally expected that the aspect ratio of the sphere to the drop, $\unicode[STIX]{x1D706}_{r}$, would make a big difference to drop spreading and retraction on the sphere, compared with drop impact onto a flat substrate. To quantitatively assess the effect of $\unicode[STIX]{x1D706}_{r}$, a diffuse-interface immersed-boundary method is adopted after being validated against experiments. With the help of numerical simulations, we identify the key regimes in the spreading and retraction, analyse the results by scaling laws, and quantitatively evaluate the effect of $\unicode[STIX]{x1D706}_{r}$ on the impact dynamics. We find that the thickness of the liquid film spreading on the sphere can be well approximated by $h_{L,\infty }(1+3/4\unicode[STIX]{x1D706}_{r}^{-3/2})$, where $h_{L,\infty }$ represents the film thickness of drop impact on a flat substrate. At the early stage of spreading, the temporal variation of the wetted area is independent of $\unicode[STIX]{x1D706}_{r}$ when the time is rescaled by the thickness of the liquid film. Drops are observed to retract on the sphere at a roughly constant speed, and the predictions of theoretical analysis are in good agreement with numerical results.
External sinusoidal actuation is employed in the axisymmetric flow focusing (AFF) for generating uniform droplets in the jetting mode. The perturbations propagating along the meniscus surface can modulate the rupture of the liquid jet. Experiments indicate that the jet breakup length and the resultant droplet size can be precisely controlled in the synchronized regime, which are further confirmed by the scaling law. The finding of this study can help for better understanding of the underlying physics of actuation-aided AFF, and this active droplet generation method with fine robustness, high productivity, and nice process control would be advantageous for various potential applications.
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