Figure 1

Early stages in the evolution of a droplet impacting a solid surface (corresponding to dimensionless parameters $ϵ=5\times {10}^{-3}$, $\gamma =1.4$, see text for definitions). The top [bottom] panel shows a snapshot of $h(x,t)$ [$p(x,t)$] as the drop approaches contact. Note the pressure maximum causes a dimple in the interface, and later splits into two maxima.Reuse & Permissions

Figure 2

Dimple height $H^{*}$ as a function of impact parameters. Left panel: $H^{*}$ versus $ϵ$ for a range of $\mathrm{St}$. Open symbols denote $\gamma =1$, while the corresponding filled symbols denote $\gamma =1.4$. The data collapse onto a single curve, with asymptotes agreeing with the predictions. Regimes 1 and 2 correspond to the experiments of Xu, Zhang, and Nagel. Right panel: Contours of constant $H^{*}$ in nm for ethanol drops of size corresponding to the experiments by Xu, Zhang, and Nagel using $\gamma =1.4$ and a range of impact velocities $V$ and gas pressures $P_0$. Filled squares denote regime 1 of threshold splashing curve observed by Xu, Zhang, and Nagel, while open squares denote their regime 2.Reuse & Permissions

Figure 3

Maximum pressure $p_{\max }$ (top) and curvature length scale $l$ (bottom) as a function of $h_{\min }$ shown in solid lines. Labels denote values of $ϵ$. The ambient pressure is subtracted from $p_{\max }$ for $ϵ=100$. The dashed lines denote various power-law estimates (see text). The value $ϵ=5.1\times {10}^{-2}$ corresponds to Fig. 1 of Xu, Zhang, and Nagel [6]. The inset on the bottom shows $h_{\min }$ against $t_0-t$, where $t_0$ is the time to contact.Reuse & Permissions

Figure 4

(Top) Evolution of a liquid droplet impacting a solid surface, with $\gamma =1.4$ and $ϵ=5\times {10}^{-3}$, with surface tension $\delta =20$. The interface no longer contacts the solid surface, and capillary waves are emitted. (Bottom) Gas pressure (circles) and capillary pressure (squares) as a function of $h_{\min }$. $h_{\min }$ stops decreasing when gas pressure balances surface tension.Reuse & Permissions