Figure 1

Still images right after impact of ${\mathrm{ZrO}}_2$ particles in water onto a smooth glass plate, for different droplet radii $r_d$ (see text above the images) and particle radii: (a)–(i) $r_p=362\mu \mathrm{m}$, (j)–(l) $r_p=138\mu \mathrm{m}$, (m)–(s) $r_p=78\mu \mathrm{m}$. The time between impact and ejection of the first particles ranges from 0.6 to 3.5 ms. Images (a)–(o) are organized in vertical columns, with drop impact speed, and therefore, $K$ increasing from top to bottom to bracket the onset of splashing, defined as the ejection of individual particles. For the $K$ values listed in the top, middle, or bottom rows we never, sometimes, or always observed particle ejection. $K={\mathrm{We}}_d^{1/2}{\mathrm{Re}}_d^{1/4}$, where we used the effective viscosity ${\mu }_e$ given by Krieger and Dougherty [26] in ${\mathrm{Re}}_d$. The blurred background in (a) and (b) is the out-of-focus image of the syringe. Note that (o) has been thresholded and dilated in order to visualize the ejected particles that would otherwise be invisible due to their small size. (p),(q) side and bottom view of a droplet that does not splash (${\mathrm{We}}_p=12$), (r),(s) side and bottom view of a splashing droplet (${\mathrm{We}}_p=26$). The scale bar in the images is 5 mm, images (a)–(o) all have the same scale. See also Ref. [36].Reuse & Permissions

Figure 2

Sketch of the ejection mechanism upon impact.Reuse & Permissions

Figure 3

Splash onset velocity $U^{*}$ as a function of the product of particle radius $r_p$ and particle density ${\rho }_p$. The cluster of seven data points at the far right corresponds to three different drop sizes (see also Figs. 1, 4) and substrates with four different roughnesses (see main text), all other data are for $r_d=2.3\mathrm{mm}$ on a smooth substrate. The solid curve gives the onset of the Weber number $\mathrm{We}_p^{*}$ calculated from a best fit to all experimental data. The dashed lines represent the upper and lower bounds for $\mathrm{We}_p^{*}$, corresponding to one standard deviation. Inset: histogram of the velocity $u_p$ of ejected particles at ${\mathrm{We}}_p=20$, for $r_p=78\mu \mathrm{m}$.Reuse & Permissions

Figure 4

Comparison between unimodal and bimodal ${\mathrm{ZrO}}_2$ suspensions. All are data for droplets made with nozzle radius $r_d=2.3\mathrm{mm}$, except for data shown in open symbols with different gray scales (magenta and cyan online) in (a) for which $r_d=1.0\mathrm{mm}$ and $r_d=4.3\mathrm{mm}$, respectively. (a) Splash onset for unimodal suspensions of large $r_p=362\mu \mathrm{m}$, open symbols) and small ($r_p=78\mu \mathrm{m}$, red dots) particles. (b) Splash onset for bimodal suspensions with volume ratio $\sim 1:1$ of small to large particles. Two distinct onsets exist: one where only small particles escape, and one where both small and large particles escape. Data symbols and colors are as in (a). All insets: examples of the unimodal and bimodal suspension droplets corresponding to the data presented in this figure, imaged from below just before impact. (c) Histogram of relative momentum changes for large particles in unimodal (gray, cyan online) and bimodal (black) suspensions at $U=2\mathrm{m}/\mathrm{s}$. (d) Same as (c), but for small particles.Reuse & Permissions