Figure 1

Photographs of splashing as a function of gas pressure and surface roughness. The left and right columns are 0.2 and 0.5 ms from the time of impact. For each value of surface roughness, the top panel is at a low pressure $P=13\text{kPa}$ and the bottom panel is at atmospheric pressure $P=100\text{kPa}$. (a) Splash on a smooth substrate which is a clean microscope slide. (b) Splash on a substrate with roughness $R_a=5\mu \text{m}$. (c) Splash on a substrate with roughness $R_a=78\mu \text{m}$.Reuse & Permissions

Figure 2

Calibration curve of stain area as a function of droplet volume. Error bars come from the fluctuation of stain areas for the same size droplet. The fitting curve is $y=233x^{0.67}-119$. $y$ is the stain area in units of pixels and $x$ is the volume of the drop in units of nanoliters.Reuse & Permissions

Figure 3

The distribution of ejected drops in a prompt splash on rough substrates. (a) $N\left(r\right)$ versus $r$ for splashes on substrates with three values of roughness: $R_a=16\mu \text{m}$ (◼), $R_a=5\mu \text{m}$ (◯), and $R_a=3\mu \text{m}$ (▴). The exponential fitting functions are —, $\text{exp}\left(-r/0.023\right)$; ---, $\text{exp}\left(-r/0.006\right)$; and $–\cdot –$, $\text{exp}\left(-r/0.004\right)$. (b) The decay constant $r_0$ of the exponential decay in $N\left(r\right)$, as a function of substrate roughness $R_a$. For small values of roughness, the decay constant is approximately linear in the roughness. At large roughness, the decay constant saturates. The sizes of particles on sandpaper are randomly distributed around an average value $R_a$. The fluctuation of particle sizes gives us $R_a$ error bars and the standard deviation from exponential fit gives the $r_0$ error bars. The inset of (b) shows one sheet of paper with ink spots produced by $R_a=25\mu \text{m}$. Most spots are randomly distributed within a narrow band.Reuse & Permissions

Figure 4

Size distribution of different impact velocities. For a fixed roughness $R_a=25\mu \text{m}$, two impact velocities were tested: $V_0=4.3\pm 0.1\text{m}/\text{s}$ (◯) and $V_0=5.2\pm 0.1\text{m}/\text{s}$ (◼). (a) $N\left(r\right)$ in linear-linear scale. It is clear that the higher velocity case produces about 20% more splash. (b) The same data in log-linear format. The two data sets now seem much closer only because of the log-linear way we plot them. We can fit both curves with the same functional form $A\text{exp}\left(-r/0.025\right)$ (the solid line), by only varying the amplitude $A$. This implies that $r_0=0.025\text{mm}$ is independent of impact velocity.Reuse & Permissions

Figure 5

Size distribution of ejected droplets in a corona splash at high pressure. The upper inset shows the corona film before it breaks up. From this picture we can estimate the film thickness to be $20-40\mu \text{m}$ by measuring the thickness of the corona rim. (Although the rim should be thicker than the film, we assume that the film and the rim are approximately the same size.) The lower inset is a reproduction of the sheet of paper with the ink spots showing that the ejected droplets hit the paper at random locations over a large area. The main panel shows the number of droplets of a given size per impact $N\left(r\right)$ versus droplet radius $r$ for a corona splash at two pressures: $P=100\text{kPa}$ (●) and $P=80\text{kPa}$ $(\times )$. The exponential fitting functions are, respectively, —, $\text{exp}\left(-r/0.020\right)$ and $–\cdot –$, $\text{exp}\left(-r/0.014\right)$.Reuse & Permissions

Figure 6

A splash just above the threshold pressure $P_T$. (a) Images of a drop splashing show the ejection of droplets and the undulations in the expanding rim. The times shown are measured with respect to the time of impact. (b) A reproduction of the sheet of paper showing that the droplets hit the paper in a well-defined horizontal line. The main panel of (b) shows the Fourier transform of the lateral positions of the spots in the inset. The peak indicates a well-defined spacing between the ejected droplets at $P_T$. (c) The number of droplets at fixed sizes $N\left(r\right)$ is plotted versus droplet radius $r$ at pressures slightly higher than $P_T$: $P=34\text{kPa}$ (●), $37\text{kPa}$ (◯), and $39\text{kPa}(\times )$. The solid line is a Gaussian fit centered at $r_0=0.11\text{mm}$. The peak in $N\left(r\right)$ shows that the average size of the droplets is approximately the size of the undulations at the rim of the expanding film.Reuse & Permissions