Drop Splashing on a Dry Smooth Surface

The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high-speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.

Figure 1

Photographs of a liquid drop hitting a smooth dry substrate. A $3.4\pm 0.1\mathrm{mm}$ diameter alcohol drop hits a smooth glass substrate at impact velocity $V_0=3.74\pm 0.02\mathrm{m}/\mathrm{s}$ in the presence of different background pressures of air. Each row shows the drop at 4 times. The first frame shows the drop just as it is about to hit the substrate. The next three frames in each row show the evolution of the drop at 0.276, at 0.552, and at 2.484 ms after impact. In the top row, with the air at 100 kPa (atmospheric pressure), the drop splashes. In the second row, with the air just slightly above the threshold pressure, $P_T=38.4\mathrm{kPa}$, the drop emits only a few droplets. In the third row, at a pressure of 30.0 kPa, no droplets are emitted and no splashing occurs. However, there is an undulation in the thickness of the rim. In the fourth row, taken at 17.2 kPa, there is no splashing and no apparent undulations in the rim of the drop.

Figure 2

Threshold pressure versus impact velocity. (a) $P_T$ is plotted versus $V_0$ in a background atmosphere of air. The data are nonmonotonic in the region $V_0<V^{*}$. The lower end of the error bars gives the pressure where droplets just begin to be discharged disconnectedly from the rim of the expanding liquid layer; the upper end of the error bars gives the pressure where fully developed splashes emanate uniformly along the entire rim. The midpoint is defined as the threshold pressure. (b) The inset shows $P_T$ versus $V_0$ for four gases: He (○), air (●), Kr (×), and ${\mathrm{SF}}_6$ (▲). The main panel shows the scaled threshold pressure, $P_T(M_G/M_{\mathrm{air}}{)}^{0.5}$, versus the impact velocity, $V_0$, in the region $V_0>V^{*}$, for the four gases shown in the inset.

Figure 3

Effect of liquid viscosity. The inset shows $P_T$ versus $V_0$ for three liquids: methanol (▽), ethanol (●), and 2-propanol (+), in a background atmosphere of air. The main panel shows the scaled threshold pressure, $P_T({\nu }_L/{\nu }_{\mathrm{eth}}{)}^{0.5}$, versus the impact velocity, $V_0$, in the region $V_0>V^{*}$, for the three liquids shown in the inset.

Figure 4

Ratio at threshold of ${\Sigma }_G$, the destabilizing stress due to the gas, to ${\Sigma }_L$, the stabilizing stress due to surface tension. ${\Sigma }_G/{\Sigma }_L$ is plotted versus $V_0$, in the region $V_0>V^{*}$, for all the liquids and gases studied.