Double Contact During Drop Impact on a Solid Under Reduced Air Pressure

Drops impacting on solid surfaces entrap small bubbles under their centers, owing to the lubrication pressure which builds up in the thin intervening air layer. We use ultrahigh-speed interference imaging, at 5 Mfps, to investigate how this air layer changes when the ambient air pressure is reduced below atmospheric. Both the radius and the thickness of the air disc become smaller with reduced air pressure. Furthermore, we find the radial extent of the air disc bifurcates, when the compressibility parameter exceeds $\sim 25$. This bifurcation is also imprinted onto some of the impacts, as a double contact. In addition to the central air disc inside the first ring contact, this is immediately followed by a second ring contact, which entraps an outer toroidal strip of air, which contracts into a ring of bubbles. We find this occurs in a regime where Navier slip, due to rarefied gas effects, enhances the rate gas can escape from the path of the droplet.

Figure 1

(a) Microbubble pattern under the center of a drop impacting a freshly cleaved mica surface at reduced air pressure ($P=6.2\mathrm{kPa}$), $V=4.94\mathrm{m}/\mathrm{s}$, $R_b=3.52\mathrm{mm}$, $\text{St}=1.06\times {10}^{-6}$, and ${\epsilon }^{-1}=386$. Scale bar is $100\mu \mathrm{m}$. (b) Sketch of the experimental setup. Drops were formed at an adjustable height nozzle fed by a syringe pump and pinched off by gravity, inside a custom-made acrylic vacuum chamber. A drop collector caught drops during depressurization and was rotated out of the drop path to take measurements. The Kirana camera captured interference fringes caused by optical path length differences from light transmission and reflection between the drop interface and glass or mica surface.

Figure 2

Reduction in the size of the air disc as the ambient pressure is lowered, while keeping the water-drop impact velocity constant, $V=2.3\mathrm{m}/\mathrm{s}$. From left to right, $P=19.7$, 9.2, and 2.8 kPa, $R_b=4.10$, 3.57, and 3.80 mm, $\text{St}=1.99\times {10}^{-6}$, $2.28\times {10}^{-6}$, and $2.14\times {10}^{-6}$, and ${\epsilon }^{-1}=21$, 43, and 144. The frames are shown, from the separate video clips, at $t=0.6$, 0.8, and $1.4\mu \mathrm{s}$ after first contact. The upper arrows mark the contact line. The lower arrow in the last panel points at a faint ring of microbubbles. These impacts are onto molecularly smooth freshly cleaved mica surfaces. The scale bar is $100\mu \mathrm{m}$ long.

Figure 3

Double contact, for a water drop impacting on a freshly cleaved mica sheet, at $P=4.3\mathrm{kPa}$, $V=2.27\mathrm{m}/\mathrm{s}$, $R_b=3.66\mathrm{mm}$, ${\epsilon }^{-1}=93$, and $\text{St}=2.22\times {10}^{-6}$. Frames are shown at times relative to the first contact, $t\simeq 0.1,0.9,1.3,2.5$, and $18\mu \mathrm{s}$. The scale bar is $100\mu \mathrm{m}$ long.

Figure 4

(a) Extended band of bubbles outside the first contact, for impact on Fisher glass, rms surface roughness $R_a=1.2\mathrm{nm}$ [29]. Shown at $t=1.2\mu \mathrm{s}$, $V=2.3\mathrm{m}/\mathrm{s}$, $P=10.2\mathrm{kPa}$, $\text{St}=2.02\times {10}^{-6}$, and ${\epsilon }^{-1}=40$. (b) Band of microbubbles for impact on Corning glass, with $R_a=7.3\mathrm{nm}$ [29], shown at $t=2.8\mu \mathrm{s}$. $V=1.5\mathrm{m}/\mathrm{s}$, $P=3.5\mathrm{kPa}$, $\text{St}=2.74\times {10}^{-6}$, and ${\epsilon }^{-1}=43$. Scale bars are $100\mu \mathrm{m}$ long.

Figure 5

The radial extent of the air disc vs the compressibility factor. The steeper curve has a slope of $-1/2$ and the shallower curve has a slope of $-1/6$. For the cases where double contact or bands of microbubbles were observed, the filled markers indicate the radial extent of the second contact or the outer edge of the band of microbubbles. The inset shows the pressure band (shaded area) where double contacts were observed, for water drops of $R_b\sim 3\mathrm{mm}$.

Figure 6

Regime map showing the important dynamics for each region for a typical water drop radius (4 mm) used in our experiments. Experimental data has been overlaid with the markers indicating which type of contact was observed. Note that all of the observed double contacts and the majority of bands of microbubbles occur within the rarefied gas regime. The transition to the compressible regime occurs for ${\epsilon }^{-1}\gtrsim 1$ (black line), and the transition to the rarefied gas regime occurs for $\text{Kn}\gtrsim 1$ (blue line). Surface tension is only significant for $V\lesssim ({\mu }_g{\sigma }^3/{\rho }_l^4{R}_b^4{)}^{1/7}$ (red line) [20]. Data from Xu et al. [3] are also included for comparison.