How Does an Air Film Evolve into a Bubble During Drop Impact?

When a liquid drop impacts a solid surface, air is generally entrapped underneath. Using ultrafast x-ray phase-contrast imaging, we directly visualized the profile of an entrapped air film and its evolution into a bubble during drop impact. We identified a complicated evolution process that consists of three stages: inertial retraction of the air film, contraction of the top air surface into a bubble, and pinch-off of a daughter droplet inside the bubble. Energy transfer during retraction drives the contraction and pinch-off of a daughter droplet. The wettability of the solid surface affects the detachment of the bubble, suggesting a method for bubble elimination in many drop-impact applications.

Figure 1

Complicated evolution of an air film during drop impact. (a) Schematic description of air film evolution; namely, when an air film is entrapped during drop impact on a solid surface, it should evolve into a bubble to minimize its surface energy. (b) Schematic of ultrafast x-ray phase-contrast imaging, which enables the tracking of dynamic changes of air-liquid interfaces in real time. (c) Representative, sequential x-ray images depicting air film evolution during the impact of a water drop with a diameter of 2.6 mm on an Si wafer from a height of 80 mm. Here the time at the impact moment was set to $t=0$ (see movie 1 of Supplemental material [25]).

Figure 2

Schematic of the complicated air film evolution process during drop impact: inertial retraction of an air film, contraction of the top air surface into a toroid bubble, and pinch-off of a daughter droplet in the bubble. The solid-line arrows denote the propagation of capillary waves, and the dashed-line arrow indicates the contact between the crest and the substrate.

Figure 3

Detailed dynamics of air film evolution. (a) The radius of the air film ($R$) was measured as a function of time ($t$) during retraction for different liquids (characterized by Oh: 0.0221 for water and 0.0223 and 0.0227 for two different mixtures of water and ethanol). There is an exponential decrease in $R$ over time, fitted by $R(t)=(1.45\times {10}^{-4})\exp (-3.34\times {10}^{4}t)$ (solid line) for water, which indicates inertial retraction based on the film thickening [18]. (b) The ratio of the daughter droplet volume to the air bubble volume, $V_D/V_B$, was evaluated with Oh. The data support the existence of a critical Oh (${\mathrm{Oh}}^{*}$) above which the pinch-off of the daughter droplet is prevented. The inset shows the x-ray images of the pinch-off moments in different liquids. (c) The volume fraction, $V_D/V_B$, for water is almost invariant with the substrate contact angle at $\sim 5.2\%$ ($\pm 0.7\%$). The dashed lines are guides for the eye. These results suggest that the energy transfer, expressed in terms of Oh, is essential for the daughter droplet generation.

Figure 4

Bubble detachment and attachment. Sequential x-ray images for water clearly show examples of (a) bubble detachment at a contact angle $\sim 35°$ and (b) bubble attachment at $\sim 45°$ (see movies 2 and 3 of Supplemental material [25]). A critical difference in bubble behavior was found after $77.3\mu \mathrm{s}$ (marked by arrows). (c) The frequency of bubble detachment and attachment for water was monitored as a function of the substrate contact angle; the threshold contact angle was $\sim 40\pm 5°$, below which the bubble preferably detached. (d) The detachment (upper, for small contact angles) and attachment (lower, for large contact angles) can be explained by geometrical relations, which suggest $\sim 42.5°$ to be the threshold angle, comparable to our measurements of (c).