Shape evolution and bubble formation of acoustically levitated drops

In this study, we investigated the shape evolution and bubble formation of acoustically levitated drops upon increasing the sound intensity. Here, a levitated liquid drop evolves progressively from an oblate spheroidal shape to a flattened film to a thin bowl-shaped film, eventually forming a closed bubble. Through systematic experiments, numerical simulation, and scaling analysis, we demonstrate that the buckled geometry of the liquid film can drastically enhance the suction effect of acoustic radiation pressure at its rim, forming a significant pressure gradient inside the film which causes an abrupt area expansion and bubble formation. Our results provide the mechanical origin responsible for the shape evolution and bubble formation of acoustically levitated drops, and highlight the role of buckled geometry in the levitation and manipulation of liquid films in an ultrasound field.

Figure 1

Shape evolution of an SDS drop (1 cmc, 10 $\mu \mathrm{l}$) upon increasing sound intensity with decrease of emitter-reflector distance D. (a) Static shapes corresponding to different sound pressure levels (SPL), from left to right: 131.5, 132.4, 133.1, and 134.1 dB. Scale bars represent 1 mm. (b) Aspect ratio $a$/$b$ as a function of SPL.

Figure 2

Buckling and bubble formation of an acoustically levitated liquid film (silicone oil 10 $\mu \mathrm{l}$). (a) Illustration of the levitation positions in the sound field. (b), (c) Acoustic streaming with an extremely flattened film just before buckling levitated at positions A and B, respectively. (d), (e) Snapshots showing bubble formation of drops at levitation positions A and B, respectively. Scale bars represent 1 mm.

Figure 3

Final bubble volume for different volumes of liquid drops. (a) Photos showing the obtained bubble (right) is significantly larger than the initial drop (left). (b) Volume of the obtained bubble, $V_b$ versus the initial drop volume $V_d$, showing $V_b$ is virtually independent of $V_d$.

Figure 4

Experimental observations for the cases not proceeding to bubble formation. (a) Atomization prior to buckling (water, 5 $\mu \mathrm{l}$); (b) atomization during buckling (SDS-2, 5 $\mu \mathrm{l}$); (c) film broken without closure (liquid Ga-In-Sn alloy, 10 $\mu \mathrm{l}$). Scale bars represent 1 mm.

Figure 5

Sound field in the levitator with a liquid drop (SDS-2, 10 μl) levitated at position A [marked in Fig. 2]. (a)–(d) correspond to different sample shapes: quasispherical (a), pancakelike (b), flat film (c), and buckled film (d).

Figure 6

Acoustic radiation pressure $P_{\mathrm{A}}$ exerted on the drop surfaces (SDS-2, 10 μl). (a)–(d) Distribution of $P_{\mathrm{A}}$ for different-shaped samples given in Fig. 5. Calculations indicate that the sample was under compression at the film center and under suction at the rim. The suction effect was significantly enhanced as it was buckled (d).

Figure 7

Distribution of $P_{\mathrm{A}}$ for different-shaped liquid drop (10 μl, SDS drop) levitated at position B marked in Fig. 2. (a)–(f) correspond to different sample shapes as shown in the inset graphics. $P_{\mathrm{A}}$ on the lower surface is always larger than that on the upper surface, which is consistent with the downward buckling direction observed in the experiments. The suction effect at the membrane rim is greatly enhanced once buckling occurs which is similar to results obtained at position A.

Figure 8

Color-coded illustration of the acoustic radiation pressure $P_{\mathrm{A}}$ on a buckled liquid film. Red and blue represent positive and negative values of $P_{\mathrm{A}}$, respectively. As the color of the membrane surface changed from blue to red from rim to center, $P_{\mathrm{A}}$ changed from negative to positive. Arrows indicate the directions of the acoustic radiation force, where $P_{\mathrm{I}}$, $P_{\mathrm{O}}$ are the acoustic radiation pressure at the inner and outer surface measured at the bottom of the buckled film; H is the height of the film rim. Acoustic radiation pressure distribution shows where the film was under downward compression force at the center and upward pulling force at the rim.

Figure 9

Bubble formation for different liquid drops. (a) Surface area variation upon increasing sound intensity of an aqueous SDS 1 drop (10 μl) divided into five stages: 1–5 correspond to slight deformation, rapid flattening, slow flattening, buckling, and abrupt expansion with rim closure, respectively. $t=0$ corresponds to the onset time of decreasing the emitter-reflector distance ($u_{\mathrm{R}}=1.00\mathrm{m}/\mathrm{s}$). Area was scaled to the initial surface area of a spherical drop ($S_0$). Inset photos show side-view snapshots corresponding to each stage. (b) Critical shape characterized by α or $S/S_0$ of the buckled film for different liquids (10 μl) corresponding to the onset of abrupt area expansion for samples levitated at position A. α is defined as the ratio between the height H of the buckled film and its radius $R^{*}$. (c) Critical driving pressure $\mathrm{\Delta }P$ versus surface tension σ for different liquid drops of varied volumes. The solid lines represent the linear fitting for each volume and indicate the critical driving pressure beyond which abrupt area expansion is triggered. The dashed lines indicate the slope of $2/h$ corresponding to each volume, where $h$ is film thickness.