Enhanced drainage and thinning of liquid films between bubbles and solids that support surface waves

We study the thinning and drainage of the intermediate liquid film between a bubble and a solid surface at close proximity in the presence of a surface acoustic wave (SAW) in the solid. Specifically, we employ the diffraction of light to observe a long air bubble confined in a solid rectangular channel filled with silicone oil. This setup, constituting a two-dimensional physical model of thin film drainage, allows us to analyze the influence of a SAW on the rate of thinning of the micron-thick liquid film separating the bubble and the solid substrate. The viscous penetration of the SAW into the liquid imposes a convective drift of mass, redistributing the fluid in the film against capillary resistance and producing a net drift of liquid out of the film. The rate of drainage of liquid from the film increases by one to several orders of magnitude in comparison to the rate of drainage due to the Laplace pressure of the bubble alone. The experimental findings agree well with a newly developed theory describing the SAW-enhanced drainage as a competition between the capillary flow and SAW-induced streaming.

Figure 1

(a) A sketch of a top view of an air bubble confined in a channel, (b) a sketch of the cross section of the channel and bubble (not to scale), and (c) a sketch of the experimental setup, where we show the (1) interdigital electrodes atop the piezoelectric substrate of the SAW actuator and the inlets for (2) oil, (3) air to the microchannel, and (4) the outlet of the fluids, fabricated within the (5) elastomer structure atop the actuator; the dashed square illustrates the area of observation.

Figure 2

A top view of the intermediate film of oil in terms of monochromatic light interference patterns, captured within the observation area in Fig. 1, for different times for 50 cSt oil in the absence (top row) and in the presence (bottom row) of a propagating SAW (along the arrow) of a measured velocity amplitude of $U_{\text{SAW}}=0.11$ m/s at the solid surface.

Figure 3

Typical evolution of the thin-film geometry ($\mathrm{\Delta }h$) in experiment (solid line) and in numerical computation (dashed line) for 50 cSt oil and (a–e) in the absence of SAW, (f–j) for $U_{\text{SAW}}=6.3$ cm/s, and (k–o) for $U_{\text{SAW}}=10$ cm/s. Gray stripes in the leftmost panels mark the position of the channel walls.

Figure 4

Typical evolution of the thin-film geometry ($\mathrm{\Delta }h$) in experiment (solid line) and in numerical computation (dashed line) for $U_{\text{SAW}}=7.9$ cm/s and (a–e) for 50 cSt silicone oil, (f–j) 100 cSt silicone oil, and (k–o) for 500 cSt silicone oil. Gray stripes in the leftmost panels mark the position of the channel walls.

Figure 5

Typical evolution of the thin-film geometry ($\mathrm{\Delta }h$) in numerical computations for 100 cSt silicone oil, where $U_{\text{SAW}}=7.9$ cm/s and $h_0(t=0)=0.1\times \mathrm{\Delta }{h}_{\text{MAX}}$ (solid line), $h_0(t=0)=0.05\times \mathrm{\Delta }{h}_{\text{MAX}}$ (dashed line), and $h_0(t=0)=0.2\times \mathrm{\Delta }{h}_{\text{MAX}}$ (dash-dot line). Gray stripes in the leftmost panels mark the position of the channel walls.

Figure 6

Evolution of the apparent volume given by Eq. (4) in the experiment and numerical computation shown in Fig. (4) for $U_{\text{SAW}}=7.9$ cm/s and (a) 50 cSt silicone oil, (b) 100 cSt silicone oil, and (c) 500 cSt silicone oil.

Figure 7

Variations of the experimental and theoretical time interval corresponding to 50% decrease of the apparent liquid volume in the intermediate film, $T_{1/2}$, against the ratio between acoustic and capillary stresses in the liquid, ${\mathrm{We}}_s$. In the absence of the SAW (${\mathrm{We}}_s$ = 0), we measured $T_{1/2}=900,3600$, and 10 800 s for 50, 100, and 500 cSt oils, respectively, shown in the inset to the left.