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Oscillations of Thin Liquid Shells under Acoustic Forcing<br />
J. Sznitman ∗ ,A.Kempe ∗ and T. Rösgen ∗<br />
Vibrations induced in two-dimensional soap films have been extensively studied<br />
both analytically and experimentally in the past 12 . In contrast however, oscillations<br />
of three-dimensional soap bubbles, a common example of a thin liquid film shaped<br />
into a spherical shell, have received comparably little attention and the literature on<br />
the subject remains surprisingly scarce. Indeed, for what may seem an intuitive and<br />
classic problem, there still lacks both experimental and analytical descriptions of the<br />
vibrations of such spherical liquid shells containing a cavity filled with gas.<br />
In the present investigation, we study the oscillations induced by acoustic forcing<br />
of soap bubbles placed in ambient air. Using a simple experimental setup, air-filled<br />
soap bubbles (size range: 5-20mm diameter) are produced at the tip of a syringe and<br />
excited by a loudspeaker at low (1-1000Hz) and high (1-20kHz) frequencies. Both oscillation<br />
displacements of the spherical liquid shell and the resulting power spectrum<br />
are obtained using a low-coherence interferometric setup 3 . Results for the oscillations<br />
of three-dimensional soap bubbles are compared with our measurements for<br />
two-dimensional soap films using low-coherence interferometry and in particular, resonance<br />
frequencies are sought. In a next step, we implement a PIV algorithm to<br />
investigate the possible influence of acoustic forcing on the internal flows present in<br />
thecavity. Theexperimental setup is then slightly modified where particle-laden soap<br />
bubbles are now observed under a microscope. Our first results show that not only<br />
may acoustic forcing induce flows within the bubble cavity, but moreover, internal<br />
convective flow fields are inherently present within the bubble, regardless of the liquid<br />
shell oscillations, due to the natural motion of the liquid film which generates a<br />
flow inside the cavity, consistent with the no-slip boundary condition at the liquid<br />
shell surface.<br />
∗ Institute of Fluid Dynamics, ETH Zurich, Switzerland<br />
1 L. Bergmann, J. Acoust. Soc. Am. 28, 6 (1956).<br />
2 A. Boudaoud et al., J. Acoust. Soc. Am. 82, 19 (1999).<br />
3 A. Kempe et al., Optics Letters, 28, 15 (2003).<br />
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