Acoustic resonances in a liquid with vapor bubbles: Effect of liquid-vapor transition on sound velocity and attenuation

Abstract

We present an experimental study of resonance frequencies of a diphasic medium that consists of diethyl ether containing vapor bubbles. We show that the liquid-vapor transfers affect the sound velocity and attenuation so that the usual liquid-gas effective-medium theory is in error at low frequency. The measurements of resonance frequency and attenuation can be used to estimate the vapor volume fraction and the bubble diameter. At high sound amplitude the shape of the resonance curve shows nonlinear effects, and acoustic bistability is observed.PACS numbers: 43.30.+m, 47.55.Kf The sound velocity in a liquid containing gas bubbles has been measured for a long time and is generally much smaller than the velocities in the homogeneous liquid or gaseous phases. In the long-wavelength limit, this is well described by effective-medium theory where the diphasic medium is modeled as a homogeneous one with average density and compressibility [1,2]. Thus, being nearly as dense as the liquid and as compressible as the gaseous phase, the diphasic medium has a smaller sound velocity than those of its two constitutive homogeneous phases. However, another effect should be taken into account when the diphasic medium consists of vapor bubbles coexisting with the liquid phase; assuming thermodynamic equilibrium, the liquid-vapor transition is shown to increase the effective compressibility of the medium, thus strongly decreasing the sound velocity [3], We have shown experimentally that even at rather low frequency this mechanism does not affect sound velocity because of the frequency cutoff corresponding to the characteristic diffusion time of latent heat over a typical bubble size [4]. We report here measurements performed at small enough frequency to detect the contribution of the liquid-vapor transition to the slowing down of sound velocity in diethyl ether with vapor bubbles. Instead of trying to measure sound velocity with the usual methods as in our previous experiments, we study the low-frequency resonance of the diphasic medium contained in a Helmholtz resonator, as a function of the vapor volume fraction. We show that the predictions of effective-medium theory are in error at low frequency, whereas a recent theoretical model taking into account liquid-vapor transition [5,6] is in agreement with our experimental results.The experimental setup is shown in Fig. 1(a). It consists of two coaxial glass tubes of length 2 m, the outer one being 32 mm in diameter and the inner one 20 mm; the inner tube is terminated by a cylindrical container, approximately 5 1 in volume (150 mm in diameter, 295 mm in height), that acts as a Helmholtz resonator. It contains the working fluid which is diethyl ether. Vapor bubbles are generated in the lower part of the inner tube with the help of four resistive wires, 50 cm long, of total resistance 11 O, heated by a stabilized dc current in the range 0-4 A. Bubbles appear on the wires above a critical heating current, and then rise in the liquid. The temperature of the upper part of the tube is m...

Cavity-type hypersonic phononic crystals

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