Prediction of Foldy’s model for the phase velocity and attenuation of sound in water with a 0.4% volume fraction of radius bubbles.
(Color online) Injection of bubbles: A capillary is moved in a preprogrammed pattern of positions within the gel, delivering rows of equally sized bubbles. Capillary speed and pressure in the syringe are the two parameters governing the bubble size and the distance between bubbles.
Images of Sample 2 (monodisperse with median radius of ) and Sample 3 (polydisperse). Arrows indicate clusters of bubbles ignored for the image analysis of the samples. The scale is the same on both images. Note that the dark spots in the background are not bubbles but dust on the back wall of the cell.
Measured radius distributions for Samples 2 (top) and 3 (bottom) and best-fitted lognormal distributions.
(Color online) Sketch of the setup for ultrasonic measurements. A piezoelectric transducer emits an acoustic pulse that traverses the cell containing the bubbly medium.
Top: The reference pulse for a central frequency of . Bottom: The corresponding pulse transmitted through Sample 1.
Top: Magnitude of the Fourier transform of the reference signal of Fig. 6 (solid line) and of the sample signal of Fig. 6 (dashed line). Bottom: The phase of the Fourier transform of the reference signal minus the phase of the Fourier transform of the sample signal.
Attenuation and velocity measured in Sample 1 (, , ). Predictions from the Foldy (continuous lines) and Henyey (dashed lines) models are shown.
Attenuation and velocity measured in Sample 2 (, , ). Predictions from the Foldy (continuous lines) and Henyey (dashed lines) models are shown.
Attenuation and velocity measured in Sample 3 (, , ). Predictions from the Foldy (continuous lines) and Henyey (dashed lines) models are shown.
Top: The reference pulse for a central frequency of . Middle: The corresponding pulse traversing Sample 1 (, , ). Bottom: The corresponding pulse traversing Sample 4 (, , ). Note factor of reduction in amplitude. Data in light grey correspond to the signal acquired when the aperture of the screen is closed.
Approximate measurements of the attenuation in Sample 4, and comparison with the Foldy (solid line) and Henyey (dashed line) models.
Measured parameters of the bubble size distributions for each sample. The number of bubbles counted for the size analysis is indicated.
Characteristics of the cell containing the bubbly medium. The walls were made of clear polycarbonate: Our measured values for density and phase velocity of sound are in agreement with values in the literature (Ref. 22).
Values of the physical parameters used for the model. The phase velocity of sound in the gel was measured by propagating an acoustic pulse through a known thickness of gel. Shear moduli were obtained by standard rheological techniques. Density was measured with a specific gravity bottle.
Article metrics loading...
Full text loading...