Image illustrating the simulated propagation of ultrasonic wave in a suspension of disk-shaped polystyrene particles. The curved separation represents an arbitrary split of the simulation domain. In the upper part of the figure, the color codes the amplitude of the displacement as a function of position (direction is parallel to the direction of propagation and is perpendicular) at a given time. The coherent wavefront may be distinguished in red below the complicated wave field corresponding to interference of waves scattered by the particles. In the lower part, the figure displays the random distribution of the particles. On the right hand side, an isolated particle is shown where black pixels correspond to elastic polystyrene.
Typical simulated rf signals: (a) The signal in water (in black) is identical in shape to the signal generated by the emitter. In gray: the rf signal transmitted in suspension made of disk-shaped polystyrene particles immersed in water. The particle concentration is . The value of the velocity (respectively, attenuation coefficient at 50 MHz) is equal to 1505 m/s (respectively, 4.46 dB/cm). (b) Backscattered rf signal obtained with the same suspension. The corresponding value of the relative backscattering intensity is equal to 10.6 dB.
Scattering cross-section obtained with the Faran model (dashed lines) and the numerical simulation (solid lines) at angles of 180° (thick lines) and 90° (thin lines) from the incident beam.
(a) Mean attenuation coefficient at 50 MHz, (b) signal to noise ratio, and (c) speed of sound as a function of concentration of polystyrene microspheres. The black solid lines correspond to numerical results. The two dashed lines in (a) and (b) represent the sum and the subtraction of the mean and of the standard deviation of each quantity. The dashed line in (c) indicates the results obtained with an effective medium model (Yang and Mal, 1994). The crosses correspond to experimental results. The vertical lines in (a) indicate the experimental standard deviations. The experimental standard deviation in (b) and (c) is equal to 1 dB and 0.1 m/s, respectively.
Number of particles accounted for in the simulation domain and the corresponding concentration.
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