Energy velocity of multiply scattered waves in strongly scattering media

Abstract

The important influence of the relative refractive index of scattering inclusions on energy transport of classical waves through disordered media is clearly demonstrated through ultrasonic experiments on monodisperse emulsions. Our ultrasonic techniques measure both the transmitted average wave field and the multiply scattered diffusive intensity, enabling a full characterization of wave transport through the media and the measurement of both the group and energy velocities over a wide range of frequencies. The emulsions were fabricated using microfluidic techniques that permit accurate control of droplet size and concentration, for droplet inclusions with very different acoustic properties relative to the yield stress fluids in which the droplets were immersed. Thus we have been able to investigate emulsions containing either "slow" fluorinated oil droplets (sound speed v 1 less than v 0 of the surrounding fluid) or "fast" liquid metallic droplets (v 1 > v 0 ). We find that the energy velocity that describes the transport of energy by the dominant diffusive waves is mainly governed by the sound speed within the scatterers, and can be either much slower or faster than any of the other wave velocities. The possibility that the energy velocity could be faster than any other wave velocity when n rel = v 0 /v 1 < 1 was not anticipated in previous work. These observations are successfully explained by theories that are valid for scalar waves in media containing a low concentration of scatterers, and are directly applicable to our dilute "all-fluid" emulsions. The role of droplet resonances on the behavior of the energy velocity is also demonstrated, and the mechanism leading to the large differences in the energy velocity in the two emulsion systems is elucidated through calculations of the energy density inside the droplets relative to the incident energy density.

Ultra slow acoustic energy transport in dense fish aggregates

“…In this way, the simultaneous measurement of and D leads to the energy velocity m/s. This value of is surprising low (an order of magnitude lower than the sound speed in water 1500 m/s) , which is a very rare observation for acoustic waves 4 , 6 , 7 , 19 , 20 . Similarly slow diffusion has been observed previously with CBS measurements in dense shoals of sea breams, sea basses ( Dicentrarchus labrax ) or croakers ( Argyrosomus regius ) 4 , but no such extreme behaviour has been found for acoustic waves in other multiply scattering media 6 , 7 , 19 , 20 .…”

“…This value of is surprising low (an order of magnitude lower than the sound speed in water 1500 m/s) , which is a very rare observation for acoustic waves 4 , 6 , 7 , 19 , 20 . Similarly slow diffusion has been observed previously with CBS measurements in dense shoals of sea breams, sea basses ( Dicentrarchus labrax ) or croakers ( Argyrosomus regius ) 4 , but no such extreme behaviour has been found for acoustic waves in other multiply scattering media 6 , 7 , 19 , 20 . However, unlike this past work on dense fish shoals, the cage considered in this paper has a sufficiently low fish concentration to allow us to neglect mesoscopic interferences that might impact the energy velocity, thereby facilitating a quantitative interpretation of the current results.…”

“…Here, we employ a microscopic model of the energy velocity 15 in order to identify the mechanisms responsible for the ultra low value. This description is based on a model that accounts for the delay induced by an immersed scatterer, and predicts a result for that may be approximated as 20 …”

“…A way to interpret the scattering delay impacting the energy velocity is the calculation of the acoustic energy density inside and outside the scatterer 20 , 25 . High values of energy density suggest that waves are “stored” in the scatterer.…”

Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

“…The role of resonant interaction between classical electromagnetic radiation and matter has been reviewed by Lagendijk and van Tiggelen [44]. The effect of resonances in the transport of light in a random system of dielectric spheres has been studied by Sapienza et al [45], by Cowan et al [46] in the transport of ultrasound in a system of disordered plastic spheres immersed in water, and by Tallon et al [47] in emulsions. In our case, however, since the formalism we have developed holds only in the loss less (B = 0) case, we cannot set ω = ω 0 in Eq.…”