Energy velocity of multiply scattered waves in strongly scattering media

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 $({v}_{1}g{v}_{0})$. 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 ${n}_{\text{rel}}={v}_{0}/{v}_{1}l1$ 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.