Unconventional acoustic wave propagation transitions induced by resonant scatterers in the high-density limit.

Experiments on ultrasound propagation through a gel doped with resonant encapsulated microbubbles provided evidence for a discontinuous transition between wave propagation regimes at a critical excitation frequency. Such behavior is unlike that observed for soft materials doped with non-resonant air or through liquid foams, and disagrees with a simple mixture model for the effective sound speed. Here, we study the discontinuous transition by measuring the transition as a function of encapsulated microbubble volume fraction. The results show the transition always occurs in the strong-scattering limit (l/λ < 1, l and λ are the mean free path and wavelength, respectively), that at the critical frequency the effective phase velocity changes discontinuously to a constant value with increasing microbubble volume fraction, and the measured critical frequency shows a power law dependence on microbubble volume fraction. The results cannot be explained by multiple scattering theory, viscous effects, mode decoupling, or a critical density of states. It is hypothesized the transition depends upon the microbubble on-resonance effective properties, and we discuss the results within the context of percolation theory. The results shed light on the discontinuous transition's physics, and suggest soft materials can be engineered in this manner to achieve a broad range of physical properties with potential application in ultrasonic actuators and switches.

Critical Role of a Nanometer-Scale Microballoon Shell on Bulk Acoustic Properties of Doped Soft Matter.

A material's acoustic properties depend critically upon porosity. Doping a soft material with gas-filled microballoons permits a controlled variation of the porosity through a scalable fabrication process while generating well-tailored spherical cavities that are impermeable to liquids. However, evidence is lacking of how the nanometer-scale polymeric shell contributes to the overall effective material properties in the regime where the wavelength is comparable to the sample thickness. Here, we measure ultrasound transmission through a microballoon-doped soft material as a function of microballoon and impurity concentration, sample thickness, and frequency. The measured longitudinal wave speeds are an order of magnitude larger than those in similar systems where no shell is present, while the transverse wave speed is found to linearly increase with microballoon concentration, also in contrast to systems with no shell. Furthermore, we find the results are independent of the soft material's elastic moduli as well as a lesser contribution of the microballoon shell on material attenuation. The results are validated with a multiple scattering model and suggest the shell contributes significantly to the material's bulk acoustic properties despite its thickness being 4 orders of magnitude smaller than the acoustic wavelength. Our results demonstrate how a nanometer-scale interface between a gas cavity and a soft polymer can be used in the submicrometer design of acoustic materials, and are important for observations of such phenomena as strong interference effects in soft matter.