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Euronoise 2018: 1.1 - Acoustic and Elastic Metamaterials

Lecture: Nonreciprocal propagation of sound in viscous fluid with asymmetric scatterers

Author(s): Krokhin Arkadii, Bozhko Andrey, Walker Ezekiel , Neogi Arup

Two common concepts of nonreciprocity in sound propagation are based on nonlinear effects and on local circulation of fluid. They originate from two known methods of breaking time reversal symmetry (T-symmetry), that is necessary for observation of nonreciprocal effects. Practical realization of both concepts requires additional devices to be installed with their own power sources. Here, we explore viscosity of fluid as a natural factor of T-symmetry breaking. We report experimental observation of the nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric aluminum rods. Asymmetry, or broken P-symmetry, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. This passive nonreciprocal linear device is cheap, robust and does not require an energy source. Our results demonstrate that viscous dissipation may lead to nonreciprocity, provided that it is appropriately introduced through the Navier-Stokes equation, which is not time-reversible. Unlike this, a widely accepted phenomenological method to introduce dissipation by adding imaginary part to elastic modulus does not give rise to nonresiprocity. While complex elastic modulus leads to exponentially decaying solution of the wave equation, the equation itself remains time-reversible. It means that sound transmission becomes irreversible (entropy increases) but still reciprocal. This explains why dissipation was not considered as factor leading to nonreciprocal effects. Our study shows that viscous dissipation allows nonreciprocal transmission of sound if the P-symmetry is also broken.\nThis work is supported by the National Science Foundation under grant no. 1741677.

Corresponding author

Name: Prof Arkadii Krokhin

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Country: United States