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The existing concepts of non-reciprocity in propagation of acoustic or elastic waves are based either on nonlinear effects, or on local circulation of linear elastic fluid that leads to red or blue Doppler shift, depending on the direction of sound wave. The same concepts exist for electromagnetic non-reciprocity, where external magnetic field may produce the effect similar to local rotation of the medium. These two concepts originate from two known methods of breaking a time-reversal symmetry (T-symmetry), that is necessary for observation of nonreciprocal wave propagation. Both concepts require additional electrical or mechanical devices to be installed with their own power sources. Here we propose to explore viscosity of fluid as a natural factor of the T-symmetry breaking through energy dissipation. We report experimental observation of the nonreciprocal transmission of ultrasound through a water-submerged phononic crystals consisting of several layers of aluminum rods arranged in a square lattice. While viscous losses break the T-symmetry, making the wave propagation thermodynamically irreversible, the transmission remains reciprocal if the scatterers are symmetrical. To generate different energy losses for opposite directions of propagation, the P-symmetry of the crystal is broken by using asymmetric scatterers. Due to asymmetry, two sound waves propagating in the opposite directions produce different distributions of velocity and pressure that leads to different local absorption. Dissipation of acoustic energy occurs mostly near the surface of the scatterers and it strongly depends on surface roughnesses. Using two phononic crystal with smooth and rough aluminum rods we demonstrate low (2-5 dB) and high (10-15 dB) level of non-reciprocity within a wide range of frequencies, 300-600 kHz. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. This nonreciprocal linear device is very cheap, robust and does not require energy source.
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Non-reciprocal acoustics in a viscous environment
It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken P symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry ( T symmetry) holds. Viscous losses break T symmetry, adding a non-reciprocal contribution to the transmission coefficient. The non-reciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analysed. The surfaces of the cylinders were specially processed in order to weakly break P symmetry and increase viscous losses through manipulation of surface features. Subsequently, the non-reciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of non-reciprocity is in agreement with the measure of broken P symmetry. The reported study contradicts commonly accepted opinion that linear dissipation cannot be a reason leading to non-reciprocity. It also opens a way for engineering passive acoustic diodes exploring the natural viscosity of any fluid as a factor leading to non-reciprocity.
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- Award ID(s):
- 1741677
- PAR ID:
- 10300046
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 476
- Issue:
- 2244
- ISSN:
- 1364-5021
- Page Range / eLocation ID:
- 20200657
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2020.0657
