The transmission spectrum of sound through a phononic crystal subjected to liquid flow

The influence of liquid-flow up to 7 mm/s is examined on transmission spectra of phononic crystals, revealing a potential use for slow liquid-flow measurement techniques. It is known that transmission of ultrasound through a phononic crystal is determined by its periodicity and depends on the material characteristics of the crystal's constituents.

Here, the crystal consists of metal rods with the space in between filled with water. Previous studies have assumed still water in the crystal, and here, we consider flowing liquid. First, the crystal bandgaps are investigated in still water, and the results of transmission experiments are compared with theoretical band structures obtained with the finite element method.

Then, changes in transmission spectra are investigated for different speeds of liquid flow. Two situations are investigated: a crystal is placed with a principal symmetry axis in the flow direction (ΓΓX) and then at an angle (ΓΓM). The good stability of the bandgap structure of the transmission spectrum for both directions is observed, which may be of importance for the application of phononic crystals as acoustic filters in an environment of flowing liquid.

Minor transmission amplitude changes on the other hand reveal a possibility for slow liquid flow measurements. Phononic crystals (PCs) are generally formed by a periodic arrangement of materials (scatterers) with elastic properties different from those of the homogeneous matrix in between the scatterers, typically scaled at the wavelengths of interest and giving rise to the emergence of transmission bandgaps.

The concept was studied by Yablonovitch1 in optics for a photonic crystal in the ultraviolet microwave regime, where he shows that bandgaps in the spectrum exist as a result of interferences between direct and reverberated paths of waves. A similar behavior of acoustic waves in phononic crystals (PCs) has been observed.

Additionally, ultrasonic waves in a periodic structure are used for sensing purposes, such as acoustic waveguides and acoustic lenses, to control, direct, and manipulate sound.2,3 The reported experiments are as follows: ultrasound is emitted by a transducer, and it travels through the PC, thereby probing its acoustic properties (density, viscosity, speed of sound,…, speed of water flow).

A specific transmission spectrum, including bandgaps, emerges, and its specific characteristics are determined by the physical properties of the PC. Over the last decade, PCs have been introduced as a platform for (still) liquid sensing purposes,4–9 based on significant spectral changes induced by composition changes of the liquid mixture.10 Many works discuss the application of PCs for fluid characterization such as viscosity, density, and concentration measurement of liquid solutions.

However, no study of possible flow-speed influence on PC filter characteristics has been reported. For the case in which fluid-flow measurements without the presence of a PC is considered, we can cite, for example, Nishimura et al.,11 for measuring the small open channel fluid flow using pulse-echo signals scattered from the particles in a pipe.

From the slope of the correlation peak amplitude with the variation in pulse-echo excitation time, the authors estimate the flow-speed of the medium, for speeds much higher than what is studied in the current paper. Here, we study the band structure and its stability and explore minor effects in actual transmission amplitudes to the flow-speed.

The low speeds involved are comparable to what one may expect on a large scale in tidal water currents for example. The phononic crystal under study consists of a square lattice arrangement of 169 steel rods, each having a diameter of 1.2 mm and a length of 150 mm. A photography of the crystal is shown in Fig. 1(a).

The rods were aligned using two supporting plates that had been machined to have periodic arrays of holes, and Fig. 1(b) shows the square lattice pattern of the cylinders and the directions of the highest symmetry, referred to as ΓΓX and ΓΓM. The lattice constant, being the distance between the centers of any two adjacent rods, was measured: a = 2.52 mm.

The crystal made of cylinders is submerged in water, such that the water in between the cylinders acts as the crystal matrix. Assuming a sound speed in water of 1480 m/s, incident ultrasound with a wavelength corresponding to the lattice constant would have a frequency on the order of 1 MHz. Steel (rods) and water (host medium) were chosen here as the constituent materials of the crystal due to the large contrast in their densities and elastic constants, as this has been shown to be an effective approach for the formation of bandgaps in other studies on phononic crystals.12–14 To study effects of liquid flow on the transmission spectrum, that spectrum was first determined using through-transmission experiments using an emitting and a receiving transducer, namely, two Valpey-Fisher IS0104GP transducers with a nominal center frequency of and a beamwidth of approximately 10 mm.

Two types of experiments have been performed on the crystal: through-transmission measurements in the ΓΓX direction and in the ΓΓM direction; the results are shown in Fig. 2.