Visualization of Surface Acoustic Waves in Thin Liquid Films

We demonstrate that the propagation path of a surface acoustic wave (SAW), excited with an interdigitated transducer (IDT), can be visualized using a thin liquid film dispensed onto a lithium niobate (LiNbO3) substrate. The practical advantages of this visualization method are its rapid and simple implementation, with many potential applications including in characterising acoustic pumping within microfluidic channels. It also enables low-cost characterisation of IDT designs thereby allowing the determination of anisotropy and orientation of the piezoelectric substrate without the requirement for sophisticated and expensive equipment. Here, we show that the optical visibility of the sound path critically depends on the physical properties of the liquid film and identify heptane and methanol as most contrast rich solvents for visualization of SAW. We also provide a detailed theoretical description of this effect.

Position of acoustic path. First we excited two opposed tapered TIDTs (with wavelengths from 23 to 24.3 μ m, 60 finger-pairs and 500 μ m aperture) at different frequencies and isopropanol for the liquid layer (Fig. 2).
The resonance frequency f of an IDT is given by f = c/λ , with the propagating velocity c of the SAW and the wavelength λ (finger distance equals λ /2). Switching the frequency changed the position of the SAW, as the finger distance varies along the aperture.
To verify our new method, the position (along the x-axis, see Fig. 2a) of the acoustic paths of two excited TIDTs of the same geometry were measured at different frequencies, fitted by a Gaussian function, and compared with vibrometer measurements and theory (Fig. 3). The theoretical values were calculated by the given finger distances of the TIDT and the theoretical SAW velocity of 3870 m/s 41 . A convincing agreement between the two measurement methods and theory was obtained. The linear shift of the sound paths´ position with increasing frequency is clearly visible. The slopes of each liner fit were measured to 51.06 ± 1.45 μ m/MHz (fluidic measurement 1), 51.36 ± 1.94 μ m/MHz (fluidic measurement 2), 53.62 ± 1.18 μ m/MHz (vibrometer measurement) and 57.79 μ m/MHz (theory). The systematic off-set between the theory and experiments can be explained by the change of the SAW velocity: The electrodes of the IDT decreased the velocity from 3978 m/s to 3870 m/s as piezoelectric shorting has to be included 41 . But this effect was reduced by the presence of an additional dielectric medium on the substrate, resulting in a higher SAW velocity than the theoretical one in the case of isopropanol covered SAW-chip [42][43][44][45][46] .
We used this new visualization method to determine the velocity of the SAW on the piezoelectric substrate accordingly. The wavelength λ of a TIDT at the excited frequency f can be measured, using the visible sound path position. The results shown in Fig. 2 41 . To demonstrate the applicability of the technique in characterising more complex IDT systems, we next used a tapered focusing IDT: in addition to a conventional focusing design, the fingers are slanted as in the case of a tapered IDT. The IDT was excited at different frequencies. As before, the position of the acoustic path changed with frequency (Fig. 4). The average wavelength for each position was measured. With these values the SAW velocity was calculated to be 3800 ± 400 m/s, 4000 ± 710 m/s and 3700 ± 600 m/s. As LiNbO 3 is an anisotropic substrate, the velocity of sound varies with the direction of travel. The experimental values are in good agreement with the literature values of 3772 m/s, 3830 m/s and 3864 m/s for the different angles at each of the positions (piezoelectric shorting is included in these velocities) 41 .
Measurement of anisotropy and focal point. As well as TIDTs, focusing IDTs are used as actuators in microfluidics for producing and merging droplets, transport and alignment of particles and other applications 13,17,47 . In one application it is necessary for alignment of a PDMS microchannel with respect to the orientation of the IDT, especially where considering the focus point of the IDT and the anisotropy of the piezoelectric substrate. To demonstrate this practical necessity and determine appropriate parameters, the sound path of a focusing IDT (wavelength of 60 μ m, opening angle of 60°, 20 finger-pairs, and radius R of 3 mm) and a tapered focusing IDT were characterised (Fig. 5). Again, isopropanol was used for wetting the chip. The acoustic path and the focal point were clearly visible. The piezoelectric substrate LiNbO 3 and hence the velocity of the SAW was anisotropic, leading to a shift Z = 900 ± 77 μ m of the focal point towards the IDT for the focusing IDT (Fig. 5b). The value determined optically again was in good agreement with the theoretical value Z = 940 μ m 48 . From the measured distance Z between geometrical and real focal point, the anisotropy factor b can be calculated with the formula by Green et al. 48 : The literature value 41 for the SAW propagation velocity was fitted with a parabolic function φ φ with the velocity v, the propagation angle φ towards the x direction and the anisotropy factor b. The parabolic fit leads to a theoretical value b fit = − 0.228 (with dimensions of degree −2 ). Our simple measurements deliver an anisotropy factor b exp = −0.216 ± 0.026. The deviation between theoretical and experimental values was less than 6%.

Influence of different fluidic layers.
To explore the dependence of the effect on the acoustic properties of the fluid layer, different solvents were used in a series of experiments (including heptane, methanol, decane, ethanol, isopropanol, acetone, water and ethylene glycol). The experimental set-up involved using a single focusing IDT, as described above. All experiments were performed with the same power of 18 dBm. A contrast increase with experimental time is caused by evaporation of the fluid. To avoid the influence of the thickness of the fluid layer over time (where a contrast increase occurs with decreasing thickness of the fluid layer) a standardized volume of liquid (20 μ l) was dispensed on the whole area of the chip. A single image was extracted of the video shortly (< 1 s) after application of the RF-signal. To determine the optical contrast, the grey value in the area in front of the IDT was averaged in vertical direction (Fig. 6) and the ratio of maximum and bottom line of the peak is measured. This ratio is independent of the type of fluids used and is therefore a practical experimental parameter for examining the relation between the acoustic actuation and the optical observation between different fluids. Figure 7 shows this optical contrast as function of the acoustic impedance. As expected, the optical contrast is raising with decreasing acoustic impedance of the fluid.
Therefore heptane and methanol were the most suitable fluids for visualizing the SAW with this new method, in that they provided the highest contrasts.

Discussion
In order to explain the optical contrast in the experiments, the coupling and reflection of the SAW has to be understood. The excited SAW on the substrate couples into the fluid under the Rayleigh angle Θ 5,49 : c LiNbO 3 and c 1 are the acoustic wave velocities of the piezoelectric substrate LiNbO 3 and the fluid, respectively. Since the acoustic wave velocity on LiNbO 3 was more than two times larger than the velocity in the fluid, the Rayleigh angle is 30° or lower, most of the acoustic pressure is pointing towards the surface of the fluid. A large acoustic impedance mismatch exists at the interface of the fluid and air, resulting in reflection of most of the acoustic energy. The reflection coefficient R was given by 49 :    The acoustic radiation pressure at the surface leads to a deformation of the fluidic surface and causes an optical contrast between excited and non-excited sections of the film visible with the microscope 52,53 . We assume, the deformations induced by the acoustic pressure are related to the curvature of the surface by Laplace's law and causes the different optical contrasts. We observed that the SAW leads to a deformation, however we cannot give an exact quantitative relation between deformation and contrast.
As an example for a qualitative explanation, the acoustic path of a focus IDT is visualized (Fig. 5b) and the grey value for the orange marked is plotted (Fig. 5c). The acoustic radiation pressure at the focal point is maximal and the curvature of the fluid surface is convex and resulting in a bright spot. The fluid close to this point is curved concave, leading to a darker area. The observed contrast depends on the acoustic pressure and the resulting curvature.
Inset of Fig. 8 shows the optical contrast for different fluids as function of the calculated acoustic radiation pressure. The amplitude of the pressure field P 0 is not known but constant for all experiments, as the applied power is kept the same. It is roughly estimated by 0.5 MPa ( =  56,57 . The greatest acoustic radiation pressure is achieved with heptane and methanol. In the experiments these fluids also give the greatest optical contrast and are therefore the most suitable fluids for visualizing the SAW with this new method. This explanation is based on the observations and explanations by Issenmann et al., who examined deformation caused by acoustic radiation pressure in their works 52,53 . They used a focusing, spherical ultrasonic transducer to excite bulk acoustic waves in the fluid to deform a liquid-liquid and liquid-air interface in the focal plane of the transducer. The surface deformation is stationary for moderate acoustic intensities. The authors also described their observations with the theory of Langevin and a one-dimensional model of a compliant Fabry-Pérot resonator. By studying the possibility of mechanical and acoustic streaming effects on the deformation, they concluded that these effects are negligible in comparison to the acoustic radiation pressure. Thus these effects could also be excluded from the theoretical explanation for our experiments. They found that the deformation height is a stationary state, where acoustic radiation pressure, gravity forces and surface tension are in balance. The deformation height depends on the pressure amplitude and applied frequency of the transducer and on the properties of the fluid: surface tension σ, density ρ and speed of sound c. The deformation height h in the centre of the acoustic path for a perpendicular incidence of the SAW is given by: E 1 is the first argument of the exponential integral function. ω is the beam waist, roughly approximated by three wavelengths in our experiments (3•60 μ m) and g the gravitational constant. The acoustic pressure amplitude P 0 is roughly estimated by 0.5 MPa, as before. The deformation height seems responsible for the optical contrast in our experiments. With higher radiation pressure, the deformation height increases as well as the observed optical contrast (Fig. 8).
For our experiments the Bond number   Fig. 2 a CKX41 microscope by Olympus, Germany, with a fixed condenser and a 10 x objective was used.). We used bright-field illumination microscopy in all experiments. High power output was used to enhance visualization (18 dBm to 25 dBm), using an amplifier ZHL-2 (Mini-Circuits). The images were recorded with a high-speed camera (Fastcam 1024 PCI, Photron) using a frame rate between 125 fps and 1000 fps. To improve the wettability, we treated the surface of the chips with an O 2 -plasma. For evaluating the optical contrast the software ImageJ 59 and Fiji 60 were used. For better visibility brightness and contrast were changed for some presented images.