# Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}, where the SAW characteristics depend on the orientation, have gained considerable attention [10]. The sensitivity of SAWs to liquid-loading on the SAW devices has led to a wide range of applications such as liquid shear viscosity measurement [11], glycerin concentration sensing in a microfluidic channel [12], early ovarian cancer detection [13,14], particle and cell separation [15,16,17], and liquid mixing and pumping in microchannels [18,19]. Other useful applications of SAWs are quantifying cell growth [20], quantifying bolt tension in bolted joints [21,22], and pH sensing in cultures [23]. By contrast, only a few applications have taken advantage of the effect of liquid-loading over a solid material (isotropic) on SAWs. One possible application would be estimating liquid height using SAWs. In literature, there are a couple of methods for determining liquid height via using a single or multiple ultrasonic transducer(s), where the basic principle works on the discrepancy in the acoustic impedance of the two media. In one of the studies, the liquid height was measured utilizing two ultrasonic transducers coupled to a tank wall. The first transducer transmits the bulk shear wave that propagates along the solid member in a zigzag path, and the second transducer receives the reflected wave from the solid–liquid interface. Based on the attenuated amplitude of the signal, the acoustic impedance of the liquid can be measured [24]. A non-contact ultrasonic PING sensor was utilized to measure water height with the aid of a microcontroller to calculate the change in the arrival times of the echoes from water [25]. Another method measured liquid height by utilizing three transducers; one transmitter was located between the two echo receiving transducers, and these transducers were encapsulated to overcome the coupling issue. The measurement was achieved by moving the transducers along the container wall, and a noticeable difference in the reflected wave energy was observed when the transmitter moved from the above liquid level to the below liquid level [26].

## 2. Methodology

#### 2.1. Operation Principle

^{2}), ρ is the density of medium (kg/m

^{3}), and c is the sound speed through the material (m/s). The reflection coefficient can be expressed in Equation (2):

_{1}with respect to the normal axis. Besides, the shear wave cannot be supported in the liquid layer [29].

_{1}can be estimated by substituting the longitudinal wave velocity of deionized water (C

_{Lw}), the leaky Rayleigh wave velocity (C

_{LR}), and the propagation angle of the SAW (θ

_{R}) into Snell’s law (see Appendix A).

_{2}with respect to the normal axis at the interface due to the large difference in the speed of sound for the two media. Hence, no refraction occurs into the air, and Snell’s law can no longer be satisfied. The critical incident angle of liquid can be obtained by substituting θ

_{air}= 90° and C

_{Lw}and C

_{air}into Snell’s law (see Appendix A).

_{1}>> c

_{ritical}, the wave will be reflected with angle θ

_{2}, which is equal to θ

_{1}, as illustrated in Figure 1a.

#### 2.2. Liquid Height Estimation

_{A}), which occurs at the solid–fluid interface, and the arrival time of the reflected wave from the top surface of the fluid (t

_{B}). Besides these values, the theoretical speed of sound for the fluid and the refraction angle at the interface (θ

_{1}) are used in determining the liquid height.

_{1}, θ

_{3}, and the geometric dimensions of the container, the first case occurs if the height is approximately in the range of (0 < h < 0.86 L). By contrast, the second case occurs if the height is higher than 0.86 L.

_{1}+ S

_{2,}as illustrated in Figure 2a. S

_{1}and S

_{2}are the distances traveled by the incident wave from the solid–liquid interface (upward) and liquid–air interface (downward), respectively, and L is the actual length of the container. Since the incident angle from the liquid (θ

_{1}) and the reflected angle at the liquid-air interface (θ

_{2}) are equal, S

_{1}= S

_{2}. For the experimental tests, the total distance traveled by a propagating wave in a medium can be expressed as:

_{B}is the arrival time of the reflected wave from the liquid–air interface, and t

_{A}is the arrival time of a leaky Rayleigh wave at the solid–liquid interface. For accuracy purposes, both arrival times should be chosen at the same phase. By substituting S

_{1}= S

_{2}into Equation (3), we get

_{Lw}, the traveling time and the incident angle at the solid–liquid interface. The derivation of the equations for the second case can be found in Appendix A.

#### 2.3. Experimental Setup

^{3}) and then the volume is divided by the height of the container (10 mm), which gives the area as 200 mm

^{2}. The primary purpose of using the container is to maintain the consistency of the area covered by liquid while recording the signal. Initial sets of experiments were conducted to verify that placing the container on the free surface of the specimen had no impact on the propagation of the SAWs. The experiment results confirm that there is no reflection from the containers, since the interface between the specimen’s surface and the container has no real area of contact. The distance between the container and transducer was selected to be 77 mm, which ensured that the container was placed beyond the near field distance (N), which can be estimated using Equation (7).

## 3. Results and Discussion

#### 3.1. The Effect of the Presence of Liquid Media on the Propagation Path of the Reflected Wave from a Defect (Edge)

_{P-RWE}). It is important to note that the wave reflected from the defect (edge or corner in this study) was not affected by the presence of DI water on the surface. By utilizing Equation (8)—where v

_{R}is the theoretical velocity of the Rayleigh wave in 1018 steel (2953 m/s) and T

_{p-wedge}is the time associated with the maximum reflection at the angle beam wedge, which is 29.2 μs—the obtained distance was 103.74 mm, where the actual distance between the transducer and the edge was 105 mm. The reasonably low 1.9% error herein could be due to the theoretical Rayleigh wave velocity or the measurement accuracy.

#### 3.2. The Reflected Wave from the Liquid on the Propagation Path

#### 3.3. Estimating Liquid Height

_{1}+ S

_{2}) and h are obtained for all cases. The actual liquid height is obtained from the relationship between the liquid volume and the cross-sectional area of the liquid, which is 200 mm

^{2}. The purpose of this section is to validate the feasibility of the method by comparing the obtained height from Equation (6) with the actual height of the fluid measured. Additionally, the obtained speed of sound for water is compared with its theoretical value.

_{1}+ S

_{2}) is not accurate. This case represents the second case that is explained in Appendix A.2. To address this issue, the total traveled distance was found via parametric CAD software (Inventor Autodesk 201), as illustrated in Figure 7, for the critical case, 1000 µL, and 1800 µL. From this figure, one can observe that the total traveled distance (S

_{1}+ S

_{2}) for 1000 µL exactly matches the value found in Table 4. By contrast, for 1800 µL, the total traveled distance does not exactly match the table. The corrected value for the case of 1800 µL from the figure is 21.31 mm, which gives a C

_{LW}of 1383 m/s and height of 9.24 mm. Therefore, the error for 1800 µL is dramatically reduced to 2.7%.

#### 3.4. Short-Time Fourier Transform Analysis for Both the Reflected Wave from the Defect (Edge) and the Liquid

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Finding the Refraction Angle

_{1}), Equation (A1) can be utilized. The theoretical value of C

_{Lw}at a temperature of 20 °C, C

_{LR}, and θ

_{LR}are 1480 m/s, 2975.3 m/s, and 90°, respectively. By substituting these values into Snell’s law, as illustrated in Equation (A1), we get:

_{air}= 90°, C

_{Lw}, and C

_{air}into Snell’s law, as in Equation (A4):

#### Appendix A.2. The Derivation Equation for the Second Case when h > 0.86 L

_{3}, and it travels a distance of S

_{3}. Therefore, the total distance traveled in the liquid is S

_{1}+ S

_{2}+ S

_{3}, as shown in Figure 2b. The angle θ

_{3}is measured by substituting the longitudinal velocity of the PLA container, which is experimentally determined to be between 2200 m/s and 2300 m/s, depending on various conditions [31], the velocity of the liquid, and angle θ

_{2}into Snell’s law. The obtained angle θ

_{3}is 50.7° when using the velocity of 2300 m/s.

_{3}value is neglected. Hence, a modification of Equation (6) should be implemented to improve the accuracy of the height measurement. Through analyzing the vector (S

_{1}, S

_{2}, S

_{3}) components with trigonometry as illustrated in Figure 2b, the imaginary part (y) and the real part (x) are derived in terms of θ

_{1}, θ

_{3}, and L as:

_{1}= h/cosθ

_{1}into the previous equations and solving for S

_{2}and S

_{3}in terms of h, θ

_{1}, θ

_{3}, and L, we obtain:

_{3}can be found as:

_{1}= 29.83°, and θ

_{3}= 50.7° and substituting these values into Equations (5), (A10), and (A11), we get S

_{1}, S

_{2}, and S

_{3}equal to 11.52 mm, 4.55 mm, and 7.816 mm, respectively. It can be observed that S

_{1}< S

_{2}+ S

_{3}, which verifies the fact that Equation (6) cannot be applicable when h > 0.86 L. Note that Equation (A11) shows that the height (h) in this case is a function of S

_{3}, whereas it is a function of S

_{2}in Equation (A9).

## References

- Chamuel, J.R. Laboratory studies on pulsed leaky Rayleigh wave components in a water layer over a solid bottom. In Shear Waves in Marine Sediments; Springer: Berlin/Heidelberg, Germany, 1991; pp. 59–66. [Google Scholar]
- Cheeke, J.D.N. Fundamentals and Applications of Ultrasonic Waves; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Überall, H. Surface waves in acoustics. Phys. Acoust.
**1973**, 10, 1–60. [Google Scholar] - Stoneley, R. Elastic waves at the surface of separation of two solids. In Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character; Royal Society: London, UK, 1924; Volume 106, pp. 416–428. [Google Scholar]
- Thompson, D.O.; Chimenti, D.E. Review of Progress in Quantitative Nondestructive Evaluation; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 18. [Google Scholar]
- Zhu, J.; Popovics, J.S.; Schubert, F. Leaky Rayleigh and Scholte waves at the fluid–solid interface subjected to transient point loading. J. Acoust. Soc. Am.
**2004**, 116, 2101–2110. [Google Scholar] [CrossRef] [Green Version] - Brekhovskikh, L. Waves in Layered Media; Elsevier: Amsterdam, The Netherlands, 2012; Volume 16. [Google Scholar]
- Ewing, M.W. Elastic Waves in Layered Media; McGraw-Hill: New York, NY, USA, 1957. [Google Scholar]
- Padilla, F.; de Billy, M.; Quentin, G. Theoretical and experimental studies of surface waves on solid-fluid interfaces when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid. J. Acoust. Soc. Am.
**1999**, 106, 666–673. [Google Scholar] [CrossRef] - Gedge, M.; Hill, M. Acoustofluidics 17: Theory and applications of surface acoustic wave devices for particle manipulation. Lab Chip
**2012**, 12, 2998–3007. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ricco, A.; Martin, S. Acoustic wave viscosity sensor. Appl. Phys. Lett.
**1987**, 50, 1474–1476. [Google Scholar] [CrossRef] - Yildirim, B.; Senveli, S.U.; Gajasinghe, R.W.; Tigli, O. Surface Acoustic Wave Viscosity Sensor with Integrated Microfluidics on a PCB Platform. IEEE Sens. J.
**2018**, 18, 2305–2312. [Google Scholar] [CrossRef] - Franier, B.D.L.; Thompson, M. Early stage detection and screening of ovarian cancer: A research opportunity and significant challenge for biosensor technology. Biosens. Bioelectron.
**2019**, 135, 71–81. [Google Scholar] [CrossRef] [PubMed] - Onen, O.; Sisman, A.; Gallant, N.D.; Kruk, P.; Guldiken, R. A urinary Bcl-2 surface acoustic wave biosensor for early ovarian cancer detection. Sensors
**2012**, 12, 7423–7437. [Google Scholar] [CrossRef] [Green Version] - Guldiken, R.; Jo, M.C.; Gallant, N.D.; Demirci, U.; Zhe, J. Sheathless size-based acoustic particle separation. Sensors
**2012**, 12, 905–922. [Google Scholar] [CrossRef] - Jo, M.C.; Guldiken, R. Active density-based separation using standing surface acoustic waves. Sens. Actuators A Phys.
**2012**, 187, 22–28. [Google Scholar] [CrossRef] - Jo, M.C.; Guldiken, R. Particle manipulation by phase-shifting of surface acoustic waves. Sens. Actuators A Phys.
**2014**, 207, 39–42. [Google Scholar] [CrossRef] - Jo, M.C.; Guldiken, R. Dual surface acoustic wave-based active mixing in a microfluidic channel. Sens. Actuators A Phys.
**2013**, 196, 1–7. [Google Scholar] [CrossRef] - Wang, T.; Ni, Q.; Crane, N.; Guldiken, R. Surface acoustic wave based pumping in a microchannel. Microsyst. Technol.
**2017**, 23, 1335–1342. [Google Scholar] [CrossRef] - Wang, T.; Green, R.; Nair, R.R.; Howell, M.; Mohapatra, S.; Guldiken, R.; Mohapatra, S.S. Surface acoustic waves (SAW)-based biosensing for quantification of cell growth in 2D and 3D cultures. Sensors
**2015**, 15, 32045–32055. [Google Scholar] [CrossRef] [PubMed] - Alhazmi, H.; Guldiken, R. Quantification of Bolt Tension by Surface Acoustic Waves: An Experimentally Verified Simulation Study. Acoustics
**2019**, 1, 794–807. [Google Scholar] [CrossRef] [Green Version] - Martinez, J.; Sisman, A.; Onen, O.; Velasquez, D.; Guldiken, R. A synthetic phased array surface acoustic wave sensor for quantifying bolt tension. Sensors
**2012**, 12, 12265–12278. [Google Scholar] [CrossRef] [Green Version] - Wang, T.; Green, R.; Guldiken, R.; Mohapatra, S.; Mohapatra, S. Multiple-layer guided surface acoustic wave (SAW)-based pH sensing in longitudinal FiSS-tumoroid cultures. Biosens. Bioelectron.
**2019**, 124, 244–252. [Google Scholar] [CrossRef] - Lynnworth, L.C.; Seger, J.L.; Bradshaw, J.E. Ultrasonic System for Measuring Fluid Impedance or Liquid Level. U.S. Patent 4,320,659, 23 March 1982. [Google Scholar]
- Mohammed, S.L.; Al-Naji, A.; Farjo, M.M.; Chahl, J. Highly Accurate Water Level Measurement System Using a Microcontroller and an Ultrasonic Sensor. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, England, 2019; Volume 518, p. 042025. [Google Scholar]
- Zhang, B.; Wei, Y.-J.; Liu, W.-Y.; Zhang, Y.-J.; Yao, Z.; Zhang, L.; Xiong, J.-J. A novel ultrasonic method for liquid level measurement based on the balance of echo energy. Sensors
**2017**, 17, 706. [Google Scholar] [CrossRef] [Green Version] - Giurgiutiu, V. Structural Health Monitoring with Piezoelectric Wafer Active Sensors: With Piezoelectric Wafer Active Sensors; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar]
- Hevin, G.; Abraham, O.; Pedersen, H.; Campillo, M. Characterization of surface cracks with Rayleigh waves: A numerical model. NDT & E Int.
**1998**, 31, 289–297. [Google Scholar] [CrossRef] - Rose, J.L. Ultrasonic Waves in Solid Media; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Ohara, Y.; Oshiumi, T.; Nakajima, H.; Yamanaka, K.; Wu, X.; Uchimoto, T.; Takagi, T.; Tsuji, T.; Mihara, T. Ultrasonic phased array with surface acoustic wave for imaging cracks. AIP Adv.
**2017**, 7, 065214. [Google Scholar] [CrossRef] [Green Version] - Parker, N.; Mather, M.; Morgan, S.; Povey, M. Longitudinal acoustic properties of poly (lactic acid) and poly (lactic-co-glycolic acid). Biomed. Mater.
**2010**, 5, 055004. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kehtarnavaz, N.; Kim, N. Digital Signal Processing System-Level Design Using LabVIEW; Elsevier: Amsterdam, The Netherlands, 2011. [Google Scholar]
- Giannakopoulos, T.; Pikrakis, A. Introduction to Audio Analysis: A MATLAB
^{®}Approach; Academic Press: Cambridge, MA, USA, 2014. [Google Scholar]

**Figure 1.**(

**a**) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid interface is larger than the critical angle; (

**b**) Schematic representation of a wave traveling in the liquid when the reflected angle at the solid–liquid interface is equal to the critical reflected angle.

**Figure 2.**(

**a**) Schematic representation of a wave traveling at a different level of liquid, including the critical case, which occurs at h < 0.86 L (first case); (

**b**) Schematic representation of a wave traveling in the liquid when the liquid height is higher than 0.86 L (case 2).

**Figure 3.**(

**a**) Schematic diagram for the experiment setup; (

**b**) The container dimensions used in this study.

**Figure 4.**The entire signal received for the empty container, including the selected windows for the reflection from the liquid and the reflection from the edge.

**Figure 7.**The CAD results for the wave traveling in the liquid, showing the actual total traveled distance for three cases: the (

**a**) critical case; (

**b**) 1000 µL case, and (

**c**) 1800 µL case.

**Figure 8.**(

**a**) Short-Time Fourier Transform for the reflection from edge/corner in all cases: (

**a1**) empty, (

**a2**) 400 µL, (

**a3**) 600 µL, (

**a4**) 1000 µL, and (

**a5**) 1800 µL; (

**b**) STFT for the reflection from the liquid in all cases: (

**b1**) empty, (

**b2**) 400 µL, (

**b3**) 600 µL, (

**b4**) 1000 µL, and (

**b5**) 1800 µL.

PRF(Hz) | Energy | Damping (50 Ω) | High Pass Filter (HPF) | Low Pass Filter (LPF) | Amplifier (Gain) |
---|---|---|---|---|---|

100 | 1 | 3 | 1 MHz | 10 MHz | 30 db |

Deionized Water | 1018 Steel | Air | PLA (25 °C) | |
---|---|---|---|---|

Density, ρ (g/cm^{3}) | 1 | 7.870 | 0.001 | 1.24 |

Speed of Sound (m/s) | 1480 | 2953 (C.R.) | 330–343 | 2200~2300 [31] |

**Table 3.**The percentage drop in the peak-to-peak amplitude of the reflected wave from the edge for all cases.

Empty | 400 µL | 600 µL | 1000 µL | 1800 µL | |
---|---|---|---|---|---|

P–P amplitude (V) | 1.90 | 0.74 | 0.72 | 0.70 | 0.70 |

$\%=\frac{x-empty}{empty}\times 100$ | - | −61.05 | −62.11 | −63.16 | −63.16 |

Actual Height (mm) | t_{A}(µs) | t_{B}(µs) | t_{c}(µs) | C_{LW}(m/s) | Error in C_{LW}(%) | S_{1} + S_{2}(mm) | h (mm) | Error in h (%) | |
---|---|---|---|---|---|---|---|---|---|

400 µL | 2 | 80.96 | 84.19 | 87.18 | 1427.5 | −3.54% | 4.8 | 2.07 | 3.7 |

600 µL | 3 | 80.96 | 85.51 | 87.18 | 1520.1 | 2.71% | 6.7 | 2.92 | −2.6 |

1000 µL | 5 | 80.96 | 88.64 | 87.21 | 1501 | 1.42% | 11.4 | 4.93 | −1.4 |

1800 µL | 9 | 80.96 | 96.36 | 87.22 | 1347.4 | −8.96% | 22.8 | 9.89 | 9.8/2.7 * |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alhazmi, H.; Guldiken, R.
Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves. *Acoustics* **2020**, *2*, 366-381.
https://doi.org/10.3390/acoustics2020021

**AMA Style**

Alhazmi H, Guldiken R.
Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves. *Acoustics*. 2020; 2(2):366-381.
https://doi.org/10.3390/acoustics2020021

**Chicago/Turabian Style**

Alhazmi, Hani, and Rasim Guldiken.
2020. "Contactless Liquid Height and Property Estimation Using Surface Acoustic Waves" *Acoustics* 2, no. 2: 366-381.
https://doi.org/10.3390/acoustics2020021