Ultrasonic Propagation in Liquid and Ice Water Drops. Effect of Porosity
2. Materials and Methods
2.1. Experiments on Frozen Drops
2.2. Theoretical Study: Simulations of Wave Propagation and Influence of Porosity on Ultrasonic Velocity
3.1. Drop Experiments
3.1.1. Compact Liquid/Ice Drops
Statistical Results for Compact Liquid/Ice Water Drops
3.1.2. Porous Liquid/Ice Drops
Drop Experiment 1 Using Sparkling Water
Drop Experiment 2, also Using Sparkling Water
Statistical Results for Porous Liquid/Ice Water Drops
3.1.3. Ethanol Drops
3.2. Numerical Simulation of Propagation Waves in Liquid Water and Ice Drops
3.2.1. Liquid Water and Compact Ice Drops
- At 0.10 µs, a longitudinal ultrasonic pulse is transmitted from the transducer and the wave front penetrates into the ice drop.
- At 0.57 µs, the wavefront encounters the curvature of the drop surface after which the longitudinal wave is reflected. These reflections contribute to a horizontal propagation within the drop. The undisturbed part of the longitudinal wave continues to propagate towards the top of the drop surface.
- At 0.75 µs, the first horizontal reflected wavefronts meet in the centre of the drop and start interfering with each other.
- At 0.94 µs, the undisturbed wavefront of the original pulse reaches the surface at the top of the drop. Meanwhile, the horizontal wavefronts from the reflections dominate the reading of the transducer. This is the reason why reflective signals are observed in the experiments before the reflection peak coming from the top of the drop.
- At 1.32 µs, the reflection from the top of the drop is travelling towards the transducer.
- At 1.70 µs, impact of the reflection of the ultrasonic signal from the top of the drop onto the transducer. This impact creates the first large peak in in the measured ultrasonic response.
- At 1.79 µs, after the impact, this strong signal will be reflected back to the top of the drop.
- At 2.45 µs, the reflected signal approaches the surface of the top of the drop again. Once more, disturbing interactions of other pressure waves interact with the transducer.
- At 2.55 µs, after this second impact it can be seen that the reflected signal is significantly attenuated by this impact.
- At 2.83 µs, interference of a curved wave front moving towards a common centre point makes the amplitude locally higher, resulting in a dark-red dot in the simulation frame moving towards the transducer now.
- At 3.21 µs, close to the transducer the wave front is more dispersed, which decreases its intensity.
- At 3.30 µs, the second impact on the transducer of the reflected wave from the top of the drop. This creates a second, smaller peak.
3.2.2. Porous Liquid and Ice Drops
- At 1.1 µs, the wave front is dispersed by pores near the transducer forming numerous peaks in the A-scan.
- At 1.5 µs, the wave front is thus considerably attenuated by the pore interactions on its way to the drop surface.
- At 2.0 µs, arrival at the top of drop surface, the weakened front wave travels back in the direction of the transducer.
- At 2.4 µs, the reflected wave front A is about to merge with two intense wave fronts; on the left, B, and on the right side, C. Wave front C was also reflected from the drop surface, while wave front B was a residual that did not reach the drop surface.
- At 3.1 µs, the coalescence of these waves produces a reinforced new front wave.
- At 3.3 µs, this new front wave interacts with the pores located around the center of the drop.
- At 3.6 µs, the new front wave is heavily dispersed by the pores.
- At 4.0 µs, the first fragment of the dispersed front wave arrives to the transducer.
- At 0.3 µs the wave front is dispersed by pores near the transducer forming numerous peaks in the A-scan.
- At 0.6 µs the wave front is considerably attenuated by the pore interactions on its way to the drop surface. Numerous high-intensity waves arrive continually to the transducer producing peaks in the A-scan. The intensity of the received signal is, however, highly variable.
- At 0.8 µs the wave front arrives at the top of drop surface. The weakened wave front then travels back in the direction of the transducer.
- At 1.0 µs, unlike the liquid drop case, there is no obvious merging of wave fronts and the reflected wave front does not find its way back to the transducer.
Comparison of Theoretical and Measured Velocity from Micromechanical Model
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
- Muñoz Caro, G.M.; Escribano, R. Laboratory Astrophysics, 1st ed.; Springer International Publishing: Berlin/Heidelberg, Germany, 2018. [Google Scholar]
- Öberg, K.I. Photochemistry and astrochemistry: photochemical pathways to interstellar complex organic molecules. Chem. Rev. 2016, 116, 9631–9663. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Cazaux, S.; Bossa, J.-B.; Linnartz, H.; Tielens, A.G.G.M. Pore evolution in interstellar ice analogues simulating the effects of temperature increase. Astron. Astrophys. 2015, 573, A16. [Google Scholar] [CrossRef][Green Version]
- Millán, C.; Santonja, C.; Domingo, M.; Luna, R.; Satorre, M.Á. An experimental test for effective medium approximations (EMAs). Porosity determination for ices of astrophysical interest. Astron. Astrophys. 2019, 628, A63. [Google Scholar] [CrossRef]
- Dohnálek, Z.; Kimmel, G.A.; Ayotte, P.; Smith, R.S.; Kay, B.D. The deposition angle-dependent density of amorphous solid water films. J. Chem. Phys. 2003, 118, 364–372. [Google Scholar] [CrossRef]
- Robinson, D.E.; Ophir, J.; Wilson, L.S.; Chen, C.F. Pulse-echo ultrasound speed measurements: Progress and prospects. Ultrasound Med. Biol. 1991, 17, 633–646. [Google Scholar] [CrossRef]
- Hellier, C.J. Handbook of Nondestructive Evaluation; McGraw-Hill Companies Inc.: New York, NY, USA, 2003; ISBN 007139947X. [Google Scholar]
- Afifi, H.A.A. Ultrasonic pulse echo studies of the physical properties of PMMA, PS, and PVC. Polym. Plast. Technol. Eng. 2006, 42, 193–205. [Google Scholar] [CrossRef]
- Carlson, J.; Nilsson, M.; Fernández, E.; Planell, J.A. An ultrasonic pulse-echo technique for monitoring the setting of CaSO4-based bone cement. Biomaterials 2003, 24, 71–77. [Google Scholar] [CrossRef][Green Version]
- Mikesell, T.D.; van Wijk, K.; Otheim, L.T.; Marshall, H.-P.; Kurbatov, A. Laser Ultrasound Observations of Mechanical Property Variations in Ice Cores. Geosciences 2017, 7, 47. [Google Scholar] [CrossRef][Green Version]
- Vaughan, M.J.; van Wijk, K.; Prior, D.J.; Bowm, M.H. Monitoring the temperature-dependent elastic and anelastic properties in isotropic polycrystalline ice using resonant ultrasound spectroscopy. Cryosphere 2016, 10, 2821–2829. [Google Scholar] [CrossRef][Green Version]
- Cheng, C.-C.; Tseng, Y.-H.; Huang, S.-C. An Innovative Ultrasonic Apparatus and Technology for Diagnosis of Freeze-Drying Process. Sensors 2019, 19, 2181. [Google Scholar] [CrossRef][Green Version]
- Gao, H.; Rose, J.L. Ice Detection and Classification on an Aircraft Wing with Ultrasonic Shear Horizontal Guided Waves. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2009, 56, 334–344. [Google Scholar]
- Liu, Y.; Bond, L.J.; Hu, H. Ultrasonic-Attenuation-Based Technique for Ice Characterization Pertinent to Aircraft Icing Phenomena. AIAA J. 2017, 55, 1602–1609. [Google Scholar] [CrossRef]
- Fuleki, D.; Sun, Z.; Wu, J.; Miller, G. Development of a Non-Intrusive Ultrasound Ice Accretion Sensor to Detect and Quantify Ice Accretion Severity. In Proceedings of the 9th AIAA Atmospheric and Space Environments Conference, Denver, CO, USA, 5–9 June 2017. [Google Scholar]
- Hernández, M.G.; Anaya, J.J.; Sanchez, T.; Segura, I. Porosity estimation of aged mortar using a micromechanical model. Ultrasonics 2006, 44, e1007–e1011. [Google Scholar] [CrossRef]
- García, J.E.; Density of Aqueous Solutions of CO2. Lawrence Berkley National Laboratory e Scholarship. 2001. Available online: http://escholarship.org/uc/item/6dn022hb (accessed on 3 May 2021).
- Molero-Armenta, M.; Iturrarán-Viveros, U.; Aparicio, S.; Hernández, M.G. Optimized OpenCL Implementation of the Elastodynamic Finite Integration Technique for viscoelastic media. Comput. Phys. Comm. 2014, 185, 2683–2696. [Google Scholar] [CrossRef]
- SimNDT. Available online: https://github.com/mmolero/SimNDT (accessed on 6 April 2021).
- OpenCL. Available online: http://www.khronos.org/opencl/ (accessed on 6 April 2021).
- Klockner, A.; Pinto, N.; Lee, Y.; Catanzaro, B.; Ivanov, P.; Fasih, A. PyCUDA and PyOpenCL: A scripting-based approach to GPU run-time code generation. Parallel Comput. 2012, 38, 157–174. [Google Scholar] [CrossRef][Green Version]
- Hernández, M.G.; Anaya, J.J.; Ullate, L.G.; Ibáñez, A. Formulation of a new micromechanic model of three phases for ultrasonic characterization of cement-based materials. Cem. Concr. Res. 2006, 36, 609–616. [Google Scholar] [CrossRef]
- Hill, R. The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A 1957, 65, 349–354. [Google Scholar] [CrossRef]
- Wu, T.T. The effect on inclusion shape on the elastic moduli of a two place material. Int. J. Solids Struct. 1966, 2, 1–8. [Google Scholar] [CrossRef]
- Vogt, C.; Laihem, K.; Wiebusch, C. Speed of sound in bubble-free ice. J. Acoust. Soc. Am. 2009, 124, 3613–3618. [Google Scholar] [CrossRef]
- Wilson, W.; Bradley, D. Ultrasonic velocity in four primary alcohols as a function of temperature and pressure. J. Acoust. Soc. Am. 1964, 36, 333–337. [Google Scholar] [CrossRef]
- D’Arrigo, G.; Paparelli, A. Sound propagation in water-ethanol mixtures at low temperatures. I. Ultrasonic velocity. J. Chern. Phys. 1988, 88, 405–415. [Google Scholar] [CrossRef]
- Vatandas, M.; Koc, A.B.; Koc, C. Ultrasonic velocity measurements in ethanol–waterand methanol–water mixtures. Eur. Food Res. Technol. 2007, 225, 525–532. [Google Scholar] [CrossRef]
|C11 (GPa)||C44 (GPa)||ρ (kg/m3)|
|VR.T.||V0 °C||V−18 °C|
|VR.T.||V0 °C||V−18 °C|
|# of useful experiments||18||8||8|
|Mean experiment (m/s)||1477.55||1454.47||3922.25|
|SD Experiments (m/s)||104.18||62.20||151.28|
|SD Experiments (%)||7.05||4.28||3.86|
|VR.T.||V0 °C||V−18 °C|
|# of useful experiments||13||20||19|
|Compact Lit. (m/s)||1481.00||1403.00||3888.50|
|Mean experiment (m/s)||1343.84||1299.97||3435.99|
|SD Experiments (m/s)||123.59||145.29||376.58|
|SD Experiments (%)||9.20||11.18||10.96|
|VR.T.||V0 °C||V−18 °C|
|Compact ice drop||Mean (m/s)||1477.55||1454.47||3922.25|
|Porous ice drop||Mean (m/s)||1343.84||1299.97||3435.99|
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
© 2021 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 (https://creativecommons.org/licenses/by/4.0/).
Mendonck, M.; Aparicio, S.; González Díaz, C.; Hernández, M.G.; Muñoz Caro, G.M.; Anaya, J.J.; Cazaux, S. Ultrasonic Propagation in Liquid and Ice Water Drops. Effect of Porosity. Sensors 2021, 21, 4790. https://doi.org/10.3390/s21144790
Mendonck M, Aparicio S, González Díaz C, Hernández MG, Muñoz Caro GM, Anaya JJ, Cazaux S. Ultrasonic Propagation in Liquid and Ice Water Drops. Effect of Porosity. Sensors. 2021; 21(14):4790. https://doi.org/10.3390/s21144790Chicago/Turabian Style
Mendonck, Michiel, Sofía Aparicio, Cristóbal González Díaz, Margarita G. Hernández, Guillermo M. Muñoz Caro, José Javier Anaya, and Stéphanie Cazaux. 2021. "Ultrasonic Propagation in Liquid and Ice Water Drops. Effect of Porosity" Sensors 21, no. 14: 4790. https://doi.org/10.3390/s21144790