Approach to nonlinearity parameter in liquids calculation based on the scaling theory of thermodynamic fluctuations

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Abstract

The nonlinearity parameter B/A is a characteristic of liquids and soft matter, which gains growing attention due to its sensibility to the composition of materials. This makes it a prospective indicator for nondestructive testing applications based on the ultrasound sounding suitable for a variety of applications from physic chemistry to biomedical studies. At the same time, the thermodynamic definition of the nonlinearity parameter requires extensive measurements at elevated pressures that are not always available; in addition, there are known certain contradiction of such data with the data obtained by methods of nonlinear acoustics. Objective. In this work, we consider a recently proposed approach to the prediction of the speed of sound at high pressures, which uses the property of invariance of the reduced pressure fluctuations and the data obtained at normal ambient pressure only. The method generalises the classic Nomoto model, which however gives only a qualitative picture, and results in the quantitative correspondence to the experimental values within their range of uncertainty. Methods. Analytical methods of the theory of thermodynamic fluctuations applied to the parameters of equations of nonlinear acoustics as well as numerical simulation in the COMSOL Multiphysics® environment. Results. Expressions for calculating the nonlinearity parameter with acceptable accuracy were obtained using thermodynamic data obtained only at atmospheric pressure. Numerical calculations were performed for toluene. In addition, the discrepancy between values of the nonlinear parameter obtained via the thermodynamic and nonlinear acoustic routes is analysed based on the numerical solution of the Westervelt equation; it is revealed that this deviation emerges when the effects of absorption of finite-amplitude waves were not properly taken into account.

About the authors

Roman N Belenkov

Kursk State University

Kursk, Radishchev str., 33

Eugene B Postnikov

Kursk State University

Kursk, Radishchev str., 33

References

  1. Зарембо Л. К., Красильников В. А. Некоторые вопросы распространения ультразвуковых волн конечной амплитуды в жидкостях // Успехи физических наук. 1959. Т. 68, № 4. С. 687–715. doi: 10.3367/UFNr.0068.195908e.0687.
  2. Fox F. E., Wallace W. A. Absorption of finite amplitude sound waves // Journal of the Acoustical Society of America. 1954. Vol. 26, no. 6. P. 994–1006. doi: 10.1121/1.1907468.
  3. Beyer R. T. Lord Rayleigh and nonlinear acoustics // Journal of the Acoustical Society of America. 1995. Vol. 98, no. 6. P. 3032–3034. doi: 10.1121/1.414465.
  4. Lord Rayleigh O. M. F. R. S. XLII. On the momentum and pressure of gaseous vibrations, and on the connexion with the virial theorem // The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1905. Vol. 10, no. 57. P. 364–374. doi: 10.1080/14786440509463381.
  5. Beyer R. T. Parameter of nonlinearity in fluids // Journal of the Acoustical Society of America. 1960. Vol. 32, no. 6. P. 719–721. doi: 10.1121/1.1908195.
  6. Shutilov V. A. Fundamental Physics of Ultrasound. London: CRC Press, 1988. 394 p. DOI: 10.1201/ 9780429332227.
  7. Cobbold R. S. C. Foundations of Biomedical Ultrasound. Oxford: Oxford University Press, 2006. 832 p.
  8. Lauterborn W., Kurz T., Akhatov I. Nonlinear acoustics in fluids // In: Rossing T. (eds) Springer Handbook of Acoustics. Springer Handbooks. New York: Springer, 2007. P. 257–297. doi: 10.1007/978-0-387-30425-0_8.
  9. Panfilova A., van Sloun R. J. G., Wijkstra H., Sapozhnikov O. A., Mischi M. A review on B/A measurement methods with a clinical perspective // Journal of the Acoustical Society of America. 2021. Vol. 149, no. 4. P. 2200–2237. doi: 10.1121/10.0003627.
  10. Duck F. A. Nonlinear acoustics in diagnostic ultrasound // Ultrasound in Medicine & Biology. 2002. Vol. 28, no. 1. P. 1–18. doi: 10.1016/S0301-5629(01)00463-X.
  11. Gan W. S. B/A nonlinear parameter acoustical imaging // In: Nonlinear Acoustical Imaging. Singapore: Springer, 2021. P. 37–48. doi: 10.1007/978-981-16-7015-2_6.
  12. Dzida M., Zorebski E., Zoreebski M., Zarska M., Geppert-Rybcznska M., Chorazewski M., Jacquemin J., Cibulka I. Speed of sound and ultrasound absorption in ionic liquids // Chemical Reviews. 2017. Vol. 117, no. 5. P. 3883–3929. doi: 10.1021/acs.chemrev.5b00733.
  13. Tiwari R. K., Verma V., Awasthi A., Trivedi S. K., Pandey P. K., Awasthi A. Comparative study of acoustic non-linearity parameter in binary mixtures of N,N-dimethylacetamide with Polyethylene Glycols at different temperatures // Journal of Molecular Liquids. 2021. Vol. 343. P. 117707. doi: 10.1016/j.molliq.2021.117707.
  14. Jordan P. M. A survey of weakly-nonlinear acoustic models: 1910–2009 // Mechanics Research Communications. 2016. Vol. 73. P. 127–139. doi: 10.1016/j.mechrescom.2016.02.014.
  15. Kaltenbacher B., Rundell W. On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements // Inverse Problems & Imaging. 2021. Vol. 15, no. 5. P. 865–891. doi: 10.3934/ipi.2021020.
  16. Nomoto O. Nonlinearity parameter of the “Rao liquid” // Journal of the Physical Society of Japan. 1966. Vol. 21, no. 4. P. 569–571. doi: 10.1143/JPSJ.21.569.
  17. Sharma B. K. Nonlinearity acoustical parameter and its relation with Rao’s acoustical parameter of liquid state // Journal of the Acoustical Society of America. 1983. Vol. 73, no. 1. P. 106–109. doi: 10.1121/1.388842.
  18. Rao M. R. Velocity of sound in liquids and chemical constitution // Journal of Chemical Physics. 1941. Vol. 9, no. 9. P. 682–685. doi: 10.1063/1.1750976.
  19. Wada Y. On the relation between compressibility and molal volume of organic liquids // Journal of the Physical Society of Japan. 1949. Vol. 4, no. 4–6. P. 280–283. doi: 10.1143/JPSJ.4.280.
  20. Daridon J.-L., Coutinho J. A. P., Ndiaye E. H. I., Paredes M. L. L. Novel data and a group contribution method for the prediction of the speed of sound and isentropic compressibility of pure fatty acids methyl and ethyl esters // Fuel. 2013. Vol. 105. P. 466–470. doi: 10.1016/j.fuel. 2012.09.083.
  21. Gupta A. K., Gardas R. L. The constitutive behavior of ammonium ionic liquids: a physiochemical approach // RSC Advances. 2015. Vol. 5, no. 58. P. 46881–46889. doi: 10.1039/C5RA02391B.
  22. Zhang Y., Zheng X., He M.-G., Chen Y. Speed of sound in methyl caprate, methyl laurate, and methyl myristate: measurement by Brillouin light scattering and prediction by Wada’s group contribution method // Energy & Fuels. 2016. Vol. 30, no. 11. P. 9502–9509. DOI: 10.1021/ acs.energyfuels.6b01959.
  23. Praharaj M. K., Misra S. Ultrasonic and conductometric studies of NaCl solutions and study of ionicity of the liquid solution through the Walden plot and various ultrasonic parameters // Journal of Thermal Analysis and Calorimetry. 2018. Vol. 132, no. 2. P. 1089–1094. doi: 10.1007/s10973- 018-7038-9.
  24. Daridon J.-L. Predicting and correlating speed of sound in long-chain alkanes at high pressure // International Journal of Thermophysics. 2022. Vol. 43, no. 5. P. 78. doi: 10.1007/s10765-022-02999-x.
  25. Postnikov E. B., Jasiok B., Melent’ev V. V., Ryshkova O. S., Korotkovskii V. I., Radchenko A. K., Lowe A. R., Chorazewski M. Prediction of high pressure properties of complex mixtures without knowledge of their composition as a problem of thermodynamic linear analysis // Journal of Molecular Liquids. 2020. Vol. 310. P. 113016. doi: 10.1016/j.molliq.2020.113016.
  26. Lu Z., Daridon J. L., Lagourette B., Ye S. A phase-comparison method for measurement of the acoustic nonlinearity parameter B/A // Measurement Science and Technology. 1998. Vol. 9, no. 10. P. 1699–1705. doi: 10.1088/0957-0233/9/10/009.
  27. Lagemann R. T., Corry J. E. Velocity of sound as a bond property // Journal of Chemical Physics. 1942. Vol. 10, no. 12. P. 759. doi: 10.1063/1.1723659.
  28. Schaaffs W. Molekularakustische Ableitung einer Zustandsgleichung fur Flussigkeiten bei hohen Drucken // Acustica. 1974. Bd. 30. S. 275–280.
  29. Kudryavtsev B. B., Samgina G. A. Use of ultrasonic measurements in the study of molecular interactions in liquids // Soviet Physics Journal. 1966. Vol. 9, no. 1. P. 5–8. DOI: 10.1007/ BF00818478.
  30. Aziz R. A., Bowman D. H., Lim C. C. An examination of the relationship between sound velocity and density in liquids // Canadian Journal of Physics. 1972. Vol. 50, no. 7. P. 646–654. doi: 10.1139/p72-089.
  31. Lemmon E. W., Span R. Short fundamental equations of state for 20 industrial fluids // Journal of Chemical & Engineering Data. 2006. Vol. 51, no. 3. P. 785–850. doi: 10.1021/je050186n.
  32. Diky V., Muzny C. D., Lemmon E. W., Chirico R. D., Frenkel M. ThermoData Engine (TDE): Software implementation of the dynamic data evaluation concept. 2. Equations of state on demand and dynamic updates over the web // Journal of Chemical Information and Modeling. 2007. Vol. 47, no. 4. P. 1713–1725. doi: 10.1021/ci700071t.
  33. Lafarge T., Possolo A. The NIST Uncertainty Machine // NCSLI Measure. 2015. Vol. 10, no. 3. P. 20–27. doi: 10.1080/19315775.2015.11721732.
  34. Шкловская-Корди В. В. Акустический метод определения внутреннего давления в жидкости // Акустический журнал. 1963. Т. 9, № 1. С. 107–111.
  35. Wu J. Handbook of Contemporary Acoustics and Its Applications. Singapore: World Scientific, 2016. 468 p. doi: 10.1142/9470.
  36. Nonlinear Acoustics – Modeling of the 1D Westervelt Equation [Electronic resource]. Application ID: 12783. COMSOL Multiphysics®, 2022. Available from: https://www.comsol.ru/model/ nonlinear-acoustics-8212-modeling-of-the-1d-westervelt-equation-12783.
  37. Hamilton M. F., Blackstock D. T. Nonlinear Acoustics. San Diego: Academic Press, 1998. 455 p.
  38. Chien L. D., Cormack J. M., Everbach E. C., Hamilton M. F. Determination of nonlinearity parameter B/A of liquids by comparison with solutions of the three-dimensional Westervelt equation // Proceedings of Meetings on Acoustics. 2021. Vol. 45, no. 1. P. 020003. DOI: 10.1121/ 2.0001563.
  39. Зарембо Л. К., Красильников В. А., Шкловская-Корди В. В. О распространении ультразвуковых волн конечной амплитуды в жидкостях // Акустический журнал. 1957. Т. 3, № 1. С. 29–36.
  40. Dukhin A. S., Goetz P. J. Bulk viscosity and compressibility measurement using acoustic spectroscopy // Journal of Chemical Physics. 2009. Vol. 130, no. 12. P. 124519. doi: 10.1063/1.3095471.
  41. Ramires M. L. V., Nieto de Castro C. A., Perkins R. A., Nagasaka Y., Nagashima A., Assael M. J., Wakeham W. A. Reference data for the thermal conductivity of saturated liquid toluene over a wide range of temperatures // Journal of Physical and Chemical Reference Data. 2000. Vol. 29, no. 2. P. 133–139. doi: 10.1063/1.556057.
  42. Jasiok B., Postnikov E. B., Pikalov I. Y., Chorazewski M. Prediction of the speed of sound in ionic liquids as a function of pressure // Journal of Molecular Liquids. 2022. Vol. 363. P. 119792. doi: 10.1016/j.molliq.2022.119792.

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