Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Isaeva E. A., Isaeva A. A., Alonova M. V. Acoustic emission method for analyzing the structural evolution of foam-like media. Izvestiya of Saratov University. Physics , 2026, vol. 26, iss. 2, pp. 225-232. DOI: 10.18500/1817-3020-2026-26-2-225-232, EDN: XHJCGF

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.06.2026
Full text:
(downloads: 4)
Language: 
Russian
Article type: 
Article
UDC: 
534.08
EDN: 
XHJCGF

Acoustic emission method for analyzing the structural evolution of foam-like media

Autors: 
Isaeva Elena Andreevna, Yuri Gagarin State Technical University of Saratov
Isaeva Anna Andreevna, Yuri Gagarin State Technical University of Saratov
Alonova Marina Vasil'evna, Yuri Gagarin State Technical University of Saratov
Abstract: 

Background and Objectives: In metastable gas-liquid foams, structural rearrangement occurs during their evolution under conditions of local mass transfer of the liquid and gas components of the system. Rearrangement and coalescence events of gas bubbles will be reflected in the foam’s acoustic emission spectrum. Structural modification of gas-liquid foams under conditions of constant volume fractions of liquid and gas is governed by capillary forces, film thickness, and the area of the foam’s liquid films. This work examines the typical behavior of the acoustic emission spectrum of a gas-liquid foam in the low-frequency region, considering the scaling dependence of the average gas cell radius on time. Materials and Methods: The acoustic emission spectrum of a model gas-liquid foam was studied during its evolution in the low–frequency range. Using microscopy methods, the temporal dependencies of changes in the average foam gas cell size were obtained. Results: The time dependence of the average size of gas cells in a model gas–liquid foam exhibits a characteristic power-law dependence on time with an exponent of 0.5. The recorded acoustic signal is generated by a set of coalescence and rearrangement events of gas cells within the medium and, during foam evolution, will be described by a characteristic spatial scale proportional to the average bubble size 〈R(t)〉. Conclusion: The possibility of using acoustic emission signal analysis to study the structural modifications in a metastable two-component system during its evolution under self-similarity conditions has been demonstrated. It has been shown that the scaling laws governing the evolution of the gas-liquid foam’s emission spectra and the dependence of the average gas cell radius reflect the dynamic self-similarity. The comparison of critical exponents allows us to analyze the kinetics of local inhomogeneity changes and the morphological evolution of the two-component system.

Acknowledgments: 
The study was supported by the Russian Science Foundation (project No. 25-29-00679, https://rscf.ru/project/25-29-00679/).
Reference: 
  1. Maksoud F. J., de la Paz M. F. V., Hann A. J., Thanarak J., Gwendolen C Reilly G. C., Claeyssens F., Green N. H., Zhang Yu S. Porous biomaterials for tissue engineering: A review. J. Mater. Chem. B, 2022, vol. 10, iss. 40, pp. 8111–8165. https://doi.org/10.1039/d1tb02628c
  2. Sultana N., Cole A., Strachan F. Biocomposite scaffolds for tissue engineering: Materials, fabrication techniques and future directions. Materials (Basel), 2024, vol. 17, no. 22, art. 5577. https://doi.org/10.3390/ma17225577
  3. Lutzweiler G., Halili A. N., Vrana N. E. The overview of porous, bioactive scaffolds as instructive biomaterials for tissue regeneration and their clinical translation. Pharmaceutics, 2020, vol. 12, no. 7, art. 602. https://doi.org/10.3390/pharmaceutics12070602
  4. Murphy C. M., Haugh M. G., O’Brien F. J. The effect of mean pore size on cell attachment, proliferation and migration in collagen–glycosaminoglycan scaffolds for bone tissue engineering. Biomaterials, 2010, vol. 31, iss. 3, pp. 461–466. https://doi.org/10.1016/j.biomaterials.2009.09.063
  5. Loh Q. L., Choong C. Three-dimensional scaffolds for tissue engineering applications: Role of porosity and pore size. Tissue Eng. Part B: Reviews, 2013, vol. 19, no. 6, pp. 485–502. https://doi.org/10.1089/ten.teb.2012.0437
  6. Matsiko A., Gleeson J. P., O’Brien F. J. Scaffold mean pore size influences mesenchymal stem cell chondrogenic differentiation and matrix deposition. Tissue Eng. Part A, 2015, vol. 21, no. 3–4, pp. 486-497. https://doi.org/10.1089/ten.tea.2013.0545
  7. Vera M. U., Saint-Jalmes A., Durian D. J. Scattering optics of foam. Appl. Opt., 2001, vol. 40, iss. 24, pp. 4210–4214. https://doi.org/10.1364/AO.40.004210
  8. Durian D. J., Weitz D. A., Pine D. J. Multiple light-scattering probes of foam structure and dynamics. Science, 1991, vol. 252, iss. 5006, pp. 686–688. https://doi.org/10.1126/science.252.5006.686
  9. Erpelding M., Guillermic R. M., Dollet B., SaintJalmes A., Crassous J. Investigating acoustic-induced deformations in a foam using multiple light scattering. Phys. Rev. E, 2010, vol. 82, art. 021409. https://doi.org/10.1103/PhysRevE.82.021409
  10. Lambert J., Mokso R., Cantat I., Cloetens P., Glazier J. A., Graner F., Delannay R. Coarsening foams robustly reach a self-similar growth regime. Phys. Rev. Lett., 2010, vol. 104, art. 248304. https://doi.org/10.1103/PhysRevLett.104.248304
  11. Al-Masry W. A., Ali E. M., Aqeel Y. A. Determination of bubble characteristics in bubble columns using statistical analysis of acoustic sound measurements. Chem. Eng. Res. Des., 2005, vol. 83, iss. 10, pp. 1196–1207. https://doi.org/10.1205/cherd.05014
  12. Leighton T. The Acoustic Bubble. London, Academic Press, 1997. 613 p.
  13. Devaud M., Hocquet T., Bacri J.-C., Leroy V. The Minnaert bubble: An acoustic approach. Eur. J. Phys., 2008, vol. 29, no. 6, pp. 1263–1285. https://doi.org/10.1088/0143-0807/29/6/014
  14. Minnaert M. XVI. On musical air-bubbles and the sound of running water. Philos. Mag., 1933, vol. 16, iss. 104, pp. 235–248. https://doi.org/10.1080/14786443309462277
  15. Ainslie M. A., Leighton T. G. Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble. J. Acoust. Soc. Am., 2011, vol. 130, iss. 5, pp. 3184–3208. https://doi.org/10.1121/1.3628324
  16. BenSalem I., Guillermic R. M., Sample C., Leroy V., Saint-Jalmes A., Dollet B. Propagation of ultrasound in aqueous foams: Bubble size dependence and resonance effects. Soft Matter, 2013, vol. 9, iss. 4, pp. 1194–1202. https://doi.org/10.1039/C2SM25545F
  17. Divoux T., Vidal V., Melo F., Géminard J.-C. Acoustic emission associated with the bursting of a gas bubble at the free surface of a non-Newtonian fluid. Phys. Rev. E, 2008, vol. 77, art. 056310. https://doi.org/10.1103/PhysRevE.77.056310
  18. Stephens R. W. B., Pollock A. A. Waveforms and frequency spectra of acoustic emissions. J. Acoust. Soc. Am., 1971, vol. 50, no. 3, pt. 2, pp. 904–910.
  19. Chen G., Luo H., Yang H., Zhang T., Li S. Water effects on the deformation and fracture behaviors of the multiscaled cellular fibrous bamboo. Acta Biomater., 2018, vol. 65, pp. 203–215. https://doi.org/10.1016/j.actbio.2017.10.005
  20. Vandewalle N., Lentz J. F., Dorbolo S., Brisbois F. Avalanches of popping bubbles in collapsing foams. Phys. Rev. Lett., 2001, vol. 86, iss. 1, pp. 179–182. https://doi.org/10.1103/PhysRevLett.86.179
  21. Marston P. L., Trinh E. H., Depew J., Asaki T. J. Response of bubbles to ultrasonic radiation pressure: Dynamics in low gravity and shape oscillations. In: Blake J. R., Boulton-Stone J. M., Thomas N. H., eds. Bubble Dynamics and Interface Phenomena. Fluid Mechanics and Its Applications. Dordrecht, Springer, 1994, vol. 23, pp. 343–353. https://doi.org/10.1007/978-94-011-0938-3_32
  22. Prosperetti A., Lezzi A. Bubble dynamics in a compressible liquid. Pt. 1. First-order theory. J. Fluid Mech., 1986, vol. 168, pp. 457–478. https://doi.org/10.1017/S0022112086000460
  23. Ding J., Tsaur F. W., Lips A., Akay A. Acoustical observation of bubble oscillations induced by bubble popping. Phys. Rev. E, 2007, vol. 76, iss. 4, pt. 1, art. 041601. https://doi.org/10.1103/PhysRevE.76.041601
  24. Ritacco H. A. Complexity and self-organized criticality in liquid foams. A short review. Adv. Colloid Interface Sci., 2020, vol. 285, art. 102282. https://doi.org/10.1016/j.cis.2020.102282
  25. Furuta Y., Oikawa N., Kurita R. Close relationship between a dry–wet transition and a bubble rearrangement in two-dimensional foam. Sci. Rep., 2016, vol. 6, art. 37506. https://doi.org/10.1038/srep37506
  26. Yanagisawa N., Kurita R. In-situ observation of collective bubble collapse dynamics in a quasi-two-dimensional foam. Sci. Rep., 2019, vol. 9, art. 5152. https://doi.org/10.1038/s41598-019-41643-x
  27. Vandewalle N., Lentz J. F. Cascades of popping bubbles along air / foam interfaces. Phys. Rev. E, 2001, vol. 64, iss. 2, pt. 1, art. 021507. https://doi.org/10.1103/PhysRevE.64.021507
  28. Shah M. S., Kleijn C. R., Kreutzer M. T., van Steijn V. Influence of initial film radius and film thickness on the rupture of foam films. Phys. Rev. Fluids, 2021, vol. 6, art. 013603. https://doi.org/10.1103/PhysRevFluids.6.013603
  29. Manev E. D., Nguyen A. V. Critical thickness of microscopic thin liquid films. Advances in Colloid and Interface Science, 2005, vol. 114–115, pp. 133–146. https://doi.org/10.1016/j.cis.2004.07.013
  30. Forel E., Dollet B., Langevin D., Rio E. Coalescence in two-dimensional foams: A purely statistical process dependent on film area. Phys. Rev. Lett., 2019, vol. 122, art. 088002. https://doi.org/10.1103/PhysRevLett.122.088002
  31. Coussot P. Scaling approach of the convective drying of a porous medium. Eur. Phys. J. B, 2000, vol. 15, pp. 557–566. https://doi.org/10.1007/s100510051160
  32. Zimnyakov D. A., Yuvchenko S. A., Isaeva A. A., Isaeva E. A., Tsypina D. V. Growth/collapse kinetics of the surface bubbles in fresh constrained foams: Transition to self-similar evolution. Colloids Surf. A, 2019, vol. 579, art. 123693. https://doi.org/10.1016/j.colsurfa.2019.123693
  33. Burnett G., Chae J. J., Tam W. Y., Almeida R. M. C., Tabor M. Structure and dynamics of breaking foams. Phys. Rev. E, 1995, vol. 51, no. 6, pp. 5788–5800. https://doi.org/10.1103/PhysRevE.51.5788
  34. Chae J. J., Tabor M. Dynamics of foams with and without wall rupture. Phys. Rev. E, 1997, vol. 55, no. 1, pp. 598–611. https://doi.org/10.1103/PhysRevE.55.598
  35. Müller W., Di Meglio J.-M. Avalanches in draining foams. J. Phys.: Condens. Matter, 1999, vol. 11, no. 21, pp. L209–L215.
Received: 
08.12.2025
Accepted: 
07.04.2026
Published: 
30.06.2026