Skip to main content

Particle-Assisted Laser-Induced Inertial Cavitation for High Strain-Rate Soft Material Characterization

Abstract

Background

While there are few reliable techniques for characterizing highly compliant and viscoelastic materials under large deformations, laser-induced Inertial Microcavitaton Rheometry (IMR) was recently developed to fill this void and to characterize soft materials at high to ultra-high strain rates (\(O(10^{3}) \sim O(10^{8})\) s\(^{-1}\)). Yet, one of the current limitations in IMR has been the dependence of the cavitation nucleation physics on the intrinsic material properties often generating extreme deformation levels and thus complicating material characterization procedures.

Objective

The objective of this study was to develop an experimental approach for modulating laser-induced cavitation (LIC) bubble amplitudes and their resulting maximum material deformations. Lowering the material stretch ratios during inertial cavitation will provide an experimental platform of broad applicability to a large class of polymeric materials and environmental conditions.

Methods

Experimental methods include using three types of micron-sized nucleation seed particles and varying laser energies in polyacrylamide hydrogels of known concentration. Using a Quadratic law Kelvin-Voigt material model, we implemented ensemble-based data assimilation (DA) techniques to robustly quantify the nonlinear constitutive material parameters, up through the first, second, and third bubble collapse cycles. Fitted values were then used to simulate bubble dynamics to compute critical bubble collapse Mach numbers, and to assess time-varying uncertainties of the full cavitation dynamics with respect to the current state-of-the art theoretical model featured in the IMR model.

Results

While varying laser energy modulated bubble amplitude, seed particles successfully expanded (more than doubled) the finite deformation regime (i.e., maximum material stretch, \(\lambda _{max} \approx\) 4 - 9). Comparing experimental data to IMR simulations, we found that fitting beyond the first bubble collapse, as well as increasing laser energy, increased the bubble radius fit error, and larger \(\lambda _{max}\) values exhibited increasingly violent bubble behavior (marked by increasing collapse Mach numbers greater than 0.08). Additionally, time-varying analysis showed the greatest model uncertainty during initial bubble collapse, where bubbles nucleated at lower laser energies and resulting \(\lambda _{max}\) had less uncertainty at collapse compared to higher laser energy and \(\lambda _{max}\) cases.

Conclusions

This study indicates IMR’s current theoretical framework might be lacking important additional cavitation and/or material physics. However, expanding the finite deformation regime of soft materials to attain lower stretch regimes enables broader applicability to a larger class of soft polymeric materials and will enable future, systematic development and incorporation of more complex physics and constitutive models including damage and failure mechanisms into the theoretical framework of IMR.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Notes

  1. The governing equations inside the bubble, i.e., the balances of mass and energy, are discretized using 1000 grid points.

References

  1. Estrada JB, Barajas C, Henann DL, Johnsen E, Franck C (2018) High strain-rate soft material characterization via inertial cavitation. J Mech Phys Solids 112:291–317. https://doi.org/10.1016/j.jmps.2017.12.006. https://linkinghub.elsevier.com/retrieve/pii/S0022509617307585

  2. Yang J, Cramer HC, Franck C (2020) Extracting non-linear viscoelastic material properties from violently-collapsing cavitation bubbles. Extreme Mech Lett 39:100839. https://doi.org/10.1016/j.eml.2020.100839. https://linkinghub.elsevier.com/retrieve/pii/S2352431620301395

  3. Gent A, Wang C (1991) Fracture mechanics and cavitation in rubber-like solids. J Mater Sci 26(12):3392–3395

    Article  Google Scholar 

  4. Barney CW, Dougan CE, McLeod KR, Kazemi-Moridani A, Zheng Y, Ye Z, Tiwari S, Sacligil I, Riggleman RA, Cai S et al (2020) Cavitation in soft matter. Proc Natl Acad Sci 117(17):9157–9165

    MathSciNet  Article  Google Scholar 

  5. Hashemnejad SM, Kundu S (2015) Nonlinear elasticity and cavitation of a triblock copolymer gel. Soft Matter 11(21):4315–4325

    Article  Google Scholar 

  6. Hutchens SB, Fakhouri S, Crosby AJ (2016) Elastic cavitation and fracture via injection. Soft Matter 12(9):2557–2566

    Article  Google Scholar 

  7. López-Fagundo C, Bar-Kochba E, Livi LL, Hoffman-Kim D, Franck C (2014) Three-dimensional traction forces of schwann cells on compliant substrates. J R Soc Interface 11(97):20140247

    Article  Google Scholar 

  8. Akhatov I, Lindau O, Topolnikov A, Mettin R, Vakhitova N, Lauterborn W (2001) Collapse and rebound of a laser-induced cavitation bubble. Phys Fluids 13(10):2805–2819

    Article  Google Scholar 

  9. Keller JB, Miksis M (1980) Bubble oscillations of large amplitude. J Acoust Soc Am 68(2):628–633

    Article  Google Scholar 

  10. Nigmatulin R, Khabeev N, Nagiev F (1981) Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid. Int J Heat Mass Transf 24(6):1033–1044

    Article  Google Scholar 

  11. Barajas C, Johnsen E (2017) The effects of heat and mass diffusion on freely oscillating bubbles in a viscoelastic, tissue-like medium. J Acoust Soc Am 141(2):908–918

    Article  Google Scholar 

  12. Vincent O, Marmottant P, Gonzalez-Avila SR, Ando K, Ohl CD (2014) The fast dynamics of cavitation bubbles within water confined in elastic solids. Soft Matter 10(10):1455–1461

    Article  Google Scholar 

  13. Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res Oceans 99(C5):10143–10162. https://doi.org/10.1029/94JC00572. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/94JC00572

  14. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45

    MathSciNet  Article  Google Scholar 

  15. Spratt JS, Rodriguez M, Schmidmayer K, Bryngelson SH, Yang J, Franck C, Colonius T (2021) Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations. J Mech Phys Solids 104455

  16. Evensen G, van Leeuwen PJ (2000) An ensemble Kalman smoother for nonlinear dynamics. Mon Weather Rev 128:1852–1867

    Article  Google Scholar 

  17. Bocquet M, Sakov P (2013) An iterative ensemble Kalman smoother. Q J R Meteorol Soc 140(682):1521–1535. https://doi.org/10.1002/qj.2236. http://dx.doi.org/10.1002/qj.2236

  18. Bocquet M, Sakov P (2013) Joint state and parameter estimation with an iterative ensemble Kalman smoother. Nonlinear Process Geophys 20(5):803–818. https://doi.org/10.5194/npg-20-803-2013http://dx.doi.org/10.5194/npg-20-803-2013

  19. Sakov P, Oliver DS, Bertino L (2012) An iterative EnKF for strongly nonlinear systems. Mon Weather Rev 140(6):1988–2004. https://doi.org/10.1175/mwr-d-11-00176.1. http://dx.doi.org/10.1175/MWR-D-11-00176.1

  20. Mancia L, Yang J, Spratt JS, Sukovich JR, Xu Z, Colonius T, Franck C, Johnsen E (2021) Acoustic cavitation rheometry. Soft Matter 17:2931–2941. https://doi.org/10.1039/D0SM02086A. http://dx.doi.org/10.1039/D0SM02086A

  21. Vogel A, Nahen K, Theisen D, Noack J (1996) Plasma formation in water by picosecond and nanosecond nd: Yag laser pulses. I. Optical breakdown at threshold and superthreshold irradiance. IEEE J Sel Top Quantum Electron 2(4):847–860

  22. Sacchi C (1991) Laser-induced electric breakdown in water. JOSA B 8(2):337–345

    Article  Google Scholar 

  23. Kennedy PK (1995) A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media. I. Theory. IEEE J Quantum Electron 31(12):2241–2249

    Article  Google Scholar 

  24. Anderson JD (2009) Fundamentals of aerodynamics. McGraw 

  25. Rayleigh L (1917) VIII. On the pressure developed in a liquid during the collapse of a spherical cavity. Lond Edinb Dublin Philos Mag J Sci 34(200):94–98

  26. Plesset M (1948) Dynamics of cavitation bubbles. J Appl Mech 16:228–231

    Google Scholar 

  27. Murakami K (2020) Spherical and non-spherical bubble dynamics in soft matter. Ph.D. thesis, University of Michigan

Download references

Acknowledgements

The authors thank Harry C. Cramer III, Dr. Mauro Rodriguez, and Dr. Spencer Bryngelson for fruitful discussions regarding the cavitation dynamics. We gratefully thank Alice Lux Fawzi for her involvement in organizing this project. We also thank Richard Knoll at the Nanoscale Imaging and Analysis Center (University of Wisconsin - Madison) for assistance in Scanning Electron Microscopy, and Todd Rumbagh at Hadland Imaging for assistance with high-speed imaging. Funding was provided by Dr. Timothy Bentley at the Office of Naval Research through grants N00014-20-1-2408 and N00014-17-1-2058.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. Franck.

Ethics declarations

Conflicts of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Buyukozturk, S., Spratt, JS., Henann, D. et al. Particle-Assisted Laser-Induced Inertial Cavitation for High Strain-Rate Soft Material Characterization. Exp Mech 62, 1037–1050 (2022). https://doi.org/10.1007/s11340-022-00861-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-022-00861-7

Keywords

  • Inertial cavitation
  • High strain-rate
  • Viscoelastic finite deformation
  • Data assimilation