Cavitation bubble dynamics inside a droplet suspended in a different host fluid. (English) Zbl 07799638
Summary: In this paper, we present a theoretical, experimental and numerical study of the dynamics of cavitation bubbles inside a droplet suspended in another host fluid. On the theoretical side, we provided a modified Rayleigh collapse time and natural frequency for spherical bubbles in our particular context, characterized by the density ratio between the two liquids and the bubble-to-droplet size ratio. Regarding the experimental aspect, experiments were carried out for laser-induced cavitation bubbles inside oil-in-water (O/W) or water-in-oil (W/O) droplets. Two distinct fluid-mixing mechanisms were unveiled in the two systems, respectively. In the case of O/W droplets, a liquid jet emerges around the end of the bubble collapse phase, effectively penetrating the droplet interface. We offer a detailed analysis of the criteria governing jet penetration, involving the standoff parameter and impact velocity of the bubble jet on the droplet surface. Conversely, in the scenario involving W/O droplets, the bubble traverses the droplet interior, inducing global motion and eventually leading to droplet pinch-off when the local Weber number exceeds a critical value. This phenomenon is elucidated through the equilibrium between interfacial and kinetic energies. Lastly, our boundary integral model faithfully reproduces the essential physics of the non-spherical bubble dynamics observed in the experiments. We conduct a parametric study spanning a wide parameter space to investigate bubble-droplet interactions. The insights from this study could serve as a valuable reference for practical applications in the field of ultrasonic emulsification, pharmacy, etc.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76T20 | Suspensions |
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 76-05 | Experimental work for problems pertaining to fluid mechanics |
Keywords:
Laplace equation; modified Rayleigh collapse time; natural bubble frequency; spherical bubble; oil-in-water/water-in-oil droplet; boundary integral method; experimental validationReferences:
| [1] | Banine, V.Y., Koshelev, K.N. & Swinkels, G.2011Physical processes in EUV sources for microlithography. J. Phys. D: Appl. Phys.44 (25), 253001. |
| [2] | Bempedelis, N., Zhou, J., Andersson, M. & Ventikos, Y.2021Numerical and experimental investigation into the dynamics of a bubble-free-surface system. Phys. Rev. Fluids6 (1), 013606. |
| [3] | Blake, J.R., Leppinen, D.M. & Wang, Q.2015Cavitation and bubble dynamics: the Kelvin impulse and its applications. Interface Focus5 (5), 20150017. |
| [4] | Brujan, E.A., Nahen, K., Schmidt, P. & Vogel, A.2001Dynamics of laser-induced cavitation bubbles near an elastic boundary. J. Fluid Mech.433, 251-281. · Zbl 0968.76503 |
| [5] | Brujan, E.-A., Noda, T., Ishigami, A., Ogasawara, T. & Takahira, H.2018Dynamics of laser-induced cavitation bubbles near two perpendicular rigid walls. J. Fluid Mech.841, 28-49. |
| [6] | Cerbus, R.T., Chraibi, H., Tondusson, M., Petit, S., Soto, D., Devillard, R., Delville, J.P. & Kellay, H.2022Experimental and numerical study of laser-induced secondary jetting. J. Fluid Mech.934, A14. |
| [7] | Chahine, G.L. & Bovis, A.1980 Oscillation and collapse of a cavitation bubble in the vicinity of a two-liquid interface. In Cavitation and Inhomogeneities in Underwater Acoustics (ed. W. Lauterborn), pp. 23-29. Springer. |
| [8] | Church, C.C.1995The effects of an elastic solid surface layer on the radial pulsations of gas bubbles. J. Acoust. Soc. Am.97 (3), 1510-1521. |
| [9] | Curtiss, G.A., Leppinen, D.M., Wang, Q.X. & Blake, J.R.2013Ultrasonic cavitation near a tissue layer. J. Fluid Mech.730, 245-272. · Zbl 1291.76057 |
| [10] | Dabiri, J.O. & Gharib, M.2004Fluid entrainment by isolated vortex rings. J. Fluid Mech.511, 311-331. · Zbl 1061.76502 |
| [11] | Didden, N.1979On the formation of vortex rings: rolling-up and production of circulation. J. Appl. Math. Phys.30, 101-116. |
| [12] | Gonzalez Avila, S.R. & Ohl, C.-D.2016Fragmentation of acoustically levitating droplets by laser-induced cavitation bubbles. J. Fluid Mech.805, 551-576. |
| [13] | Han, L., Zhang, T., Yang, D., Han, R. & Li, S.2023Comparison of vortex cut and vortex ring models for toroidal bubble dynamics in underwater explosions. Fluids8, 131. |
| [14] | Han, R., Li, S., Zhang, A.M. & Wang, Q.X.2016Modelling for three dimensional coalescence of two bubbles. Phys. Fluids28 (6), 062104. |
| [15] | Han, R., Zhang, A.M., Tan, S. & Li, S.2022Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales. J. Fluid Mech.932, A8. |
| [16] | Hsiao, C.T., Jayaprakash, A., Kapahi, A., Choi, J.K. & Chahine, G.L.2014Modelling of material pitting from cavitation bubble collapse. J. Fluid Mech.755, 142-175. |
| [17] | Janzen, C., Fleige, R., Noll, R., Schwenke, H., Lahmann, W., Knoth, J., Beaven, P., Jantzen, E., Oest, A. & Koke, P.2005Analysis of small droplets with a new detector for liquid chromatography based on laser-induced breakdown spectroscopy. Spectrochim. Acta B60 (7), 993-1001. |
| [18] | Kang, Y.J. & Cho, Y.2019Gravity-capillary jet-like surface waves generated by an underwater bubble. J. Fluid Mech.866, 841-864. |
| [19] | Kannan, Y.S., Balusamy, S., Karri, B. & Sahu, K.C.2020Effect of viscosity on the volumetric oscillations of a non-equilibrium bubble in free-field and near a free-surface. Exp. Therm. Fluid Sci.116, 110113. |
| [20] | Klaseboer, E. & Khoo, B.C.2004aBoundary integral equations as applied to an oscillating bubble near a fluid-fluid interface. Comput. Mech.33 (2), 129-138. · Zbl 1067.76067 |
| [21] | Klaseboer, E. & Khoo, B.C.2004bAn oscillating bubble near an elastic material. J. Appl. Phys.96 (10), 5808-5818. |
| [22] | Klein, A.L., Kurilovich, D., Lhuissier, H., Versolato, O.O., Lohse, D., Villermaux, E. & Gelderblom, H.2020Drop fragmentation by laser-pulse impact. J. Fluid Mech.893, A7. |
| [23] | Li, S., Van Der Meer, D., Zhang, A.-M., Prosperetti, A. & Lohse, D.2020aModelling large scale airgun-bubble dynamics with highly non-spherical features. Intl J. Multiphase Flow122, 103143. |
| [24] | Li, S., Prosperetti, A. & Van Der Meer, D.2020bDynamics of a toroidal bubble on a cylinder surface with an application to geophysical exploration. Intl J. Multiphase Flow129, 103335. |
| [25] | Li, S., Zhang, A.-M. & Han, R.20233D model for inertial cavitation bubble dynamics in binary immiscible fluids. J. Comput. Phys.494, 112508. · Zbl 07766222 |
| [26] | Liang, Y., Jiang, Y., Wen, C.-Y. & Liu, Y.2020Interaction of a planar shock wave and a water droplet embedded with a vapour cavity. J. Fluid Mech.885, R6. |
| [27] | Luo, J., Xu, W. & Khoo, B.C.2021Stratification effect of air bubble on the shock wave from the collapse of cavitation bubble. J. Fluid Mech.919, A16. · Zbl 1492.76122 |
| [28] | Minnaert, M.1933XVI. on musical air-bubbles and the sounds of running water. Lond. Edinb. Dubl. Phil. Mag. J. Sci.16 (104), 235-248. |
| [29] | Minsier, V., De Wilde, J. & Proost, J.2009Simulation of the effect of viscosity on jet penetration into a single cavitating bubble. J. Appl. Phys.106 (8), 084906. |
| [30] | Obreschkow, D., Kobel, P., Dorsaz, N., De Bosset, A., Nicollier, C. & Farhat, M.2006Cavitation bubble dynamics inside liquid drops in microgravity. Phys. Rev. Lett.97 (9), 094502. |
| [31] | Orthaber, U., Zevnik, J., Petkovšek, R. & Dular, M.2020Cavitation bubble collapse in a vicinity of a liquid-liquid interface – basic research into emulsification process. Ultrason. Sonochem.68, 105224. |
| [32] | Pearson, A., Blake, J.R. & Otto, S.R.2004Jets in bubbles. J. Engng Maths48 (3-4), 391-412. · Zbl 1041.76506 |
| [33] | Perdih, S.T., Zupanc, M. & Dular, M.2019Revision of the mechanisms behind oil-water (O/W) emulsion preparation by ultrasound and cavitation. Ultrason. Sonochem.51, 298-304. |
| [34] | Plesset, M.S.1954On the stability of fluid flows with spherical symmetry. J. Appl. Phys.25 (1), 96-98. · Zbl 0055.18501 |
| [35] | Popinet, S. & Zaleski, S.2002Bubble collapse near a solid boundary: a numerical study of the influence of viscosity. J. Fluid Mech.464, 137-163. · Zbl 1019.76018 |
| [36] | Poulain, S., Guenoun, G., Gart, S., Crowe, W. & Jung, S.2015Particle motion induced by bubble cavitation. Phys. Rev. Lett.114 (21), 214501. |
| [37] | Prosperetti, A.1977Viscous effects on perturbed spherical flows. Q. Appl. Maths34 (4), 339-352. · Zbl 0354.76017 |
| [38] | Raman, K.A., Rosselló, J.M. & Ohl, C.-D.2022aCavitation induced oil-in-water emulsification pathways using a single laser-induced bubble. Appl. Phys. Lett.121 (19), 194103. |
| [39] | Raman, K.A., Rosselló, J.M., Reese, H. & Ohl, C.-D.2022bMicroemulsification from single laser-induced cavitation bubbles. J. Fluid Mech.953, A27. |
| [40] | Rayleigh, Lord1917VIII. On the pressure developed in a liquid during the collapse of a spherical cavity. Lond. Edinb. Dubl. Phil. Mag. J. Sci.34 (200), 94-98. · JFM 46.1274.01 |
| [41] | Ren, Z., Han, H., Zeng, H., Sun, C., Tagawa, Y., Zuo, Z. & Liu, S.2023Interactions of a collapsing laser-induced cavitation bubble with a hemispherical droplet attached to a rigid boundary. J. Fluid Mech.976, A11. |
| [42] | Ren, Z., Zuo, Z., Wu, S. & Liu, S.2022Particulate projectiles driven by cavitation bubbles. Phys. Rev. Lett.128 (4), 044501. |
| [43] | Rosselló, J.M., Reese, H., Raman, K.A. & Ohl, C.-D.2023Bubble nucleation and jetting inside a millimetric droplet. J. Fluid Mech.968, A19. |
| [44] | Saade, Y., Jalaal, M., Prosperetti, A. & Lohse, D.2021Crown formation from a cavitating bubble close to a free surface. J. Fluid Mech.926, A5. · Zbl 1482.76127 |
| [45] | Saini, M., Tanne, E., Arrigoni, M., Zaleski, S. & Fuster, D.2022On the dynamics of a collapsing bubble in contact with a rigid wall. J. Fluid Mech.948, A45. · Zbl 1537.76162 |
| [46] | Sullivan, I.S., Niemela, J.J., Hershberger, R.E., Bolster, D. & Donnelly, R.J.2008Dynamics of thin vortex rings. J. Fluid Mech.609, 319-347. · Zbl 1147.76011 |
| [47] | Supponen, O., Obreschkow, D., Tinguely, M., Kobel, P., Dorsaz, N. & Farhat, M.2016Scaling laws for jets of single cavitation bubbles. J. Fluid Mech.802, 263-293. |
| [48] | Tomita, Y. & Sato, K.2017Pulsed jets driven by two interacting cavitation bubbles produced at different times. J. Fluid Mech.819, 465-493. |
| [49] | Udepurkar, A.P., Clasen, C. & Kuhn, S.2023Emulsification mechanism in an ultrasonic microreactor: influence of surface roughness and ultrasound frequency. Ultrason. Sonochem.94, 106323. |
| [50] | Wang, J., Li, H., Guo, W., Wang, Z., Du, T., Wang, Y., Abe, A. & Huang, C.2021Rayleigh-Taylor instability of cylindrical water droplet induced by laser-produced cavitation bubble. J. Fluid Mech.919, A42. · Zbl 1487.76040 |
| [51] | Wang, Q., Liu, W., Corbett, C. & Smith, W.R.2022Microbubble dynamics in a viscous compressible liquid subject to ultrasound. Phys. Fluids34 (1), 012105. |
| [52] | Wang, Q.X., Yeo, K.S., Khoo, B.C. & Lam, K.Y.1996Nonlinear interaction between gas bubble and free surface. Comput. Fluids25 (7), 607-628. · Zbl 0898.76005 |
| [53] | Wu, W.H., Eskin, D.G., Priyadarshi, A., Subroto, T., Tzanakis, I. & Zhai, W.2021New insights into the mechanisms of ultrasonic emulsification in the oil-water system and the role of gas bubbles. Ultrason. Sonochem.73, 105501. |
| [54] | Yamamoto, T., Matsutaka, R. & Komarov, S.V.2021High-speed imaging of ultrasonic emulsification using a water-gallium system. Ultrason. Sonochem.71, 105387. |
| [55] | Yi, L., Li, S., Jiang, H., Lohse, D., Sun, C. & Mathai, V.2021Water entry of spheres into a rotating liquid. J. Fluid Mech.912, R1. |
| [56] | Zeng, Q., An, H. & Ohl, C.-D.2022Wall shear stress from jetting cavitation bubbles: influence of the stand-off distance and liquid viscosity. J. Fluid Mech.932, A14. · Zbl 1514.76097 |
| [57] | Zeng, Q., Gonzalez-Avila, S.R. & Ohl, C.-D.2020Splitting and jetting of cavitation bubbles in thin gaps. J. Fluid Mech.896, A28. · Zbl 1460.76814 |
| [58] | Zeng, Q., Gonzalez-Avila, S.R., Voorde, S.T. & Ohl, C.-D.2018Jetting of viscous droplets from cavitation-induced Rayleigh-Taylor instability. J. Fluid Mech.846, 916-943. · Zbl 1404.76267 |
| [59] | Zhang, A.M., Li, S. & Cui, J.2015Study on splitting of a toroidal bubble near a rigid boundary. Phys. Fluids27 (6), 062102. |
| [60] | Zhang, A.-M., Li, S.-M., Cui, P., Li, S. & Liu, Y.-L.2023aTheoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation. Sci. China Phys. Mech. Astron.66 (12), 124711. |
| [61] | Zhang, A.-M., Li, S.-M., Cui, P., Li, S. & Liu, Y.-L.2023bA unified theory for bubble dynamics. Phys. Fluids35 (3), 033323. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
