Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T12:09:23.650Z Has data issue: false hasContentIssue false
  • English
  • Français

The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool

Published online by Cambridge University Press:  26 April 2007

Q. DENG ,
A. V. ANILKUMAR  and
T. G. WANG
Q. DENG
Affiliation:
Department of Mechanical Engineering, Vanderbilt University Nashville, TN-37235, USA
A. V. ANILKUMAR*
Affiliation:
Department of Mechanical Engineering, Vanderbilt University Nashville, TN-37235, USA
T. G. WANG
Affiliation:
Department of Mechanical Engineering, Vanderbilt University Nashville, TN-37235, USA
*
†Author to whom correspondence should be addressed
Get access Rights & Permissions [Opens in a new window]

Abstract

The phenomenon of liquid drop impact onto the surface of a deep pool of the same liquid is studied in the context of bubble entrapment, using high-resolution digital photography. Three liquids, pure water, glycerin/water mixtures, and silicon oil, have been used to investigate the effect of viscosity (μ) and surface tension (σ) on regular bubble entrapment, and the associated impact crater signatures. The global viscous effect is seen as a shift in the classical inviscid bubble entrapment limits, whereas, at the impact crater, the local effect is seen as a weakening of the capillary wave, which is responsible for bubble pinching, and a weakening of the intensity of crater rebound. Bubble entrapment, which results from a competition between concentric capillary pinching of the crater cusp and viscous damping, is captured well by the capillary number Ca (Ca = mu Viσ, where Vi is the drop impact velocity). The measured peak entrapped bubble size decreases exponentially as capillary number increases, with the cut-off capillary number for bubble entrapment estimated to be around 0.6. The critical crater cone angle for peak bubble pinch-off weakly increases with capillary number, with the measured value in agreement with theory in the inviscid limit (low Ca). Additionally, the growth of the main body of the high-speed thin jet, formed immediately following bubble pinch-off, is fitted to a power-law singularity model. This suggests that the thin jet is similar to the hydraulic jets produced by the collapse of free-surface standing waves.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 578 , 10 May 2007 , pp. 119 - 138
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFRENCES

Andsager, K., Beard, K. V. & Laird, N. F. 1999 Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci. 56, 2673–2683.Google Scholar
Anilkumar, A. V., Lacik, I. & Wang, T. G. 2001 A novel reactor for making uniform capsules. Biotech. Bioengng 75, 581–589.Google Scholar
Anilkumar, A. V., Lee, C. P. & Wang, T. G. 1991 Surface-tension-induced mixing following coalescence of initially stationary drops. Phys. Fluids A 3, 2587–2591.Google Scholar
Bergmann, R., Meer, D. V. D., Stijnaman, M., Sandtke, M., Posperetti, A. & Lohse, D. 2006 Giant bubble pinch-off. Phys. Rev. Lett. 96, 154505.CrossRefGoogle ScholarPubMed
Burton, J. C., Waldrep, R. & Taborek, P. 2005 Scaling and instabilities in bubble pinch-off. Phys. Rev. Lett. 94, 184502.Google Scholar
Chapman, D. S. & Critchlow, P. R. 1967 Formation of vortex rings from falling drops. J. Fluid Mech. 29, 177–185.Google Scholar
Cresswell, R. W. & Morton, B. R. 1995 Drop-formed vortex rings – the generation of vorticity. Phys. Fluids 7, 1363–1369.Google Scholar
Dooley, B. S., Warncke, A. E., Gharib, M. & Tryggvason, G. 1997 Vortex ring generation due to the coalescence of a water drop at a free surface. Exps. Fluids 22, 369–374.Google Scholar
Durst, F. 1996 Penetration length and diameter development of vortex rings generated by impacting water drops. Exps. Fluids 21, 110–117.Google Scholar
Elmore, P. A., Chahine, G. L. & Oguz, H. N. 2001 Cavity and flow measurements of reproducible bubble entrainment following drop impacts. Exps. Fluids 31, 664–673.Google Scholar
Engel, O. G. 1967 Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts. J. Appl. Phys. 38, 3935–3940.Google Scholar
Gordillo, J. M., Sevilla, A., Rodriguez-Rodriguez, J. & Martinez-Bazan, C. 2005 Axisymmetric bubble pinch-off at high Reynolds numbers. Phys. Rev. Lett. 95, 194501.Google Scholar
Hogrefe, J. E., Peffley, N. L., Goodridge, C. L., Shi, W. T. Hentschel, H. G. E. & Lathrop, D. P. 1998 Power-law singularities in gravity-capillary waves. Physica D 123, 183–205.Google Scholar
Hsiao, M., Lichter, S. & Quintero, L. G. 1988 The critical Weber number for vortex and jet formation for drops impacting on a liquid pool. Phys. Fluids, 31, 3560–3562.Google Scholar
Jeong, J. T. & Moffat, H. K. 1992 Free-surface cusps associated with flow at low Reynolds numbers. J. Fluid Mech. 241, 1–22.Google Scholar
Lamb, H. 1945 Hydrodynamics. Dover.Google Scholar
Leng, L. J. 2001 Splash formation by spherical drops. J. Fluid Mech. 427, 73–105.Google Scholar
Leppinen, D. & Lister, J. R. 2003 Capillary pinch-off in inviscid fluids. Phys. Fluids, 15, 568–578.Google Scholar
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C. Meer, D. V. D. Versluis, M. Weele, K. V. D. Hoef, M. V. D. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.CrossRefGoogle ScholarPubMed
Longuet-Higgins, M. S. 1983 Bubbles, breaking waves and hyperbolic jets at a free surface. J. Fluid Mech. 127, 103–121.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1990 An analytic model of sound production by raindrops. J. Fluid Mech. 214, 395–410.Google Scholar
Longuet-Higgins, M. S. & Oguz, H. 1995 Critical microjets in collapsing cavities. J. Fluid Mech. 290, 183–201.Google Scholar
Mohamed-Kassim, Z. & Longmire, E. K. 2004 Drop coalescence through a liquid/liquid interface. Phys. Fluids 16, 2170–2181.CrossRefGoogle Scholar
Morton, D., Rudman, M. & Leng, L. J. 2000 An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12, 747–763.Google Scholar
Oddershede, L. & Nagel, S. R. 2000 Singularity during the onset of an electrohydrodynamic spout. Phys. Rev. Lett. 85, 1234–1237.Google Scholar
Oguz, H. N. & Prosperetti, A. 1990 Bubble entrainment by impact of drops on liquid surfaces. J. Fluid Mech. 219, 143–179.Google Scholar
Oguz, H. N. & Prosperetti, A. 1991 Numerical calculations of the underwater noise of rain. J. Fluid Mech. 228, 417–442.Google Scholar
Peck, B. & Sigurdson, L. 1994 The three-dimensional vortex structure of an impacting water drop. Phys. Fluids 6, 564–576.Google Scholar
Prosperetti, A. 1976 Viscous effects on small-amplitude surface waves. Phys. Fluids 19, 195–203.Google Scholar
Prosperetti, A. & Oguz, H. 1993 The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577–602.CrossRefGoogle Scholar
Pumphrey, H. C. & Elmore, P. A. 1990 The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567.CrossRefGoogle Scholar
Rein, M. 1996 The transitional regime between coalescing and splashing drops. J. Fluid Mech. 306, 145–165.Google Scholar
Rodriguez, F. & Mesler, R. 1988 The penetration of drop-formed vortex rings into pools of liquid. J. Colloid Interface Sci. 121, 121–129.Google Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.Google Scholar
Wang, T., Lacik, I., Brissova, M., Anilkumar, A. V. Prokop, A. Hunkeler, D. Green, R. Shahrokhi, K. & Powers, A. C. 1997 An encapsulation system for the immunoisolation of pancreatic islets. Nature Biotechnol. 15, 358–362.CrossRefGoogle ScholarPubMed
Weiss, D. A. & Yarin, A. L. 1999 Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation. J. Fluid Mech. 385, 229–254.Google Scholar
Worthington, A. M. 1908 A Study of Splash. Longman's, Green and Company, London.Google Scholar
Zeff, B. W., Kleber, B., Fineberg, J. & Lathrop, D. P. 2002. Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403, 401–404.Google Scholar