Skip to main content Accessibility help
×
×
Home

Capillary breakup of a liquid bridge: identifying regimes and transitions

  • Yuan Li (a1) and James E. Sprittles (a2)
Abstract

Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous–inertial balances, that is, different limits of the Ohnesorge number $Oh$ . To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low- $Oh$ viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous–inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Capillary breakup of a liquid bridge: identifying regimes and transitions
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Capillary breakup of a liquid bridge: identifying regimes and transitions
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Capillary breakup of a liquid bridge: identifying regimes and transitions
      Available formats
      ×
Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email addresses for correspondence: y.li.2@bham.ac.uk, J.E.Sprittles@warwick.ac.uk
References
Hide All
Ambravaneswaran, B., Phillips, S. D. & Basaran, O. A. 2000 Theoretical analysis of a dripping faucet. Phys. Rev. Lett. 85, 53325335.
Ambravaneswaran, B., Subramani, H. J., Phillips, S. D. & Basaran, O. A. 2004 Dripping–jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.
Ashgriz, N. & Mashayek, F. 1995 Temporal analysis of capillary jet breakup. J. Fluid Mech. 291, 163190.
Barenblatt, G. I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press.
Basaran, O. A. 2002 Small scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 18421848.
Bernoff, A. J., Bertozzi, A. L. & Witelski, T. P. 1998 Axisymmetric surface diffusion: dynamics and stability of self-similar pinchoff. J. Stat. Phys. 93, 725776.
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6, 625631.
Brenner, M. P., Lister, J. R., Joseph, K., Nagel, S. R. & Shi, X. D. 1997 Breakdown of scaling in droplet fission at high Reynolds number. Phys. Fluids 9, 15731590.
Brenner, M. P., Lister, J. R. & Stone, H. A. 1996 Pinching threads, singularities and the number 0.0304…. Phys. Fluids 8, 28272836.
Brenner, M. P., Shi, X. D. & Nagel, S. R. 1994 Iterated instabilities during droplet fission. Phys. Rev. Lett. 73, 33913394.
Brown, R. A. & Scriven, L. E. 1980 On the multiple equilibrium shapes and stability of an interface pinned on a slot. J. Colloid Interface Sci. 78, 528542.
Burton, J. C., Rutledge, J. E. & Taborek, P. 2004 Fluid pinch-off dynamics at nanometer length scales. Phys. Rev. Lett. 92, 244505.
Castrejón-Pita, J. R., Castrejón-Pita, A. A., Hinch, E. J., Lister, J. R. & Hutchings, I. M. 2012 Self-similar breakup of near-inviscid liquids. Phys. Rev. E 86, 015301.
Castrejón-Pita, J. R., Castrejón-Pita, A. A., Thete, S. S., Sambath, K., Hutchings, I. M., Hinch, E. J., Lister, J. R. & Basaran, O. A. 2015 Plethora of transitions during breakup of liquid filaments. Proc. Natl Acad. Sci. USA 112, 45824587.
Chen, A. U. & Basaran, O. A. 2002 A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production. Phys. Fluids 14, L1L4.
Chen, A. U., Notz, P. K. & Basaran, O. A. 2002 Computational and experimental analysis of pinch-off and scaling. Phys. Rev. Lett. 88, 174501.
Collins, R. T., Jones, J. J., Harris, M. T. & Basaran, O. A. 2008 Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4, 149154.
Day, R. F., Hinch, J. & Lister, J. R. 1998 Self-similar capillary pinch-off in an inviscid fluid. Phys. Rev. Lett. 80, 704707.
Derby, B. 2010 Inkjet printing of functional and structural materials: fluid property requirements, feature stability and resolution. Annu. Rev. Mater. Res. 40, 395414.
Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 34583460.
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865929.
Eggers, J. 2005 Drop formation – an overview. Z. Angew. Math. Mech. 85, 400410.
Eggers, J. 2012 Stability of a viscous pinching thread. Phys. Fluids 24, 072103.
Eggers, J. 2014 Post-breakup solutions of Navier–Stokes and Stokes threads. Phys. Fluids 26, 072104.
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 179.
Fawehinmi, O. B., Gaskell, P. H., Jimack, P. K., Kapur, N. & Thompson, H. M. 2005 A combined experimental and computational fluid dynamics analysis of the dynamics of drop formation. Proc. Inst. Mech. Engrs 219, 933947.
Fordham, S. 1948 On the calculation of surface tension from measurements of pendant drops. Proc. R. Soc. Lond. A 194, 116.
Gaudet, S., McKinley, G. H. & Stone, H. A. 1996 Extensional deformation of Newtonian liquid bridges. Phys. Fluids 8, 25682579.
Gresho, P. M. & Sani, R. L. 1999 Incompressible Flow and the Finite Element Method. Vol. 2. Isothermal Laminar Flow. Wiley.
Hysing, S., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S. & Tobiska, L. 2009 Quantitative benchmark computations of two-dimensional bubble dynamics. Intl J. Numer. Meth. Fluids 60, 12591288.
Keller, J. B. & Miksis, M. J. 1983 Surface tension driven flows. SIAM J. Appl. Maths 43, 268277.
Kistler, S. F. & Scriven, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (ed. Pearson, J. R. A. & Richardson, S. M.), pp. 243299. Applied Science Publishers.
Li, J. & Fontelos, M. A. 2003 Drop dynamics on the beads-on-string structure for viscoelastic jets: a numerical study. Phys. Fluids 15, 922937.
Lister, J. R. & Stone, H. A. 1998 Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10, 27582764.
Lötstedt, P. & Petzold, L. 1986 Numerical solution of nonlinear differential equations with an algebraic constraints 1: convergence results for backward differentiation formulas. Maths Comput. 46, 491516.
Lowry, B. J. & Steen, P. H. 1995 Capillary surfaces: stability from families of equilibria with application to the liquid bridge. Proc. R. Soc. Lond. A 449, 411439.
McGough, P. T. & Basaran, O. A. 2006 Repeated formation of fluid threads in breakup of a surfactant-covered jet. Phys. Rev. Lett. 96, 054502.
McKinley, G. H. & Tripathi, A. 2000 How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44, 653670.
Meseguer, J. & Sanz, A. 1985 Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges. J. Fluid Mech. 153, 83101.
Rubio-Rubio, M., Sevilla, A. & Gordillo, J. M. 2013 On the thinnest steady threads obtained by gravitational stretching of capillary jets. J. Fluid Mech. 729, 471483.
Notz, P. K., Chen, A. U. & Basaran, O. A. 2001 Satellite drops: unexpected dynamics and change of scaling during pinch-off. Phys. Fluids 13, 549552.
Papageorgiou, D. T. 1995a Analytical description of the breakup of liquid jets. J. Fluid Mech. 301, 109132.
Papageorgiou, D. T. 1995b On the breakup of viscous liquid threads. Phys. Fluids 7, 15291544.
Paulsen, J. D. 2013 Approach and coalescence of liquid drops in air. Phys. Rev. E 88, 063010.
Paulsen, J. D., Burton, J. C., Nagel, S. R., Appathurai, S., Harris, M. T. & Basaran, O. 2012 The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl Acad. Sci. USA 109, 68576861.
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 58385866.
Pozrikidis, C. 1999 Capillary instability and breakup of a viscous thread. J. Engng Maths 36, 255275.
Rothert, A., Richter, R. & Rehberg, I. 2001 Transition from symmetric to asymmetric scaling function before drop pinch-off. Phys. Rev. Lett. 87, 084501.
Rothert, A., Richter, R. & Rehberg, I. 2003 Formation of a drop: viscosity dependence of three flow regimes. New J. Phys. 5, 59.159.13.
Ruschak, K. J. 1980 A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Intl J. Numer. Meth. Engng 15, 639648.
Schulkes, R. M. S. M. 1994 The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278, 83100.
Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.
Simmons, J. A., Sprittles, J. E. & Shikhmurzaev, Y. D. 2015 The formation of a bubble from a submerged orifice. Eur. J. Mech. (B/Fluids) 53, 2436.
Slobozhanin, L. A. & Perales, J. M. 1993 Stability of liquid bridges between equal disks in an axial gravity field. Phys. Fluids A 5, 13051314.
Sprittles, J. E. 2015 Air entrainment in dynamic wetting: Knudsen effects and the influence of ambient air. J. Fluid Mech. 769, 444481.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012a The dynamics of liquid drops and their interaction with solids of varying wettabilities. Phys. Fluids 24, 082001.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012b A finite element framework for describing dynamic wetting phenomena. Intl J. Numer. Meth. Fluids 68, 12571298.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2013 Finite element simulation of dynamic wetting flows as an interface formation process. J. Comput. Phys. 233, 3465.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2014a Dynamics of liquid drops coalescing in the inertial regime. Phys. Rev. E 89, 063006.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2014b A parametric study of the coalescence of liquid drops in a viscous gas. J. Fluid Mech. 753, 279306.
Stone, H. A., Stroock, A. D. & Adjari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381411.
Suryo, R. & Basaran, O. A. 2006 Local dynamics during pinch-off of liquid threads of power law fluids: scaling analysis and self-similarity. J. Non-Newtonian Fluid Mech. 138, 134160.
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2005 The coalescence speed of a pendent and sessile drop. J. Fluid Mech. 527, 85114.
Wilkes, E. D., Phillips, S. D. & Basaran, O. A. 1999 Computational and experimental analysis of dynamics of drop formation. Phys. Fluids 11, 35773598.
Yildirim, O. E. & Basaran, O. A. 2001 Deformation and breakup of stretching bridges of Newtonian and shear-thinning liquids: comparison of one- and two-dimensional models. Chem. Engng Sci. 56, 211233.
Yue, P., Feng, J. J., Liu, C. & Sheen, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293317.
Zhou, C., Yue, P. & Feng, J. J. 2006 Formation of simple and compound drops in microfluidic devices. Phys. Fluids 18, 092105.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Type Description Title
VIDEO
Movies

Li et al. supplementary movie
A movie showing the liquid bridge geometry and the entire process of breakup for Oh=0.16. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (10.5 MB)
10.5 MB
VIDEO
Movies

Li et al. supplementary movie
A movie showing the liquid bridge geometry and the entire process of breakup for Oh=0.16. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (3.8 MB)
3.8 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=10, characteristic of the V-regime. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (1.8 MB)
1.8 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=10, characteristic of the V-regime. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (1.3 MB)
1.3 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=0.16, characteristic of the VI-regime. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (1.8 MB)
1.8 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=0.16, characteristic of the VI-regime. The thread remains connected at all stages, with a microthread connecting regions which appear to have separated in the movie.

 Video (1.3 MB)
1.3 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=0.001, characteristic of the I-regime.

 Video (1.9 MB)
1.9 MB
VIDEO
Movies

Li et al. supplementary movie
A close-up of the breakup at Oh=0.001, characteristic of the I-regime.

 Video (871 KB)
871 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed