Skip to main content

On the thinnest steady threads obtained by gravitational stretching of capillary jets

  • M. Rubio-Rubio (a1), A. Sevilla (a1) and J. M. Gordillo (a2)

Experiments and global linear stability analysis are used to obtain the critical flow rate below which the highly stretched capillary jet, generated when a Newtonian liquid issues from a vertically oriented tube, is no longer steady. The theoretical description, based on the one-dimensional mass and momentum equations retaining the exact expression for the interfacial curvature, accurately predicts the onset of jet self-excited oscillations experimentally observed for wide ranges of liquid viscosity and nozzle diameter. Our analysis, which extends the work by Sauter & Buggisch (J. Fluid Mech. vol. 533, 2005, pp. 237–257), reveals the essential stabilizing role played by the axial curvature of the jet, the latter effect being especially relevant for injectors with a large diameter. Our findings allow us to conclude that, surprisingly, the size of the steady threads produced at a given distance from the exit can be reduced by increasing the nozzle diameter.

Corresponding author
Email address for correspondence:
Hide All
Ambravaneswaran B., Subramani H. J., Phillips S. D. & Basaran O. A. 2004 Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.
Anna S. L., Bontoux N. & Stone H. A. 2003 Formation of dispersions using flow focusing in microchannels. Appl. Phys. Lett. 82, 364366.
Barrero A. & Loscertales I. G. 2007 Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89106.
Basaran O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 18421848.
Briggs R. J. 1964 Electron-stream Interaction with Plasmas. Research Monograph No. 29. MIT.
Canuto C., Hussaini M. Y., Quarteroni A. & Zang T. A. 2006 Spectral methods. Fundamentals in Single Domains. Scientific Computation, Springer.
Castro-Hernández E., Campo-Cortés F. & Gordillo J. M. 2012 Slender-body theory for the generation of micrometre-sized emulsions through tip streaming. J. Fluid Mech. 698, 89106.
Clanet C. & Lasheras J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307326.
Coullet P., Mahadevan L. & Riera C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 117.
Denn M. M. 1980 Continuous drawing of liquids to form fibres. Annu. Rev. Fluid Mech. 12, 365387.
Doshi J. & Reneker D. H. 1995 Electrospinning process and applications of electrospun fibres. J. Electrostat. 35, 151160.
Eggers J. & Dupont T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205222.
Eggers J. & Villermaux E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.
Frankel I. & Weihs D. 1985 Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289307.
Gañán-Calvo A. M. 1998 Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80 (2), 285288.
Gañán-Calvo A. M. & Gordillo J. M. 2001 Perfectly monodisperse microbubbling by capillary flow focusing. Phys. Rev. Lett. 87, 274501.
García F. J. & Castellanos A. 1994 One-dimensional models for slender axisymmetric viscous liquid jets. Phys. Fluids 6 (8), 26762689.
Guerrero J., González H. & García F. J. 2012 Spatial modes of capillary jets, with application to surface stimulation. J. Fluid Mech. 702, 354377.
Huerre P. & Monkewitz P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151168.
Keller J. B., Rubinow S. I. & Tu Y. O. 1972 Spatial instability of a jet. Phys. Fluids 16, 20522055.
Landau L. D. 1946 On the vibrations of the electronic plasma. J. Phys. U.S.S.R. 10 (25), 445460.
Le Dizès S. 1997 Global modes in falling capillary jets. Eur. J. Mech. B/Fluids 16, 761778.
Leib S. J. & Goldstein M. E. 1986 The generation of capillary instabilities on a liquid jet. J. Fluid Mech. 168, 479500.
Loscertales I. G., Barrero A., Guerrero I., Cortijo R., Marquez M. & Ganan-Calvo A. M. 2002 Micro/nano encapsulation via electrified coaxial liquid jets. Science 295, 16951698.
Marín A. G., Campo-Cortés F. & Gordillo J. M. 2009 Generation of micron-sized drops and bubbles through viscous coflows. Colloid Surf. A 344, 27.
Marín A. G., Loscertales I. G., Marquez M. & Barrero A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.
Pearson J. R. A. & Matovich M. A. 1969 Spinning a molten threadline. Ind. Engng Chem. Fundam. 8, 605609.
Plateau J. 1873 Statique Expérimentale et Théorique des Liquides. Gauthier-Villars.
Rayleigh Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 413.
Sauter U. S. & Buggisch H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237257.
Schulkes R. M. S. M. 1994 The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278, 83100.
Senchenko S. & Bohr T. 2005 Shape and stability of a viscous thread. Phys. Rev. E 71, 056301.
Sevilla A. 2011 The effect of viscous relaxation on the spatiotemporal stability of capillary jets. J. Fluid Mech. 684, 204226.
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 Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18, 082102.
Tomotika S. 1936 Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate. Proc. R. Soc. Lond. 153, 302318.
Utada A. S., Chu L.-Y., Fernandez-Nieves A., Link D. R., Holtze C. & Weitz D. A. 2007a Dripping, jetting, drops, and wetting: the magic of microfluidics. MRS Bull. 32, 702708.
Utada A. S., Fernandez-Nieves A., Stone H. A. & Weitz D. A. 2007b Dripping to jetting transitions in coflowing liquid streams. Phys. Rev. Lett. 99, 094502.
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? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 60 *
Loading metrics...

Abstract views

Total abstract views: 198 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.