Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T09:32:26.570Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  24 July 2013

M. Rubio-Rubio ,
A. Sevilla  and
J. M. Gordillo
M. Rubio-Rubio
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain
A. Sevilla*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain
J. M. Gordillo
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avda. de los Descubrimientos s/n, 41092 Sevilla, Spain
*
†Email address for correspondence: alejandro.sevilla@uc3m.es
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Instability: Absolute/convective instability Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 471 - 483
Copyright
©2013 Cambridge University Press 

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

Ambravaneswaran, B., Subramani, H. J., Phillips, S. D. & Basaran, O. A. 2004 Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.Google Scholar
Anna, S. L., Bontoux, N. & Stone, H. A. 2003 Formation of dispersions using flow focusing in microchannels. Appl. Phys. Lett. 82, 364–366.CrossRefGoogle Scholar
Barrero, A. & Loscertales, I. G. 2007 Micro- and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89–106.Google Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 1842–1848.Google Scholar
Briggs, R. J. 1964 Electron-stream Interaction with Plasmas. Research Monograph No. 29. MIT.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 2006 Spectral methods. Fundamentals in Single Domains. Scientific Computation, Springer.Google Scholar
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, 89–106.Google Scholar
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.CrossRefGoogle Scholar
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 1–17.Google Scholar
Denn, M. M. 1980 Continuous drawing of liquids to form fibres. Annu. Rev. Fluid Mech. 12, 365–387.Google Scholar
Doshi, J. & Reneker, D. H. 1995 Electrospinning process and applications of electrospun fibres. J. Electrostat. 35, 151–160.CrossRefGoogle Scholar
Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205–222.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Frankel, I. & Weihs, D. 1985 Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289–307.Google Scholar
Gañán-Calvo, A. M. 1998 Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80 (2), 285–288.Google Scholar
Gañán-Calvo, A. M. & Gordillo, J. M. 2001 Perfectly monodisperse microbubbling by capillary flow focusing. Phys. Rev. Lett. 87, 274501.Google Scholar
García, F. J. & Castellanos, A. 1994 One-dimensional models for slender axisymmetric viscous liquid jets. Phys. Fluids 6 (8), 2676–2689.Google Scholar
Guerrero, J., González, H. & García, F. J. 2012 Spatial modes of capillary jets, with application to surface stimulation. J. Fluid Mech. 702, 354–377.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Keller, J. B., Rubinow, S. I. & Tu, Y. O. 1972 Spatial instability of a jet. Phys. Fluids 16, 2052–2055.Google Scholar
Landau, L. D. 1946 On the vibrations of the electronic plasma. J. Phys. U.S.S.R. 10 (25), 445–460.Google Scholar
Le Dizès, S. 1997 Global modes in falling capillary jets. Eur. J. Mech. B/Fluids 16, 761–778.Google Scholar
Leib, S. J. & Goldstein, M. E. 1986 The generation of capillary instabilities on a liquid jet. J. Fluid Mech. 168, 479–500.Google Scholar
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, 1695–1698.Google Scholar
Marín, A. G., Campo-Cortés, F. & Gordillo, J. M. 2009 Generation of micron-sized drops and bubbles through viscous coflows. Colloid Surf. A 344, 2–7.Google Scholar
Marín, A. G., Loscertales, I. G., Marquez, M. & Barrero, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.CrossRefGoogle ScholarPubMed
Pearson, J. R. A. & Matovich, M. A. 1969 Spinning a molten threadline. Ind. Engng Chem. Fundam. 8, 605–609.CrossRefGoogle Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides. Gauthier-Villars.Google Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Sauter, U. S. & Buggisch, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237–257.Google Scholar
Schulkes, R. M. S. M. 1994 The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278, 83–100.CrossRefGoogle Scholar
Senchenko, S. & Bohr, T. 2005 Shape and stability of a viscous thread. Phys. Rev. E 71, 056301.Google Scholar
Sevilla, A. 2011 The effect of viscous relaxation on the spatiotemporal stability of capillary jets. J. Fluid Mech. 684, 204–226.Google Scholar
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, 381–411.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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, 302–318.Google Scholar
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, 702–708.Google Scholar
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.Google Scholar

Rubio-Rubio et al. supplementary movie

Globally stable jet of silicone oil with a viscosity of 200 cSt, injected through a needle of 6 mm outer diameter at a constant flow rate of 3.7 ml/min, showing steady behaviour. The movie was acquired at a rate of 300 images per second, and is displayed at 30 images per second.

Download Rubio-Rubio et al. supplementary movie(Video)
Video 8.7 MB

Rubio-Rubio et al. supplementary movie

Globally unstable jet of silicone oil with a viscosity of 200 cSt, injected through a needle of 6 mm outer diameter at a constant flow rate of 3.6 ml/min, showing the spontaneous growth of self-excited oscillations. The movie was acquired at a rate of 300 images per second, and is displayed at 30 images per second.

Download Rubio-Rubio et al. supplementary movie(Video)
Video 9.6 MB

Rubio-Rubio et al. supplementary movie

Globally stable jet of silicone oil with a viscosity of 100 cSt, injected through a needle of 2.5 mm outer diameter at a constant flow rate of 4.8 ml/min, showing damped oscillations after an external disturbance. The movie was acquired at a rate of 300 images per second, and is displayed at 30 images per second.

Download Rubio-Rubio et al. supplementary movie(Video)
Video 10.3 MB