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Capillary jet breakup by noise amplification

Published online by Cambridge University Press:  25 November 2016

S. Le Dizès  and
E. Villermaux
S. Le Dizès*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France
E. Villermaux
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France Institut Universitaire de France, Paris, France
*
†Email address for correspondence: ledizes@irphe.univ-mrs.fr
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Abstract

A liquid jet falling by gravity ultimately destabilizes by capillary forces. Accelerating as it falls, the jet thins and stretches, causing a capillary instability to develop on a spatially varying substrate. We discuss quantitatively the interplay between instability growth, jet thinning and longitudinal stretching for two kinds of perturbations, either solely introduced at the jet nozzle exit or affecting the jet all along its length. The analysis is conducted for any values of the liquid properties for a sufficiently large flow rate. In all cases, we determine the net gain of the most dangerous perturbation for all downstream distances, thus predicting the jet length, the wavelength at breakup and the resulting droplet size.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 810 , 10 January 2017 , pp. 281 - 306
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Copyright
© 2016 Cambridge University Press 

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References

Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.Google Scholar
Bers, A. 1983 Space–Time Evolution of Plasma Instabilities – Absolute and Convective, vol. 1, chap. 3.2. North-Holland.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.Google Scholar
Clarke, N. S. 1969 The asymptotic effects of surface tension and viscosity on an axially-symmetric free jet of liquid under gravity. Q. J. Mech. Appl. Maths 22, 247–256.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of fluid jets. Rep. Prog. Phys. 71, 1–79.CrossRefGoogle 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.CrossRefGoogle Scholar
Frankel, I. & Weihs, D. 1987 Influence of viscosity on the capillary instability of a stretching jet. J. Fluid Mech. 185, 361–383.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Javadi, A., Eggers, J., Bonn, D., Habibi, M. & Ribe, N. M. 2013 Delayed capillary breakup of falling viscous jets. Phys. Rev. Lett. 110 (14), 144501.Google ScholarPubMed
Le Dizès, S. 1997 Global modes in falling capillary jets. Eur. J. Mech. (B/Fluids) 16 (6), 761–778.Google Scholar
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, 471–483.CrossRefGoogle Scholar
Sauter, U. S. & Buggisch, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237–257.CrossRefGoogle Scholar
Schlichting, H. 1987 Boundary Layer Theory. McGraw-Hill.Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.CrossRefGoogle Scholar
Senchenko, S. & Bohr, T. 2005 Shape and stability of a viscous thread. Phys. Rev. E 71, 056301.Google ScholarPubMed
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. A 153 (879), 302–318.Google Scholar
Trouton, F. T. 1906 On the coefficient of viscous traction and its relation to that of viscosity. Proc. R. Soc. Lond. A 77, 426–440.Google Scholar
Villermaux, E. 2012 The formation of filamentary structures from molten silicates: Pele’s hair, angel hair, and blown clinker. C. R. Méc. 340, 555–564.CrossRefGoogle Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. Mech. 2, 136–154.CrossRefGoogle Scholar