Skip to main content Accessibility help
×
Home

Atomization of undulating liquid sheets

  • N. BREMOND (a1), C. CLANET (a1) and E. VILLERMAUX (a1)

Abstract

The fragmentation of a laminar undulating liquid sheet flowing in quiescent air is investigated. Combining various observations and measurements we propose a sequential atomization scenario describing the overall sheet–drop transition in this configuration. The undulation results from a controlled primary Kelvin–Helmholtz instability. As the liquid travels through the undulating pattern, it experiences transient accelerations perpendicular to the sheet. These accelerations trigger a secondary instability responsible for the amplification of spanwise thickness modulations of the sheet. This mechanism, called the ‘wavy corridor’, is responsible for the sheet free edge indentations from which liquid ligaments emerge and break, forming drops. The final drop size distribution is of a Gamma type characterized by a unique parameter independent of the operating conditions once drop sizes are normalized by their mean.

Copyright

Corresponding author

Also at: Institut Universitaire de France.

References

Hide All
Asare, H. R., Takahashi, R. K. & Hoffman, M. A. 1981 Liquid sheet jet experiments: comparison with linear theory. Trans. ASME: J. Fluids Engng 103, 395604.
Bayvel, L. & Orzechowski, Z. 1993 Liquid atomization. Taylor & Francis.
Bond, W. N. 1935 The surface tension of a moving water sheet. Proc. Phys. Soc. 47, 549558.
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121130.
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273306.
Bush, J. W. M. & Aristoff, J. M. 2003 The influence of surface tension on the circular hydraulic jump. J. Fluid Mech. 489, 229238.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
Clanet, C. & Villermaux, E. 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307340.
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 11281129.
Dombrowski, N. & Johns, W. R. 1963 The aerodynamics instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203214.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Dupré, A. 1868 Théorie mécanique de la chaleur. Ann. Chim. Phys. 11, 194.
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69 (3), 865929.
Einsenklam, P. 1964 On ligament formation from spinning disks and cups. Chem. Engng Sci. 19, 693694.
Fraser, R. P., Eisenklam, P., Dombrowski, N. & Hasson, D. 1962 Drop formation from rapidly moving liquid sheet. AIChE J. 8, 672680.
de Gennes, P. G. 1996 Mechanics of soft interfaces. Faraday Disc. 104, 18.
Hagerty, W. W. & Shea, J. F. 1955 A study of the stability of plane fluid sheets. J. Appl. Mech. 22, 509514.
Heidmann, M. F., Priem, R. J. & Humphrey, J. C. 1957 A study of sprays formed by two impacting jets. NACA Tech. Note 3835.
von Helmholtz, H. 1868 On discontinuous movements of fluids. Phil. Mag. 36, 337346.
Huang, J. C. P. 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305319.
James, A. J., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003 Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 128.
Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25, 918921.
Kelvin, Lord 1871 Hydrokinetic solutions and observations. Philo. Mag. 42, 362377.
Kim, I. & Sirignano, W. A. 2000 Three-dimensional wave distortion and disintegration of thin planar liquid sheets. J. Fluid Mech. 410, 147183.
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.
Lin, S. P. 2003 Breakup of Liquid Sheets and Jets. Cambridge University Press.
Lozano, A., Garcia-Olivares, A. & Dopazo, C. 1998 The instability growth leading to a liquid sheet break up. Phys. Fluids 10, 21882197.
Mansour, A. & Chigier, N. 1990 Disintegration of liquid sheets. Phys. Fluids A 2, 706719.
Marmottant, P. & Villermaux, E. 2004 a Fragmentation of stretched liquid ligaments. Phys. Fluids 16, 27322741.
Marmottant, P. & Villermaux, E. 2004 b On spray formation. J. Fluid Mech. 498, 73112.
Mason, B. J. 1971 The Physics of Clouds. Clarendon.
Meier, G. E. A., Klopper, A. & Grabitz, G. 1992 The influence of kinematic waves on jet break down. Exps. Fluids 12, 173180.
Pandit, A. B. & Davidson, J. F. 1990 Hydrodynamics of the rupture of thin liquid films. J. Fluid Mech. 212, 1124.
Park, J., Huh, K. Y., Li, X. & Renksizbulut, M. 2004 Experimental investigation on cellular breakup of a planar liquid sheet from an air-blast nozzle. Phys. Fluids 16, 625632.
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Paris, Gauthiers Villars.
Rayleigh, Lord 1879 On the instability of jets. Proc. Lond. Math. Soc. 4, 10.
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. R. Soc. Lond. 14, 170177.
Rayleigh, Lord 1891 Some applications of photography. Nature XLIV, 249254.
Safran, S. A. 2003 Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Westview Press.
Savart, F. 1833 a Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Ann. de chim. 53, 337398.
Savart, F. 1833 b Mémoire sur le choc de deux veines liquides animées de mouvements directement opposés. Ann. de chim. 55, 257310.
Savart, F. 1833 c Mémoire sur le choc d'une veine liquide lancée sur un plan circulaire. Ann. de chim. 54, 5687.
Simmons, H. C. 1977 a The correlation of drop-size distributions in fuel nozzle sprays. part i: the drop-size/volume-fraction distribution. J. Engng Power 7, 309314.
Simmons, H. C. 1977 b The correlation of drop-size distributions in fuel nozzle sprays. part ii: the drop-size/number distribution. J. Engng Power 7, 315319.
Squire, H. B. 1953 Investigation of the stability of a moving liquid film. Brit. J. Appl. Phys. 4, 167169.
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their plane.i. Proc. R. Soc. Lond. A 201, 192196.
Taylor, G. I. 1959 a The dynamics of thin sheets of fluid ii. waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296312.
Taylor, G. I. 1959 b The dynamics of thin sheets of fluid iii. disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.
Taylor, G. I. 1960 Formation of thin flat sheets of water. Proc. R. Soc. Lond. A 259, 117.
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 341363.
Villermaux, E., Marmottant, P. & Duplat, J. 2004 Ligament-mediated spray formation. Phys. Rev. Let. 92, 074501.
Weihs, D. 1978 Stability of thin, radially moving liquid sheets. J. Fluid Mech. 87, 289298.
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green & Co.
York, J. L., Stubbs, H. E. & Tek, M. R. 1953 The mechanism of disintegration of liquid sheets. Trans. ASME, pp. 1279–1286.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Atomization of undulating liquid sheets

  • N. BREMOND (a1), C. CLANET (a1) and E. VILLERMAUX (a1)

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.