Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-04T19:27:40.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes

Published online by Cambridge University Press:  16 May 2014

Theo Driessen ,
Pascal Sleutel ,
Frits Dijksman ,
Roger Jeurissen  and
Detlef Lohse
Theo Driessen*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Pascal Sleutel
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Frits Dijksman
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Roger Jeurissen
Affiliation:
Department of Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We experimentally, numerically and theoretically demonstrate a novel method of producing a stream of widely spaced high-velocity droplets by imposing a superposition of two Rayleigh–Plateau-unstable modes on a liquid jet. The wavelengths of the two modes are chosen close to the wavelength of the most unstable mode. The interference pattern of the two superimposed modes causes local asymmetries in the capillary tension. The velocity of the initial droplets depends on these local asymmetries. Due to their different velocities, the droplets coalesce to produce a stream of larger droplets spaced at a much larger distance than the initial droplets. We analytically derive the perturbations that robustly induce this process and investigate the influence of the nonlinear interactions of the two Rayleigh–Plateau-unstable modes on the coalescence process. Experiments and numerical simulations demonstrate that the jet breakup and the subsequent droplet merging are fully governed by the selected modes.

JFM classification

Drops and Bubbles: Drops and Bubbles Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 275 - 296
Copyright
© 2014 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., Wilkes, E. D. & Basaran, O. A. 2002 Drop formation from a capillary tube: comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops. Phys. Fluids 14 (8), 2606–2621.Google Scholar
Ashgriz, N. & Mashayek, F. 1995 Temporal analysis of capillary jet breakup. J. Fluid Mech. 291, 163–190.Google Scholar
Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183–204.Google Scholar
Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169–198.Google Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48 (9), 1842–1848.Google Scholar
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45 (1), 85–113.CrossRefGoogle Scholar
Baumert, B. M. & Muller, S. J. 1997 Flow regimes in model viscoelastic fluids in a circular Couette system with independently rotating cylinders. Phys. Fluids 9 (3), 566–586.CrossRefGoogle Scholar
Bennett, W. D., Brown, J. S., Zeman, K. L., Hu, S. C., Scheuch, G. & Sommerer, K. 2002 Targeting delivery of aerosols to different lung regions. J. Aerosol Med. 15 (2), 179–188.Google Scholar
van der Bos, J. A., van der Meulen, M. P., Driessen, T. W., van den Berg, M., Reinten, H., Wijshoff, H., Versluis, M. & Lohse, D. 2014 Velocity profile inside piezo-acoustic inkjet droplets: comparison between experiments and numerical simulations. Phys. Rev. Appl 1, 014004.Google Scholar
Brenn, G. & Lackermeier, U. 1997 Drop formation from a vibrating orifice generator driven by modulated electrical signals. Phys. Fluids 9 (12), 3658–3669.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover Publications.Google Scholar
Chaudhary, K. C. & Maxworthy, T. 1980 The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation. J. Fluid Mech. 96 (02), 275–286.Google Scholar
van Deventer, H., Houben, R. & Koldeweij, R. 2013 New atomization nozzle for spray drying. Drying Technol. 31 (8), 891–897.Google Scholar
Driessen, T. & Jeurissen, R. 2011 A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid. Intl J. Comput. Fluid Dyn. 25 (6), 333–343.Google Scholar
Driessen, T., Jeurissen, R., Wijshoff, H., Toschi, F. & Lohse, D. 2013 Stability of viscous long liquid filaments. Phys. Fluids 25, 062109.Google Scholar
Eggers, J. 1993 Universal pinching of 3d axisymmetric free-surface flow. Phys. Rev. Lett. 71 (21), 3458–3460.Google Scholar
Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205–221.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.Google Scholar
García, F. J. & González, H. 2008 Normal-mode linear analysis and initial conditions of capillary jets. J. Fluid Mech. 602, 81–117.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quere, D. 2004 Capillarity and Wetting Phenomena. Springer.Google Scholar
González, H. & García, F. J. 2009 The measurement of growth rates in capillary jets. J. Fluid Mech. 619, 179–212.Google Scholar
van Hoeve, W., Gekle, S., Snoeijer, J. H., Versluis, M., Brenner, M. P. & Lohse, D. 2010 Breakup of diminutive Rayleigh jets. Phys. Fluids 22 (12), 122003.Google Scholar
Huynh, H., Ashgriz, N. & Mashayek, F. 1996 Instability of a liquid jet subject to disturbances composed of two wavenumbers. J. Fluid Mech. 320, 185–210.Google Scholar
Keller, J. B., Rubinow, S. I. & Tu, Y. O. 1973 Spatial instability of a jet. Phys. Fluids 16 (12), 2052–2055.CrossRefGoogle Scholar
Lafrance, P. 1975 Nonlinear breakup of a laminar liquid jet. Phys. Fluids 18 (4), 428–432.Google Scholar
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510.Google Scholar
Notz, P. K. & Basaran, O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223–256.Google Scholar
Oliveira, M. S. N. & McKinley, G. H. 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers. Phys. Fluids 17 (7), 071704.Google Scholar
Orme, M. 1991 On the genesis of droplet stream microspeed dispersions. Phys. Fluids A 3 (12), 2936–2947.CrossRefGoogle Scholar
Orme, M. & Muntz, E. P. 1987 New technique for producing highly uniform droplet streams over an extended range of disturbance wavenumbers. Rev. Sci. Instrum. 58 (2), 279–284.Google Scholar
Orme, M. & Muntz, E. P. 1990 The manipulation of capillary stream breakup using amplitude-modulated disturbances: a pictorial and quantitative representation. Phys. Fluids A 2 (7), 1124–1140.Google Scholar
Papageorgiou, D. T. & Orellana, O. 1998 Study of cylindrical jet breakup using one-dimensional approximations of the Euler equations. SIAM J. Appl. Maths 59 (1), 286–317.CrossRefGoogle Scholar
Pimbley, W. T. & Lee, H. C. 1977 Satellite droplet formation in a liquid jet. IBM J. Res. Dev. 21 (21), 385–388.Google Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier-Villars.Google Scholar
Rayleigh, J. W. S. 1878 On the instability of jets. Proc. Lond. Math. Soc. 1 (1), 4–13.CrossRefGoogle Scholar
Rayleigh, J. W. S. 1892 On the instability of a cylinder of viscous liquid under capillary force. Phil. Mag. 34 (207), 145–154.Google Scholar
Rohani, M., Jabbari, F. & Dunn-Rankin, D. 2010 Breakup control of a liquid jet by disturbance manipulation. Phys. Fluids 22 (10), 107103.Google Scholar
Rutland, D. F. & Jameson, G. J. 1970 Theoretical prediction of the sizes of drops formed in the breakup of capillary jets. Chem. Engng Sci. 25 (11), 1689–1698.Google Scholar
Savart, F. 1833 Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Ann. Chim. 53, 337–386.Google Scholar
Srivastava, S., Perlekar, P., ten Thije Boonkkamp, J. H. M., Verma, N. & Toschi, F. 2013 Axisymmetric multiphase lattice Boltzmann method. Phys. Rev. E 88, 013309.Google Scholar
Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.Google Scholar
Takahashi, F., Schmoll, W. J. & Dressler, J. L. 1994 Characterization of a velocity-modulation atomizer. Rev. Sci. Instrum. 65, 3563–3569.Google Scholar
Taub, H. H. 1976 Investigation of nonlinear waves on liquid jets. Phys. Fluids 19 (8), 1124–1129.Google Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. Mech. 11 (2), 136–154.Google Scholar
Wijshoff, H. 2010 The dynamics of the piezo inkjet printhead operation. Phys. Rep. 491 (4–5), 77–177.Google Scholar
Wilkes, E. D., Phillips, S. D. & Basaran, O. A. 1999 Computational and experimental analysis of dynamics of drop formation. Phys. Fluids 11 (12), 3577–3598.Google Scholar
Xu, Q. & Basaran, O. A. 2007 Computational analysis of drop-on-demand drop formation. Phys. Fluids 19 (10), 102111.Google Scholar
Yarin, A. L. 1993 Free Liquid Jets and Films: Hydrodynamics and Rheology. Wiley.Google Scholar
Yuen, M.-C. 1968 Nonlinear capillary instability of a liquid jet. J. Fluid Mech. 33, 151–163.Google Scholar