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The breakup of viscous jets with large velocity modulations

Published online by Cambridge University Press:  26 April 2006

D. W. Bousfield ,
I. H. Stockel  and
C. K. Nanivadekar
D. W. Bousfield
Affiliation:
Department of Chemical Engineering, University of Maine, Orono, ME 04469, USA
I. H. Stockel
Affiliation:
Department of Chemical Engineering, University of Maine, Orono, ME 04469, USA
C. K. Nanivadekar
Affiliation:
Department of Chemical Engineering, University of Maine, Orono, ME 04469, USA Present address: Hercules Research Center, Wilmington, DE 19894, USA.
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Abstract

The surface-tension-driven breakup of viscous jets is observed for a range of Weber and Ohnesorge numbers. The breakup is enhanced with a sinusoidal modulation or pulsation of the jet's exit velocity; the velocity modulation amplitudes and wavenumbers are larger than previous values reported in the literature. The combinations of modulation amplitude and wavenumber that produce uniform droplets are identified for each pair of Weber and Ohnesorge numbers. Satellite droplets are eliminated at values of the Ohnesorge number greater than 1.6. Droplet pairing and merging occurs at high wavenumbers; droplet merging has not been reported in the jet breakup literature. The timescale for breakup is predicted within the data scatter by the thin filament equation of Bousfield et al. (1986) with no fitted parameters. An upper bound on satellite droplet size is predicted by the thin-filament equation and the average satellite droplet volume is qualitatively predicted. An algebraic expression is derived to predict the breakup time of viscous jets with large velocity modulation amplitudes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 601 - 617
Copyright
© 1990 Cambridge University Press

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References

Achenbach, E.: 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209.Google Scholar
Araki, N. & Kasuda, A., 1978 Production of droplets of uniform size by vibration. In Proc. First Intl Conf. on Liquid Atomization and Spraying Systems, vol. 8–1, p. 173.
Bogy, D. B.: 1978 Use of one-dimensional Cosserat theory to study instability in a viscous liquid jet. Phys. Fluids 21, 190.Google Scholar
Bogy, D. B.: 1979a Breakup of a liquid jet: third perturbation Cosserat solution. Phys. Fluids 22, 224.Google Scholar
Bogy, D. B.: 1979b Drop formation in a circular liquid jet. Ann. Rev. Fluid Mech. 11, 207.Google Scholar
Bogy, D. B., Shine, S. J. & Talke, F. E., 1980 Finite difference solution of the Cosserat fluid jet equations. J. Comput. Phys. 38, 294.Google Scholar
Bousfield, D. W.: 1988 Filament splitting between separating plates. Chem. Engng Commun. 73, 19.Google Scholar
Bousfield, D. W. & Denn, M. M., 1987 Jet breakup enhanced by an initial pulse. Chem. Engng Commun. 53, 219.Google Scholar
Bousfield, D. W., Keunings, R., Marrucci, G. & Denn, M. M., 1986 Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. J. Non-Newtonian Fluid Mech. 21, 79.Google Scholar
Busker, D. P., Lamers, A. P. G. G. & Nieuwenhuizen, J. K. 1989 The non-linear break-up of an inviscid liquid jet using the spatial-instability method. Chem. Engng Sci. 44, 377.Google Scholar
Chaudhary, K. C. & Maxworthy, T., 1980a The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation. J. Fluid Mech. 96, 275.Google Scholar
Chaudhary, K. C. & Maxworthy, T., 1980b The nonlinear capillary instability of a liquid jet. Part 3. Experiments on satellite drop formation and control. J. Fluid Mech. 96, 287.Google Scholar
Chaudhary, K. C. & Redekopp, L. G., 1980 The nonlinear capillary instability of a liquid jet. Part 1. Theory J. Fluid Mech. 96, 257.
Goedde, E. F. & Yuen, M. C., 1970 Experiments on liquid jet instability. J. Fluid Mech. 40, 495.Google Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R., 1969 Breakup of a laminar capillary jet of viscoelastic fluid. J. Fluid Mech. 38, 689.Google Scholar
Green, A. E.: 1976 On the non-linear behavior of fluid jets. Intl J. Engng Sci. 14, 49.Google Scholar
Keunings, R.: 1986 A transient finite element method for solving deformable surface flows. J. Comput. Phys. 62, 199.Google Scholar
Kurabayashi, T. & Karasawa, T., 1982 Production of uniform droplets by non-circular nozzles. In Proc. Second Intl Congr. on Liquid Atomisation and Spraying Systems. Vol. 2–3, p. 55.
Lafrance, P.: 1975 Nonlinear breakup of a laminar liquid jet. Phys. Fluids 18, 428.Google Scholar
Lee, H. C.: 1974 Drop formation in a liquid jet. IBM J. Res. Dev. 18, 364.Google Scholar
Leib, S. J. & Goldstein, M. E., 1986 The generation of capillary instabilities on a liquid jet. J. Fluid Mech. 168, 479.Google Scholar
McCarthy, J. J. & Molloy, N. A., 1974 Review of stability of liquid jets and the influence of nozzle design. Chem. Engng 7, 1.Google Scholar
Nayfeh, A. H.: 1970 Nonlinear stability of a liquid jet. Phys. Fluids 13, 841.Google Scholar
Pao, H. P. & Kao, T. W., 1977 Vortex structure in the wake of a sphere. Phys. Fluids 20, 187.Google Scholar
Pimbley, W. T. & Lee, H. C., 1977 Satellite droplet formation in a liquid jet. IBM J. Res. Dev. 21, 21.Google Scholar
Plateau, J.: 1873 Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires. Paris: Gauthier-Villars.
Rajagopalan, R. & Tien, C., 1973 Production of monodispersed drops by forced vibration of a liquid jet. Can. J. Chem. Engng 51, 272.Google Scholar
Rayleigh, Lord: 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4.Google Scholar
Rutland, D. F. & Jameson, G. J., 1970 Theoretical prediction of the sizes of drops in the breakup of capillary jets. Chem. Engng. Sci. 25, 1689.Google Scholar
Rutland, D. F. & Jameson, G. J., 1971 A nonlinear effect in the capillary instability of liquid jets. J. Fluid Mech. 46, 267.Google Scholar
Sakai, T., Sadakata, M., Saito, M., Hoshino, N. & Senuma, S., 1982 Uniform size droplets by longitudinal vibration of Newtonian and non-Newtonian fluids. In Proc. Second Intl Conf. on Liquid Atomisation and Spraying Systems, vol. 2, p. 37.
Schneider, J. M. & Hendricks, C. D., 1964 Source of uniform droplets. Rev. Sci. Instrum. 35, 1349.Google Scholar
Schummer, P. & Tebel, K. H., 1982 Germ. Chem. Engng 5, 209.
Shokoohi, F.: 1976 Numerical investigation of the disintegration of liquid jets. Ph.D. thesis. Columbia University, New York. 132 pp.
Sterling, A. M. & Sleicher, C. A., 1975 The instability of capillary jets. J. Fluid Mech. 68, 477.Google Scholar
Stockel, I. H.: 1988 Research on droplet formation for application to kraft black liquors. Department of Energy Tech. Rep. 4, DOE/CE/40626-T4.Google Scholar
Taub, H. H.: 1976 Investigation of nonlinear waves on liquid jets. Phys. Fluids 19, 1124.Google Scholar
Wang, D. P.: 1968 Finite amplitude effect on the stability of a jet of circular cross-section. J. Fluid Mech. 34, 299.Google Scholar
Weast, R. C.: 1975 Handbook of Chemistry and Physics. Cleveland, Ohio: CRC Press.
Weber, C.: 1931 Zum Zerfall eines Flussigkeitsstrahles. Z. Angew. Math. Mech. 11, 136.Google Scholar
Yuen, M. C.: 1968 Non-linear capillary instability of a liquid jet. J. Fluid Mech. 33, 151.Google Scholar