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Satellite and subsatellite formation in capillary breakup

Published online by Cambridge University Press:  26 April 2006

M. Tjahjadi ,
H. A. Stone  and
J. M. Ottino
M. Tjahjadi
Affiliation:
Department of Chemical Engineering, Northwestern University. Evanston. IL 60208, USA Current address: General Electric Company, Corporate Research and Development, Schenectady, NY 12301, USA
H. A. Stone
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA
J. M. Ottino
Affiliation:
Department of Chemical Engineering, Northwestern University. Evanston. IL 60208, USA
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Abstract

An investigation of the interfacial-tension-driven fragmentation of a very long fluid filament in a quiescent viscous fluid is presented. Experiments covering almost three orders of magnitude in viscosity ratio reveal as many as 19 satellite droplets in between the largest droplets; complementary boundary-integral calculations are used to study numerically the evolution of the filament as a function of the viscosity ratio of the fluids and the initial wavenumber of the interface perturbation. Satellite drops are generated owing to multiple breakup sequences around the neck region of a highly deformed filament. In low-viscosity ratio systems, p < O(0.1), the breakup mechanism is self-repeating in the sense that every pinch-off is always associated with the formation of a neck, the neck undergoes pinch-off, and the process repeats. In general the agreement between computations and experiments is excellent; both indicate that the initial wavenumber of the disturbance is important in the quantitative details of the generated drop size distributions. However, these details are insignificant when compared with the large variations produced in the drop size distributions owing to variation in the viscosity ratio.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 297 - 317
Copyright
© 1992 Cambridge University Press

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References

Bentley, B. J. & Leal, L. G. 1986 An experimental investigation of drop deformation and breakup in steady two-dimensional linear flows. J. Fluid Mech. 167, 241–283.Google Scholar
Bogy, D. B. 1979 Drop formation in a circular liquid jet. Ann. Rev. Fluid Mech. 11, 207–228.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, 275–286.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, 287–297.Google Scholar
Chaudhary, K. C. & Redekopp, L. G. 1980 The nonlinear capillary instability of a liquid jet. Part 1. Theory. J. Fluid Mech. 96, 257–274.Google Scholar
Elemans, P. H. M. 1989 Modeling of the processing of incompatible polymer blends. PhD thesis, Eindhoven Technical University, The Netherlands.
Elemans, P. H. M., Janssen, J. M. H. & Meijer, H. E. H. 1990 The measurement of interfacial tension in polymer/polymer systems: the breaking thread method. J. Rheol. 34, 1311–1325.Google Scholar
Goedde, E. F. & Yuen, M. C. 1970 Experiments on liquid jet instability. J. Fluid Mech. 40, 495–511.Google Scholar
Lee, S. H. & Leal, L. G. 1982 The motion of a sphere in the presence of a deformable interface. II. A numerical study of the translation of a sphere normal to an interface. J. Colloid Interface Sci. 87, 81–106.Google Scholar
Mansour, N. & Lundgren, T. S. 1990 Satellite formation in capillary jet breakup.. Phys. Fluid A 2, 1141–1144.Google Scholar
Mikami, T., Cox, R. & Mason, R. G. 1975 Breakup of extending liquid threads. Intl J. Multiphase Flow 2, 113–118.Google Scholar
Muzzio, F. J., Swanson, P. D. & Ottino, J. M. 1991 The statistics of stretching and stirring in chaotic flows.. Phys. Fluids A 3, 822–834.Google Scholar
Muzzio, F. J., Tjahjadi, M. & Ottino, J. M. 1991 Self-similar drop size distributions produced by breakup in chaotic flows. Phys. Rev. Lett. 67, 54–57.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1986 Numerical Recipes. Cambridge University Press.
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191–209.Google Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Rumscheidt, F. D. & Mason, S. G. 1962 Breakup of stationary liquid threads. J. Colloid Sci. 17, 260–269.Google Scholar
Sax, J. E. & Ottino, J. M. 1985 Influence of morphology on the transport properties of polystyrene/polybutadiene blends: experimental results. Polymer 26, 1073–1080.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
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow.. Proc. R. Soc. Lond. A 146, 501–523.Google Scholar
Tjahjadi, M. & Ottino, J. M. 1991 Stretching and breakup of droplets in chaotic flows. J. Fluid Mech. 232, 191–219.Google Scholar
Tjahjadi, M., Stone, H. A. & Ottino, J. M. 1992 Estimating interfacial tension via breakup of highly extended fluid filaments and relaxation of moderately extended droplets. In preparation.
Tomotika, S. 1935 On the stability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid.. Proc. R. Soc. Lond. A 150, 322–337.Google Scholar
Tomotika, S. 1936 Breakup of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate.. Proc. R. Soc. Lond. A 153, 302–318.Google Scholar