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An experimental study of transient effects in the breakup of viscous drops

Published online by Cambridge University Press:  21 April 2006

H. A. Stone ,
B. J. Bentley  and
L. G. Leal
H. A. Stone
Affiliation:
Chemical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA
B. J. Bentley
Affiliation:
Chemical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA Current address: Bentley Systems, Inc., 180 Gordon Dr., Lionville, PA 19353, USA.
L. G. Leal
Affiliation:
Chemical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

A computer-controlled four-roll mill is used to examine two transient modes of deformation of a liquid drop: elongation in a steady flow and interfacial-tension-driven motion which occurs after the flow is stopped abruptly. For modest extensions, drop breakup does not occur with the flow on, but may occur following cessation of the flow as a result of deterministic motions associated with internal pressure gradients established by capillary forces. These relaxation and breakup phenomena depend on the initial drop shape and the relative viscosities of the two fluids. Capillary-wave instabilities at the fluid-fluid interface are observed only for highly elongated drops. This study is a natural extension of G. I. Taylor's original studies of the deformation and burst of droplets in well-defined flow fields.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 131 - 158
Copyright
© 1986 Cambridge University Press

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References

Acrivos, A. 1983 The breakup of small drops and bubbles in shear flows. 4th Int Conf. on Physiochemical Hydrodynamics, Ann. N. Y. Acad. Sci. 404, 1–11.Google Scholar
Bentley, B. J. & Leal, L. G. 1986a A computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows. J. Fluid Mech. 167, 219–240.Google Scholar
Bentley, B. J. & Leal, L. G. 1986b An experimental investigation of drop deformation and breakup in steady two-dimensional linear flows. J. Fluid Mech. 167, 241–283.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 98, 305–328.Google Scholar
Geller, A. S., Lee, S. H. & Leal, L. G. 1986 The creeping motion of a spherical particle normal to a deformable interface. J. Fluid Mech. 169, 27–69.Google Scholar
Girault, H. H., Schiffrin, D. J. & Smith, B. D. V. 1982 Drop image processing for surface and interfacial tension measurements. J. Electroanal. Chem. 137, 207–217.Google Scholar
Girault, H. H., Schiffrin, D. J. & Smith, B. D. V. 1984 The measurement of interfacial tension of pendant drops using a video image profile digitizer. J. Colloid Interface Sci. 101, 257–266.Google Scholar
Grace, H. P. 1971 Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Eng. Found. Res. Conference Mixing, 3rd Andover, N.H. Republished 1982 in Chem. Engng Commun. 14, 225–277.Google Scholar
Hinch, E. J. 1980 The evolution of slender inviscid drops in an axisymmetric straining flow. J. Fluid Mech. 101, 545–553.Google Scholar
Hinch, E. J. & Acrivos, A. 1980 Long slender drops in a simple shear flow. J. Fluid Mech. 98, 305–328.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
Lee, W.-K. & Flumerfelt, R. W. 1981 Instability of stationary and uniformly moving cylindrical fluid bodies. I. Newtonian systems. Intl J. Multiphase Flow 7, 363–383.Google Scholar
Lee, W.-K., Yu, K.-L. & Flumerfelt, R. W. 1981 Instability of stationary and uniformly moving cylindrical fluid bodies. II. Viscoelastic threads and experimental observations. Intl J. Multiphase Flow 7, 385–400.Google Scholar
Mikami, T., Cox, R. G. & Mason, S. G. 1975 Breakup of extending liquid threads. Intl J. Multiphase Flow 2, 113–138.Google Scholar
Rallison, J. M. 1980 Note on the time-dependent deformation of a viscous drop which is almost spherical. J. Fluid Mech. 98, 625–633.Google Scholar
Rallison, J. W. 1981 A numerical study of the deformation and burst of a viscous drop in general shear flows. J. Fluid Mech. 109, 465–482.Google Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Ann. Rev. Fluid Mech. 16, 45–66.Google Scholar
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, 191–200.Google Scholar
Rumscheidt, F. D. & Mason, S. G. 1961 Breakup of stationary liquid threads. J. Colloid Sci. 17, 260–269.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A138, 41–48.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A146, 501–523.Google Scholar
Taylor, G. I. 1964 Conical free surfaces and fluid interfaces. In Proc. Intl Congr. Appl. Mech., 11th, Munich, pp. 790–796.
Tomotika, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A150, 322–337.Google Scholar
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. A153, 302–318.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1972 Particle motions in sheared suspensions. XXVII. Transient and steady deformation and burst of liquid drops. J. Colloid Interface Sci. 38, 395–411.Google Scholar
Youngren, G. K. & Acrivos, A. 1976 On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76, 433–442.Google Scholar