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An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows

Published online by Cambridge University Press:  21 April 2006

B. J. Bentley  and
L. G. Leal
B. J. Bentley
Affiliation:
Chemical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA
L. G. Leal
Affiliation:
Chemical Engineering Department, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

We consider the deformation and burst of small fluid droplets in steady linear, two-dimensional motions of a second immiscible fluid. Experiments using a computer-controlled, four-roll mill to investigate the effect of flow type are described, and the results compared with predictions of several available asymptotic deformation and burst theories, as well as numerical calculations. The comparison clarifies the range of validity of the theories, and demonstrates that they provide quite adequate predictions over a wide range of viscosity ratio, capillary number, and flow type.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 241 - 283
Copyright
© 1986 Cambridge University Press

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References

Acrivos, A. 1983 The breakup of small drops and bubbles in shear flows. Ann. N. Y. Acad. Sci. 404, 1–11.Google Scholar
Acrivos, A. & Lo, T. S. 1978 Deformation and breakup of a single slender drop in an extensional flow. J. Fluid Mech. 86, 641–672.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973a Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1–21.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973b The rheology of suspensions and its relation to phenomenological theories for non-Newtonian Fluids. Intl J. Multiphase Flow 1, 1–24.Google Scholar
Bentley, B. J. 1985 Drop deformation and burst in two-dimensional flows. Ph.D. thesis, California Institute of Technology.
Bentley, B. J. & Leal, L. G. 1986 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
Buckmaster, J. D. 1972 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385–400.Google Scholar
Buckmaster, J. D. 1973 The bursting of pointed drops in slow viscous flow. Trans. ASME E: J. Appl. Mech. 40, 18–24Google Scholar
Chaffey, C. E., Takano, M. & Mason, S. G. 1965 Particle motions in sheared suspensions. 16. Orientations of rods and disks in hyperbolic and other flows. Can. J. Phys. 43, 1269–1287.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37, 601–623.Google Scholar
Frankel, N. A. & Acrivos, A. 1970 The constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 65–78.Google Scholar
Fuller, G. G. & Leal, L. G. 1981 Flow birefringence of concentrated polymer solutions in two-dimensional flows. J. Polymer Sci. Polymer Phys. Ed. 19, 557–587.Google Scholar
Giesekus, H. 1962 Strömungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von dar in suspendierten Teilchen. Teil II: Ebene Strömungen und eine experimentelle Anordnung zu ihrer Realisierung. Rheol. Ada. 2, 113–121.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. Conf.Mixing, 3rd, Andover, N.H. Republished 1982 in Chem. Engng Commun. 14, 225–277.Google Scholar
Hakimi, F. S. & Schowalter, W. R. 1980 The effects of shear and vorticity on deformation of a drop. J. Fluid Mech. 98, 635–645.Google Scholar
Hinch, E. J. & Acrivos, A. 1979 Steady long slender droplets in two-dimensional straining motion. J. Fluid Mech. 91, 401–414.Google Scholar
Hinch, E. J. & Acrivos, A. 1980 Long slender drops in a simple shear flow. J. Fluid Mech. 98, 305–328.Google Scholar
Rallison, J. M. 1980 A note on the time-dependent deformation of a viscous drop which is almost spherical. J. Fluid Mech. 98, 625–633.Google Scholar
Rallison, J. M. 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, 191–209.Google Scholar
Rumscheidt, F. D. & Mason, S. G. 1961 Particle motions in sheared suspensions. 12. Deformation and burst of fluid drops in shear and hyperbolic flows. J. Colloid Interface Sci. 16, 238–261.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.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
Taylor, G. I. 1964 Conical free surfaces and fluid interfaces. Proc. Intl Congr. Appl. Mech. llth, Munich, pp. 790–796.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1972 Particle motions in sheared suspension. 27. 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