Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T19:10:57.339Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

H. A. Stone  and
L. G. Leal
H. A. Stone
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Transient effects associated with the deformation and breakup of a drop following a step change from critical to suberitical flow conditions are studied experimentally and numerically. In the experiments, we consider step changes in both the shear rate and flow type for two-dimensional linear flows generated in a four-roll mill. Numerically we consider step changes in shear rate only for a uniaxial extensional flow. Depending upon the degree of deformation prior to the change in flow conditions, the drop may either return to a steady deformed shape, or continue to stretch at a reduced rate, or, for intermediate cases, the drop may break without large-scale stretching. This behaviour is a consequence of the complicated interaction between changes of shape due to interfacial tension and changes of shape due to the motion of the suspending fluid. This mode of breakup is most pronounced for high viscosity ratios, because very large extensions are necessary to guarantee breakup if the flow is stopped abruptly. For drops that are not too deformed, the sudden addition of vorticity to the external flow is characterized by rapid rotation of the drop to a new steady orientation followed by deformation and/or breakup according to the effective flow conditions at the new orientation. Finally, for viscous drops in flows with vorticity, it is demonstrated experimentally that breakup can be achieved if the initial shape is sufficiently non-spherical even though the same drop could not be made to break in the same flow at any capillary number when beginning with a near-spherical shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 223 - 263
Copyright
© 1989 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

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 slender drop in an extensional flow. J. Fluid Mech. 86, 641–672.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
Goedde, E. F. & Yuen, M. C. 1970 Experiments on liquid jet instability. J. Fluid Mech, 40, 495–511.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. Engng Found. Res. Conf. Mixing, 3rd, Andover, N.H. (Republished 1982 in Chem. Engng Commun. 14, 225–277.)
Kang, I. S. & Leal, L. G. 1987 Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number I. Finite-difference scheme and its application to the deformation of a bubble in a uniaxial straining flow. Phys Fluids 7, 1929–1940.CrossRefGoogle Scholar
Lasheras, J. C., Fernandez-Pello, A. C. & Dryer, F. L. 1979 Initial observations on the free droplet combustion characteristics of water-in-fuel emulsions. Combust. Sci. Tech. 21, 1–14.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
Peregrine, D. H. 1986 The dripping of drops, or the bifurcation of liquid bridges. IUTAM Symposium: Fluid Mechanics in the Spirit of G. I. Taylor, Symposium Abstracts.
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 general shear flows. J. Fluid Mech. 89, 191–200.Google Scholar
Seward, T. P. 1974 Elongation and spheriodization of phase-separated particles in glass. J. Non-Cryst. Solids 15, 487–504.Google Scholar
Sherwood, J. D. 1988 Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188, 133–146.Google Scholar
Stone, H. A. 1988 Dynamics of drop deformation and breakup in time-dependent flows at low Reynolds numbers. Ph.D. thesis. California Institute of Technology.
Stone, H. A., Bentley, H. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.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. 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
Torza, S., Cox, R. G. & Mason, S. G. 1971 Electrohydrodynamic deformation and burst of liquid drops.. Phil. Trans. R. Soc. Lond. A 269, 295–319.Google Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1972 Particle motions in sheared suspensions. 27. Transient and steady deformation and burst of liquid drops. J. Colloid Interface Sci. 38, 395–411.Google Scholar
Van Dyke, M. 1982 An Album of Fluid Motion, p. 73. Parabolic.