Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-17T06:07:26.470Z Has data issue: false hasContentIssue false
  • English
  • Français

Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid

Published online by Cambridge University Press:  21 April 2006

H. A. Stone  and
L. G. Leal
H. A. Stone
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Present address: 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

In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 399 - 427
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. NY 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
Ascoli, E. P.: 1987 Low-Reynolds number hydrodynamic interaction of a solid particle with a planar wall. MS thesis, California Institute of Technology.
Barthes-Biesel, D. & Acrivos, A.1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1–21.Google Scholar
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
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, 79–97.Google Scholar
Brady, J. F. & Acrivos, A., 1982 The deformation and breakup of a slender drop in an extensional flow: inertial effects. J. Fluid Mech. 115, 443–451.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
Goedde, E. F. & Yuen, M. C., 1970 Experiments on liquid jet instability. J. Fluid Mech. 40, 495–511.Google Scholar
Goren, S. L.: 1964 The shape of a thread of liquid undergoing break-up. J. Colloid Sci. 19, 81–86.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. 3rd Andover, N. H. (Republished 1982 in Chem. Engng Commun.14, 225–277.)Google Scholar
Greenspan, H. P. & McCay, B. M., 1981 On wetting of a surface by a very viscous fluid. Stud. Appl. Maths 64, 95–112.Google Scholar
Higdon, J. J. L.: 1985 Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J. Fluid Mech. 159, 195–226.Google Scholar
Khakhar, D. V. & Ottino, J. M., 1987 Breakup of liquid threads in linear flows. Intl J. Multiphase Flow 13, 147–180.Google 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
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, 363–384.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.: 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., 1962 Break-up of stationary liquid threads. J. Colloid Sci. 17, 260–269.Google Scholar
Rutland, D. F. & Jameson, G. J., 1971 A non-linear effect in the capillary instability of liquid jets. J. Fluid Mech. 46, 262–271.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., Bentley, B. 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
Taylor, G. I.: 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A A138, 41–48.Google Scholar
Taylor, G. I.: 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A A146, 501–523.Google Scholar
Tomotika, S.: 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A 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. A 153, 302–318.Google Scholar
Youngren, G. K. & Acrivos, A., 1975 Stokes flow past a particle of arbitrary shape; a numerical method of solution. J. Fluid Mech. 69, 377–403 (corrigendum 69, 813).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
Yuen, M.-C.: 1968 Non-linear capillary instability of a liquid jet. J. Fluid Mech. 33, 151–163.Google Scholar