Hostname: page-component-6b989bf9dc-vmcqm Total loading time: 0 Render date: 2024-04-14T18:54:28.753Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of the deformation and burst of a viscous drop in general shear flows

Published online by Cambridge University Press:  20 April 2006

J. M. Rallison
J. M. Rallison
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
Get access Rights & Permissions [Opens in a new window]

Abstract

The time-dependent deformation and burst of a viscous drop in an arbitrary shear flow at zero Reynolds number is studied. The viscosities of the drop and the suspending fluid are assumed to be equal. A numerical scheme to track the (non-axisymmetric) drop shape in time is presented, and used to investigate the deformation induced by two-dimensional shear and orthogonal rheometer flows. Steady deformations, critical flow rates and burst modes are determined, and compared with asymptotic (small and large) deformation theories, and with experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 465 - 482
Copyright
© 1981 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. & Lo, T. S. 1978 Deformation and breakup of a single slender drop in an extensional flow. J. Fluid Mech. 86, 641.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1.Google Scholar
Grace, H. P. 1971 Dispersion phenomena in high viscosity immiscible fluid systems and applications of static mixers as dispersion devices in such systems. Engng Found. 3rd Res. Conf. Mixing, Andover, New Hampshire.
Hakimi, F. S. & Schowalter, W. R. 1980 The effects of shear and vorticity on deformation of a drop. J. Fluid Mech. 98, 635.Google Scholar
Hinch, E. J. & Acrivos, A. 1979 Steady long slender droplets in two-dimensional straining motion. J. Fluid Mech 91, 401.Google Scholar
Hinch, E. J. & Acrivos, A. 1980 Long slender drops in a simple shear flow. J. Fluid Mech. 98, 305.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.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.Google Scholar
Rumscheidt, F. D. & Mason, S. G. 1961 Particle motions in sheared suspensions. XII. Deformation and burst of fluid drops in shear and hyperbolic flows. J. Colloid Sci. 16, 238.Google Scholar
Schowalter, W. R. 1979 Some consequences of suspension models for non-viscometric flows. J. Non-Newtonian Fluid Mech. 5, 285.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501.Google Scholar
Taylor, G. I. 1964 Conical free surfaces and fluid interfaces. Proc. 11th Int. Cong. Appl. Mech., Munich.
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.Google Scholar