Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-28T23:46:36.305Z Has data issue: false hasContentIssue false
  • English
  • Français

Deformation and burst of a liquid droplet freely suspended in a linear shear field

Published online by Cambridge University Press:  29 March 2006

D. Barthès-Biesel  and
A. Acrivos
D. Barthès-Biesel
Affiliation:
Department of Chemical Engineering, Stanford University Université de Technologie de Compiègne, 25, rue Eugène Jacquet, 60206 Compiègne, France.
A. Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter ε and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 1 , 23 October 1973 , pp. 1 - 22
Copyright
© 1973 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

Barthès-Biesel, D. 1972 Ph.D. dissertation, Stanford University.
Buckmaster, J. D. 1972 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385.Google Scholar
Buckmaster, J. D. 1973 The bursting of pointed drops in slow viscous flow. J. Appl. Mech. E, 40, 18.Google Scholar
Chaffey, C. E. & Brenner, H. 1967 A second-order theory for shear deformation of drops. J. Colloid Sci. 24, 258–269.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
Grace, H. P. 1971 Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Engng Foundation 3rd Res. Conf. on Mixing, Andover, New Hampshire.Google Scholar
Rivlin, R. S. 1955 Further remarks on the stress deformation relations for isotropic materials. J. Rat. Mech. Anal. 4, 681–702.Google Scholar
Rumscheidt, F. D. & Mason, S. G. 1961 Particle motion in sheared suspensions. XII. Deformation and burst of fluid drops in shear and hyperbolic flows. J. Colloid Sci. 16, 238–261.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. Roy. Soc. A 138, 41–48.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501–523.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