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Note on the time-dependent deformation of a viscous drop which is almost spherical

Published online by Cambridge University Press:  19 April 2006

J. M. Rallison
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Abstract

The theory of the shear-induced small deformation of viscous drops at zero Reynolds number is reviewed. The general result for arbitrary shear and surface tension is presented, and the asymptotic forms for weak flow and for high internal viscosity are derived from it. In the latter case, numerical solutions are compared with the experiments of Torza, Cox & Mason (1972).

Type
Research Article
Copyright
© 1980 Cambridge University Press

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References

Barthès-Biesel, D. & Acrivos, A. 1973a Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 121.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973b The rheology of suspensions and its relation to phenomenological theories for non-Newtonian fluids. Int. J. Multiphase Flow 1, 124.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37, 601623.Google Scholar
Frankel, N. A. & Acrivos, A. 1970 The constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 6578.Google Scholar
Hakimi, F. S. & Schowalter, W. R. 1980 The effects of shear and vorticity on deformation of a drop. J. Fluid Mech. 98, 635645.Google Scholar
Rallison, J. M. 1978 The effects of Brownian rotations in a dilute suspension of rigid particles of arbitrary shape. J. Fluid Mech. 84, 237263.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501523.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, 395411.Google Scholar