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The effects of shear and vorticity on deformation of a drop

Published online by Cambridge University Press:  19 April 2006

F. S. Hakimi  and
W. R. Schowalter
F. S. Hakimi
Affiliation:
Department of Chemical Engineering, Princeton University, New Jersey 08540 Present address: Amoco Minerals Company, Chicago, Illinois 60601.
W. R. Schowalter
Affiliation:
Department of Chemical Engineering, Princeton University, New Jersey 08540
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Abstract

A fluid drop immersed in a second incompressible fluid is deformed by a motion which, far from the drop, varies linearly with distance. Deformation of the drop is then determined by both the rate of deformation and the vorticity of the continuous fluid phase far from the drop. Experiments are described in which the vorticity and rate of deformation were independently varied by means of an eccentric-disk rheometer field. It is shown that predictions from a small-parameter expansion to first order in ε = μ0Gb/σ are in good agreement with experiment to values of ε as large as 0·4, where μ0 is viscosity of the continuous phase, G a measure of the flow strength, b the drop radius, and σ the interfacial tension.

Of the several terms which arise in the O(ε) expansion, only that one which contains a Jaumann derivative of the deformation parameter provides an important contribution beyond Taylor's original analysis of the problem. This fact greatly simplifies the computation of drop shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 3 , 12 June 1980 , pp. 635 - 645
Copyright
© 1980 Cambridge University Press

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References

Abbott, T. N. G. & Walters, K. 1970 Rheometrical flow systems. Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations. J. Fluid Mech. 40, 205–213.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, 1–21.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
Hakimi, F. S. 1976 The effects of shear and vorticity on the deformation of a drop. Ph.D. dissertation, Princeton University.
Rallison, J. M. 1980 Time dependent drop deformations for small deviations from sphericity. J. Fluid Mech. 98, 625–633.Google Scholar
Schowalter, W. R. 1979 Some consequences of suspension models for non-viscometric flows. J. Non-Newtonian Fluid Mech. 5, 285–296.Google Scholar
Schowalter, W. R., Chaffey, C. E. & Brenner, H. 1968 Rheological behaviour of a dilute emulsion. J. Colloid Interface Sci. 26, 152–160.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