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Tip streaming from slender drops in a nonlinear extensional flow

Published online by Cambridge University Press:  20 April 2006

J. D. Sherwood
J. D. Sherwood
Affiliation:
Dowell Schlumberger, B.P. 90, 42003 St Etienne, France
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Abstract

The deformation of inviscid and slightly viscous drops is studied using slender-body theory. The imposed axisymmetric flow is a combination of a linear extensional flow, with velocity uz = G1 z along the axis of symmetry, together with a cubic flow uz = G3z3. When G3/G1 is sufficiently small the viscous drop breaks in a manner similar to that described by Acrivos & Lo (1978). For larger G3 > 0 the drop breaks by a rapid growth at its end. Steady-state experiments in a 4-roll mill show the ejection of a column of liquid from the tip of the drop, though this is probably caused by a change in the pressure gradient rather than the mechanism described above. The ejected column then breaks into droplets via the Rayleigh instability. It is hypothesized that one or other of these mechanisms corresponds to tip streaming as observed by Taylor (1934).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 281 - 295
Copyright
© 1984 Cambridge University Press

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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
Buckmaster, J. 1972 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385.Google Scholar
Buckmaster, J. 1973 The bursting of pointed drops in slow viscous flow. Trans. ASME E: J. Appl. Mech. 40, 18.Google Scholar
Fuller, G. G., Rallison, J. M., Schmidt, R. L. & Leal, L. G. 1980 The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy. J. Fluid Mech. 100, 555.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
Sherwood, J. D. 1981 Spindle-shaped drops in a viscous extensional flow. Math. Proc. Camb. Phil. Soc. 90, 529.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501.Google Scholar