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The bursting of two-dimensional drops in slow viscous flow

Published online by Cambridge University Press:  29 March 2006

J. D. Buckmaster  and
J. E. Flaherty
J. D. Buckmaster
Affiliation:
Mason Laboratory, Yale University, New Haven, Connecticut
J. E. Flaherty
Affiliation:
Mathematics Department, Rensselaer Polytechnic Institute, Troy, N.Y.
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Abstract

We consider the deformation of two-dimensional drops when immersed in a slow viscous corner flow. The problem is formulated as one of analytic function theory and simplified by assuming that both the drop and the exterior fluid have the same viscosity. An approximate analysis is carried out, in which the conditions at the interface are satisfied in an average sense, and this reveals the following features of the solution. A drop of given physical properties (volume, surface tension and viscosity), when immersed in a corner flow, has no steady equilibrium shape if the rate of strain of the applied flow is too large. On the other hand, if the rate of strain is small enough for a steady solution to exist, then in general there are two possible solutions. These features are confirmed by formulating the exact problem in terms of a nonlinear integro-differential equation, which is solved numerically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 4 , 9 October 1973 , pp. 625 - 639
Copyright
© 1973 Cambridge University Press

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References

Brazier-Smith, P. R. 1971 Phys. Fluids, 14, 1.
Buckmaster, J. D. 1972 J. Fluid Mech. 55, 385.
Buckmaster, J. D. 1973 J. Appl. Mech. E, 40, 18.
Keller, J. B., Rubenfeld, L. A. & Molyneux, J. E. 1967 J. Fluid Mech. 30, 97.
Mancino, O. G. 1967 J. A.C.M. 14, 341.
Richardson, S. 1968 J. Fluid Mech. 33, 475.
Robinson, S. M. 1966 SIAM J. Numer. Anal. 3, 650.
Rumscheidt, F. D. & Mason, S. G. 1961 J. Colloid Sci. 16, 238.
Taylor, G. I. 1934 Proc. Roy. Soc. A, 146, 501.
Taylor, G. I. 1964a Proc. 11th Int. Congr. Appl. Mech., Munich, p. 790. Springer.
Taylor, G. I. 1964b Proc. Roy. Soc. A, 280, 383.
Wegener, P. P., Sundell, R. E. & Parlange, J.-Y. 1971 Z. Flugwiss. 19, 347.