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The effects of capillarity on free-streamline separation

Published online by Cambridge University Press:  29 March 2006

R. C. Ackerberg
R. C. Ackerberg
Affiliation:
Department of Chemical Engineering, Polytechnic Institute of New York, Brooklyn
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Abstract

The effect of a small surface-tension coefficient on the classical theory of free-streamline separation from a sharp trailing edge is studied. The classical solution fails in a small region surrounding the edge, where it predicts singular behaviour, and an inner solution, satisfying linear boundary conditions, is required to obtain a uniformly valid first approximation. The solution valid near the edge removes the curvature and pressure-gradient singularities of the classical solution and predicts a standing capillary wave along the free streamline.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 2 , 29 July 1975 , pp. 333 - 352
Copyright
© 1975 Cambridge University Press

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References

Ackerberg, R. C. 1968a On a non-linear theory of thin jets. Part 1. J. Fluid Mech. 31, 583.Google Scholar
Ackerberg, R. C. 1968b On a non-linear theory of thin jets. Part 2. A linear theory for small injection angles. J. Fluid Mech. 33, 261.Google Scholar
Ackerberg, R. C. 1970 Boundary-layer separation at a free streamline. Part 1. Two-dimensional flow. J. Fluid Mech. 44, 211.Google Scholar
Ackerberg, R. C. 1973a Boundary-layer separation at a free streamline. Part 3. Axisymmetric flow and the flow downstream of separation. J. Fluid Mech. 59, 645.Google Scholar
Ackerberg, R. C. 1973b Axisymmetric potential flow separation at a sharp trailing edge. Studies in Appl. Math. 52, 377.Google Scholar
Ackerberg, R. C. & Pal, A. 1968 On the interaction of a two-dimensional jet with a parallel flow. J. Math. Phys. 47, 32.Google Scholar
Carter, D. S. 1961 Local behaviour of plane gravity flows at the confluence of free boundaries and analytic fixed boundaries. J. Math. Mech. 10, 441.Google Scholar
Crapper, G. D. 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 532.Google Scholar
Geller, M. 1963 A table of integrals involving powers, exponentials, logarithms and the exponential integral. Jet Propulsion Lab. Tech. Rep. no. 32–469.Google Scholar
Gurevich, M. I. 1961 Influence of capillary forces upon the coefficient of contraction of a jet. Prikl. Mat. Mekh. 25, 1586.(English trans.).Google Scholar
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. Academic.
Lamb, H. 1945 Hydrodynamics. Dover.
Mcleod, E. B. 1955 The explicit solution of a free boundary problem involving surface tension. J. Rat. Mech. Anal. 4, 557.Google Scholar
Milne-Thomson, L. M. 1957 Theoretical Hydrodynamics, 3rd edn. Macmillan.
Noble B. 1958 Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations. Pergamon.