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Development of the boundary layer at a free surface from a uniform shear flow

Published online by Cambridge University Press:  28 March 2006

Simon L. Goren
Affiliation:
Department of Chemical Engineering, University of California, Berkeley, California

Abstract

The development of the boundary layer accompanying the formation of a free surface at y′ = 0, from the two-dimensional uniform shear flow u′ = ωyω, is discussed. The analysis shows that the surface velocity and surface position vary as the cube root of the distance downstream, while the mass-transfer coefficient varies inversely as the cube root of this distance. It is shown how these may be applied to the formation of capillary jets.

Type
Research Article
Copyright
© 1966 Cambridge University Press

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References

Glauert, M. B. 1957 The boundary layer in simple shear flow past a flat plate. J. Aero. Sci. 24, 848.Google Scholar
Goldstein, S. 1930 Concerning some solutions of the boundary layer equations of hydrodynamics. Proc. Cambridge Phil. Soc. 26, 1.Google Scholar
Goldstein, S. 1933 On the two-dimensional steady flow of a viscous fluid behind a solid body—I. Proc. Roy. Soc., A 142, 545.Google Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics. Oxford: Clarendon Press.
Goren, S. L. & Wronski, S. 1966 The shape of low-speed capillary jets of Newtonian liquids. J. Fluid Mech. 25, 185.Google Scholar
Li, T. Y. 1955 Simple shear flow past a flat plate in an incompressible fluid of small viscosity. J. Aero. Sci. 22, 651.Google Scholar
Li, T. Y. 1956 Effects of free-stream vorticity on the behaviour of a viscous boundary layer. J. Aero. Sci. 23, 1128.Google Scholar
Li, T. Y. 1957 Reply to comments of Glauert. J. Aero. Sci. 24, 849.Google Scholar
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams. Quart. J. Mech. & Appl. Math. 4, 42.Google Scholar
Meksyn, D. 1961 Mew Methods in Laminar Boundary-Layer Theory. Oxford: Pergamon Press.
Murray, J. D. 1961 The boundary layer on a flat plate in a stream with uniform shear. J. Fluid Mech. 11, 309.Google Scholar
Potter, O. E. 1957 Mass transfer between co-current streams and boundary layer solutions. Chem. Eng. Sci. 6, 170.Google Scholar
Rideal, E. K. & Sutherland, K. L. 1952 The variation of the surface tension of solutions with time. Trans. Faraday Soc. 48, 1109.Google Scholar
Scriven, L. E. & Pigford, R. L. 1959 Fluid dynamics and diffusion calculations for laminar liquid jets. A.I.Ch.E.J. 5, 397.Google Scholar
Ting, L. 1960 Boundary layer over a flat plate in the presence of shear flow. Phys. Fluids, 3, 78.Google Scholar