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Steady draw-down of a liquid jet under surface tension and gravity

Published online by Cambridge University Press:  20 April 2006

D. B. Bogy
D. B. Bogy
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley
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Abstract

When a water tap is turned off gradually, a critical point is reached at which the flow changes abruptly from a continuous stream to a series of drops that form at the tap. This problem is studied within the context of a one-dimensional (Cosserat) jet theory. The exact inviscid, steady, nonlinear jet equations are solved and steady draw-down shapes are obtained for various values of Weber and Bond numbers. A critical Weber number is obtained (as a function of Bond number) below which no steady solution is found that satisfies the constraints imposed at the nozzle. The results are compared with classical experiments and appear to explain the observed ‘first critical velocity’.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 157 - 176
Copyright
© 1981 Cambridge University Press

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References

Bogy, D. B. 1978 Phys. Fluids 21, 190–197.
Bogy, D. B. 1979a Phys. Fluids 22, 224–230.
Bogy, D. B. 1979b Ann. Rev. Fluid Mech. 11, 207–228.
Caulk, D. A. & Naghdi, P. M. 1979a Arch. Rat. Mech. Anal. 69, 1–30.
Caulk, D. A. & Naghdi, P. M. 1979b J. Appl. Mech. 46, 291–297.
Duda, J. L. & Vrentas, J. S. 1967 Chem. Eng. Sci. 22, 855–869.
Goren, S. L. & Wronski, S. 1966 J. Fluid Mech. 25, 185–198.
Green, A. E. 1976 Int. J. Engng Sci. 14, 49–63.
Green, A. E., Naghdi, P. M. & Wenner, M. L. 1974 Proc. Roy. Soc. A 337, 485–507.
Harmon, D. B. 1955 J. Franklin Inst. 259, 519–522.
Lienhard, J. H. 1968 Trans. A.S.M.E. D, J. Basic Engng 90, 262–268.
Middleman, S., & Gavis, J. 1961 Phys. Fluids 4, 355–359.
Naghdi, P. M. 1979 Proc. IUTAM Symp. on Non-Newtonian Fluid Mech. J. Non-Newtonian Fluid Mech. 5, 233–265.Google Scholar
Pitts, E. 1974 J. Fluid Mech. 63, 487–508.
Rayleigh, Lord 1879 Proc. London Math. Soc. 10, 4–13.
Savart, F. 1833 Ann. de Chim. 53. 337–386.
Scheele, G. F. & Meister, B. J. 1968 A.I.Ch.E. J. 14, 15–19.
Scriven, L. E. & Pigford, R. L. 1959 A.I.Ch.E. J. 5, 397–402.
Smith, S. W. J. & Moss, H. 1917 Proc. Roy. Soc. A 93, 373–393.
Tyler, E. & Richardson, E. T. 1925 Proc. Phys. Soc. London 37, 297–311.