Hostname: page-component-848d4c4894-89wxm Total loading time: 0 Render date: 2024-07-08T02:06:37.944Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute and convective instability of a viscous liquid curtain in a viscous gas

Published online by Cambridge University Press:  10 February 1997

C. H. Teng ,
S. P. Lin  and
J. N. Chen
C. H. Teng
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
S. P. Lin
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
J. N. Chen
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
Get access Rights & Permissions [Opens in a new window]

Extract

The linear instability of a viscous liquid flowing in a vertical sheet sandwiched between two viscous gases bounded externally by two vertical walls is investigated. The critical Weber number below which the flow is absolutely unstable and above which the flow is convectively unstable is found to be approximately equal to one and is weakly dependent on the rest of the parameters. The Weber number is defined as We ≡ ρ1 U20d/S where S is the surface tension, ρ1is the liquid density, U0 is the centreline velocity of the liquid sheet, and d is the half-thickness of the uniform liquid sheet. The sinuous mode is found to have a greater amplification rate than the varicose mode in the convective instability regime. While absolute instability is caused by the surface tension, convective instability is caused by the amplification of disturbances near the liquid-gas interface. The surface tension, and viscosities of liquids and gases all suppress the amplification of the convectively unstable disturbances. An increase in the gravitational force or the gas density results in an enhancement of the amplification rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 105 - 120
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akyias, T. R. & Benney, D. J. 1980 Stud. Appl. Maths 63, 209.Google Scholar
Antoniades, M. G. & Lin, S. P. 1980 J. Colloid Interface Sci. 77, 583.Google Scholar
Bkrs, A. 1983 Handbook of Plasma Physics, vol. 1, pp. 452–516. North-Holland.Google Scholar
Briggs, R. J. 1964 Electron Stream Interaction with Plasmas. MIT Press.Google Scholar
Brown, D. R. 1961 J. Fluid Mech. 10, 297.CrossRefGoogle Scholar
Clark, C. J. & Ril, N. 1972 Proc. R. Soc. Lond. A 329, 467.Google Scholar
Crapper, G. D., Dombrowski, N., Jepson, W. P. & Pyott, G. A. D. 1973 J. Fluid Mech. 57, 671.Google Scholar
Crapper, G. D., Dombrowski, N. & Pyott, G. A. D. 1975 Proc. R. Soc. Lond. A 342, 209.Google Scholar
Drazin, P. G. & Reid, W. H. 1985 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Gottlieb, D. & Orszag, S. G. 1977 Numerical Analysis of Spectral Methods; Theory and Applications. Cbms-Nsf Regional Conference Series in Applied Mathematics, vol. 26, SLAM, PA.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 J. Fluid Mech. 159, 151.Google Scholar
Kelly, R. E., Goussis, D. A., Lin, S. P. & Hsu, F. K. 1989 Phys. Fluids A 1, 819.Google Scholar
Kistler, S. F. & SCRIVEN, L. E. 1984 Ml J. Numer. Meth. Fluids 4, 207.CrossRefGoogle Scholar
Lanczos, C. 1956 Applied Analysis. Prentice-Hall.Google Scholar
Leib, S. J. & Goldstein, M. E. 1986 J. Fluid Mech. 168, 479.Google Scholar
Leib, S. J. & Goldstein, M. E. 19866 Phys. Fluids 29, 952.Google Scholar
Lin, S. P. 1981 J. Fluid Mech, 104, 111.Google Scholar
Lin, S. P. & Lian, Z. W. 1989 Phys. Fluids A 1, 490.Google Scholar
Lin, S. P., Lian, Z. W. & Creighton, B. J. 1990 J. Fluid Mech. 220, 673.Google Scholar
Lin, S. P. & Roberts, G. 1981 J. Fluid Mech. 112, 443.Google Scholar
Muller, D. E. 1956 Mathematical Tables and Aid to Computation, vol. 10, pp. 208–230.Google Scholar
Orszag, S. A. 1971 J. Fluid Mech. 50, 689.Google Scholar
Renardy, Y. 1987 Phys. Fluids 30, 1638.CrossRefGoogle Scholar
Rombers, S. 1984 Problem Solving Software for Mathematical and Statistical FORTRAN Programming. I & II. Imsl.Google Scholar
Taylor, G. I. 1959a Proc. R. Soc. Lond. A 253, 289.Google Scholar
Taylor, G. I. 19596 Proc. R. Soc. Lond. A 252, 296.Google Scholar
Taylor, G. I. 1959c Proc. R. Soc. Lond. A 253, 313.Google Scholar
Taylor, G. I. 1963 The Scientific Papers ofG. I. Taylor, vol. 3, no. 25. Cambridge University Press.Google Scholar
Weihs, D. 1978 J. Fluid Mech. 87, 289.CrossRefGoogle Scholar