Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T10:58:33.660Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrohydrodynamics of a current-carrying semi-insulating jet

Published online by Cambridge University Press:  29 March 2006

J. R. Melcher  and
E. P. Warren
J. R. Melcher
Affiliation:
Department of Electrical Engineering, Massachusetts Institute of Technology
E. P. Warren
Affiliation:
Department of Electrical Engineering, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

A quasi-one-dimensional non-linear model is developed for the axisymmetric dynamics. Streaming is coaxial with a cylindrical ‘wall’ supporting a potential having a linear axial dependence. In addition to a tangential field due to an axial current, the stream surface supports charges in proportion to the stream-wall potential difference; hence it is driven by normal and shear electric stresses. Free charge and polarization waves compete with the destabilizing effect of capillarity. With supercritical steady flow (the local jet velocity exceeds the wave velocity), it is found that the stream accelerates or decelerates in accordance with whether an equivalent longitudinal force density is respectively positive or negative. With subcritical flow, the effect of the force is reversed. Experiments demonstrate accelerating and decelerating flow régimes. Model and experiment are in agreement with regard to choking at a critical radius, and the dependence of radius and potential on position. Hysteretic switching between flow régimes is obtained by adjustment of stream and wall potentials, and is explained in terms of the model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 1 , 14 May 1971 , pp. 127 - 143
Copyright
© 1971 Cambridge University Press

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

Basset, A. B. 1894 Amer. J. Math. 16, 93.
Carson, R. S. & Hendricks, C. D. 1964 AIAA 4th Electric Propulsion Conf. Philadelphia, Paper no. 64–675.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New York: Interscience.
Heil, H. & Scott, B. W. 1969 IEEE, Paper no. 69 C 42 ED, New York.
Hogan, J. J., Carson, R. S., Schneider, M. J. & Hendricks, C. D. 1964 AIAA J. 2, 1460.
Melcher, J. R. 1963 Field-coupled Surface Waves. M.I.T.
Melcher, J. R. & Schwarz, W. J. 1968 Phys. Fluids, 11, 2604.
Melcher, J. R. 1970 Electric Fields and Moving Media. Education Development Center, 39, Chapel St., Newton, Mass. 02160: Education Development Center for the National Committee on Electrical Engineering Films.
Miller, E. P. & Spiller, L. L. 1964 Paint and Varnish Production (June—July).
Nayyer, N. K. & Murty, G. S. 1960 Proc. Phys. Soc. 75, 369.
Peskin, R. L., Raco, R. J., Yeh, P. S. & Morehouse, J. 1965 API Res. Conf. Distillate Fuel Combustion, Paper no. CP65-6-1965.
Saville, D. A. 1971 Phys. Fluids, 13, 2897.
Shapiro, A. H. 1953 Compressible Fluid Flow (vol. 1). New York: Ronald Press.
Stoker, J. J. 1957 Water Waves. New York: Interscience.
Sweet, R. G. 1964 Stanford Electronics Laboratories, Stanford, Calif. Pub. no. 1722–1.
Taylor, G. I. 1959a Proc. Roy. Soc. A, 253, 289.
Taylor, G. I. 1959b Proc. Roy. Soc. A, 253, 296.
Taylor, G. I. 1959c Proc. Roy. Soc. A, 253, 313.
Taylor, G. I. 1968 Proc. Roy. Soc. A, 306, 423.
Taylor, G. I. 1969a The stability of a fine fluid jet in a longitudinal field. Presented at Int. Symp. Electrohydrodynamics, M.I.T., Cambridge, Mass.
Taylor, G. I. 1969b Proc. Roy. Soc. A, 313, 453.
Zeleny, J. 1917 Phys. Rev. 10, 1.