Transient radial spray from electrified viscous jets

Fine jets of slightly conducting viscous fluids and thicker jets or drops of less viscous ones can be drawn from conducting tubes by electric forces. As the potential of the tube relative to a neighbouring plate rises, viscous fluids become nearly conical and fine jets come from the vertices. The potentials at which these jets or drops first appear was measured and compared with calculations. The stability of viscous jets depends on the geometry of the electrodes. Jets as small as 20 μm in diameter and 5 cm long were produced which were quite steady up to a millimetre from their ends. Attempts to describe them mathematically failed. Their stability seems to be due to mechanical rather than electrical causes, like that of a stretched string, which is straight when pulled but bent when pushed. Experiments on the stability of water jets in a parallel electric field reveal two critical fields, one at which jets that are breaking into drops become steady and another at which these steady jets become unsteady again, without breaking into drops. Experiments are described in which a cylindrical soap film becomes unstable under a radial electric field. The results are compared with calculations by A. B. Basset and after a mistake in his analysis is corrected, agreement is found over the range where experiments are possible. Basset’s calculations for axisymmetrical disturbances are extended to those in which the jet moves laterally. Though this is the form in which the instability appears, calculations about uniform jets do not seem to be relevant. In an appendix M. D. Van Dyke calculates the attraction between a long cylinder and a perpendicular plate at a different potential.

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The steady navier-stokes problem for low reynolds number viscous jets into a half space

The Navier-Stokes Equations II — Theory and Numerical Methods - Lecture Notes in Mathematics ◽

10.1007/bfb0090335 ◽

1992 ◽

pp. 85-96 ◽

Cited By ~ 4

Author(s):

Huakang Chang

Keyword(s):

Reynolds Number ◽

Half Space ◽

Stokes Problem ◽

Low Reynolds Number ◽

Navier Stokes ◽

Viscous Jets ◽

Low Reynolds

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The breakup of viscous jets with large velocity modulations

Journal of Fluid Mechanics ◽

10.1017/s0022112090001136 ◽

1990 ◽

Vol 218 (-1) ◽

pp. 601 ◽

Cited By ~ 18

Author(s):

D. W. Bousfield ◽

I. H. Stockel ◽

C. K. Nanivadekar

Keyword(s):

Large Velocity ◽

Viscous Jets

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Viscous jets from nonnarrow orifices

AIAA Journal ◽

10.2514/3.2475 ◽

1964 ◽

Vol 2 (5) ◽

pp. 949-951

Author(s):

A. POZZI

Keyword(s):

Viscous Jets

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On the Onset of Breakup in Inviscid and Viscous Jets

Journal of Applied Mechanics ◽

10.1115/1.3424544 ◽

1979 ◽

Vol 46 (2) ◽

pp. 291-297 ◽

Cited By ~ 12

Author(s):

D. A. Caulk ◽

P. M. Naghdi

Keyword(s):

Linear Equations ◽

Three Dimensional ◽

Periodic Wave ◽

One Dimensional ◽

Periodic Wave Solutions ◽

Viscous Jets ◽

Elliptical Jet ◽

Basic Equations ◽

The One ◽

Small Disturbances

This paper is concerned with the instability of inviscid and viscous jets utilizing the basic equations of the one-dimensional direct theory of a fluid jet based on the concept of a Cosserat (or a directed) curve. First, a system of differential equations is derived for small motions superposed on uniform flow of an inviscid straight circular jet which can twist along its axis. Periodic wave solutions are then obtained for this system of linear equations; and, with reference to a description of growth in the unstable mode, the resulting dispersion relation is found to agree extremely well with the classical (three-dimensional) results of Rayleigh. Next, constitutive equations are obtained for a viscous elliptical jet and these are used to discuss both the symmetric and the antisymmetric small disturbances in the shape of the free surface of a circular jet. Through a comparison with available three-dimensional numerical results, the solution obtained is shown to be an improvement over an existing approximate solution of the problem.

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