Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-21T12:14:24.826Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of residual axial gravity on the stability of liquid columns subjected to electric fields

Published online by Cambridge University Press:  26 April 2006

Heliodoro González  and
Antonio Castellanos
Heliodoro González
Affiliation:
Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, 41012 Seville, Spain
Antonio Castellanos
Affiliation:
Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, 41012 Seville, Spain
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability criterion for almost cylindrical dielectric liquid bridges subjected to axial electric fields in the presence of residual axial gravity is obtained. In its absence, a perfectly cylindrical equilibrium solution is allowed for all values of the relevant parameters, which are the slenderness of the liquid bridge, the electrical Bond number and the relative permittivity between the outer and inner media. This basic solution is unstable beyond a critical slenderness which varies with the electrical parameters (González et al. 1989). The destabilization takes place axisymmetrically. The inclusion of the gravitational Bond number as a new, small parameter may be treated by means of the Lyapunov-Schmidt Method, a well-known projection technique that gives the local bifurcation diagram relating the admissible equilibrium amplitudes for the liquid bridge and the aforementioned parameters. As in the absence of applied electric field, the gravitational Bond number breaks the pitchfork diagram into two isolated branches of axisymmetric equilibrium solutions. The stable one has a turning point whose location determines the new stability criterion. Quantitative results are presented after solving the resulting set of linear recursive problems by means of the method of lines.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 249 , April 1993 , pp. 185 - 206
Copyright
© 1993 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

Collin, R. E. 1991 Field Theory of Guided Waves. New York: IEEE Press.
Coriell, S. R. & Cordes, M. R. 1977 Theory of molten zone shape and stability. J. Cryst. Growth 42, 466– 472.Google Scholar
Coriell, S. R., Hardy, S. C. & Cordes, M. R. 1977 Stability of liquid zones. J. Colloid Interface Sci. 60, 126– 136.Google Scholar
González, H. & Castellanos, A. 1990 The effect of an axial electric field on the stability of a rotating dielectric cylindrical liquid bridge. Phys. Fluids A 2(11), 2069– 2071.Google Scholar
González, H., McCluskey, F. M. J., Castellanos, A. & Barrero, A. 1989 Stabilization of dielectric liquid bridges by electric fields in the absence of gravity. J. Fluid Mech. 206, 545– 561.Google Scholar
Graney, L. & Richardson, A. A. 1981 The numerical solution of non-linear partial differential equations by the method of lines. J. Comput. Appl. Maths 7(4), 229– 235.Google Scholar
Iooss, G. & Joseph, D. D. 1980 Elementary Stability and Bifurcation Theory. Springer.
Martínez, I. 1983 Stability of axisymmetric liquid bridges. In Material Sciences under Microgravity, ESA SP-191, pp. 267– 273.
Mikhail, N. M. 1987 On the validity and stability of the method of lines for the solution of partial differential equations. Appl. Maths Comput. 22, 89– 98.Google Scholar
Myshkis, A. D., Babskii, V. G., Kopachevskii, N. D., Slobozhanin, L. A. & Tyupsov, A. D. 1987 Low-gravity Fluid Mechanics. Springer.
Perales, J. M. 1987 Non-axisymmetric effects on long liquid bridges. Acta Astronautica 15(8), 561– 565.Google Scholar
Perales, J. M., Sanz, A. & Rivas, D. 1990 Eccentric rotation of a liquid bridge. Appl. Microgravity Tech. 2(4), 193– 197.Google Scholar
Ramos, A. & Castellanos, A. 1993 Bifurcation diagrams of axisymmetric liquid bridges of arbitrary volume in electric and gravitational axial fields. J. Fluid Mech. 249, 207– 225.Google Scholar
Vega, J. M. & Perales, J. M. 1983 Almost cylindrical isorotating liquid bridges for small Bond numbers. In Material Sciences under Microgravity, ESA SP-191, pp. 247– 252.