Construction of Exact Solutions for Equilibrium Configurations of the Boundary of a Conducting Liquid Deformed By an External Electric Field
- 22 Downloads
In a two-dimensional plane-symmetric formulation, we consider the problem of the equilibrium configurations of the free surface of a conducting capillary liquid placed in an external electric field. We find a one-parameter family of exact solutions of the problem according to which the fluid takes the shape of a blade. Such a configuration provides formally unlimited local field amplification: the field strength is maximum at the edge of the blade and drops to zero at the periphery. For a given potential difference between the liquid and the flat electrode located above it, we find threshold values of the electric field strength at the edge of the liquid blade, the radius of curvature of the edge, and the distance from the edge to the electrode limiting the region of existence of the solutions.
Keywordsequilibrium configuration exact solution free surface conductive fluid surface tension electrostatic force conformal map method
Unable to display preview. Download preview PDF.
- 3.J. R. Melcher, Field-Coupled Surface Waves, MIT Press, Cambridge, Mass. (1963).Google Scholar
- 19a.“Exact solution for the steady-state surface profile of a liquid metal in an external electric field,” Tech. Phys. Lett., 25, 920–921 (1999).Google Scholar
- 21.M. I. Gurevich, The Theory of Jets in an Ideal Fluid [in Russian], Nauka, Moscow (1979); English transl. prev. ed. (Intl. Series Monogr. Pure Appl. Math., Vol. 93), Pergamon, Oxford (1966).Google Scholar