Influence of bounded geometry on the initial growth of electrocapillary instability for a liquid metal under electric field

• Published in: Applied surface science Vol. 87; pp. 91 - 98
• Main Authors: Néron de Surgy, G., González, H., Chabrerie, J.-P.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 02.03.1995; Elsevier Science
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Physics; Surface-tension-driven instability; Capillary waves; Stability; Cylindrical configuration; Non viscous fluid; Electric field effects; Numerical simulation; Liquid metals; Free surface
• ISSN: 0169-4332; 1873-5584
• DOI: 10.1016/0169-4332(94)00523-0

The deformation of an initially plane liquid metal surface by a normal electric field is known and analyzed since the works of Tonks, Frenkel, Taylor, Melcher, etc. It has been established that until a critical value of the field no destabilization occurs (the surface remains flat) while above this onset a peak pattern with defined wavelength appears where wavelength and the critical field depend on physical values of the liquid. For higher fields a whole band of wavelengths is unstable and a linear analysis of the first stage of the peak growth can show which wavelength dominates. Nevertheless, these works deal with large horizontal geometries. The influence of bounded geometry lead to modifications of the onset values that can be found thanks to a static analysis. This means that they are independent of the viscosity and of the geometry of the bath walls. In this paper we show how the initial deformation evolves (dynamical analysis) in confined geometry. The chosen geometry is a cylindrical liquid bath with the liquid anchored at the circular contact line and with constant volume. Both these assumptions being necessary to allow the growth of a pattern. The liquid is supposed to be inviscid as most liquid metals are.