Bifurcation diagrams of axisymmetric liquid bridges of arbitrary volume in electric and gravitational axial fields

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Abstract
Finite-amplitude bifurcation diagrams of axisymmetric liquid bridges anchored between two plane parallel electrodes subjected to a potential difference and in the presence of an axial gravity field are found by solving simultaneously the Laplace equation for the electric potential and the Young–Laplace equation for the interface by means of the Galerkin/finite element method. Results show the strong stabilizing effect of the electric field, which plays a role somewhat similar to the inverse of the slenderness. It is also shown that the electric field may determine whether the breaking of the liquid bridge leads to two equal or unequal drops. Finally, the sensitivity of liquid bridges to an axial gravity in the presence of the electric field is studied.