Bifurcation diagrams of axisymmetric liquid bridges subjected to axial electric fields

Abstract

The stability of dielectric liquid bridges between plane parallel electrodes when an electric potential difference is applied between them is studied for an axisymmetric configuration regarding arbitrary volume, axial gravity, and unequal coaxial anchoring disks attached to the electrodes. The stability is determined from the bifurcation diagrams related to the static problem. Two mathematical approaches are presented which are different in scope. First, the Lyapunov–Schmidt projection technique is applied to give the liquid bridge bifurcation diagrams for the bridge considered as an imperfect cylindrical one. The imperfection parameters, i.e., the relative difference of radii to the mean diameter, the deviation from the cylindrical volume, and the gravitational Bond number, are assumed to be small. Second, a Galerkin/finite element technique is used to obtain numerically bifurcation diagrams for arbitrary values of all the parameters. Agreement between both methods is good for small enough values of the imperfection parameters. The effect of the polarization charges existing at the free surface is highlighted. As in the absence of applied electric field, the gravitational Bond number and the relative difference of radii separately decrease the stability of the liquid column, but both effects conveniently combined may cancel out.