Criteria for disintegration of an uncharged conducting liquid jet in a transverse electric field

An uncharged conducting liquid cylindrical column (a jet for applications) placed between a pair of flat electrodes is considered. In the trivial case, when the electric field is absent, the jet with circular cross-section is the only possible equilibrium configuration of the system. In the presence of a potential difference between the electrodes, the jet is deformed by the electrostatic forces: its cross-section stretches along the electric field lines. In the case of the mutual compensation of the electrostatic and capillary forces, a new equilibrium configuration of the jet can appear. In a sufficiently strong field, the balance of the forces becomes impossible, and the jet disintegrates (splits into two separate jets). In the present work, we find the range of the parameters (the applied potential difference and the interelectrode distance), where the problem of finding the equilibrium configurations of the jet has solutions. Also we obtain the conditions under which the solutions do not exist and, consequently, the jet splits. The results are compared with the previously studied limiting case of infinite interelectrode distance.