{'fraction_non_alphanumeric': 0.013610315186246419, 'fraction_numerical': 0.0028653295128939827, 'mean_word_length': 5.467592592592593, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The effect of residual axial gravity on the stability of liquid columns subjected to electric fields

The stability criterion for almost cylindrical dielectric liquid bridges subjected to axial electric fields in the presence of residual axial gravity is obtained. In its absence, a perfectly cylindrical equilibrium solution is allowed for all values of the relevant parameters, which are the slenderness of the liquid bridge, the electrical Bond number and the relative permittivity between the outer and inner media. This basic solution is unstable beyond a critical slenderness which varies with the electrical parameters (González et al. 1989). The destabilization takes place axisymmetrically. The inclusion of the gravitational Bond number as a new, small parameter may be treated by means of the Lyapunov-Schmidt Method, a well-known projection technique that gives the local bifurcation diagram relating the admissible equilibrium amplitudes for the liquid bridge and the aforementioned parameters. As in the absence of applied electric field, the gravitational Bond number breaks the pitchfork diagram into two isolated branches of axisymmetric equilibrium solutions. The stable one has a turning point whose location determines the new stability criterion. Quantitative results are presented after solving the resulting set of linear recursive problems by means of the method of lines.