Liquid bridges between horizontal cylinders: effects of gravity and electric fields

Abstract

Liquid bridges suspended between two parallel horizontal cylinders are studied using experiments, reduced-order mathematical modelling and numerical simulations. Both non-electrified and electrified configurations are considered, with the cylinders acting as electrodes between which a potential difference can be applied. The initial focus is on equilibrium bridge shapes, while the dynamics is examined only in the non-electrified case. In the experiments, transformer-oil bridges are investigated and modelled as perfect dielectrics. The electric field counteracts the gravitational effects and causes the bridges to rise and become flatter, with shapes that are well described by Young--Laplace-type equations containing non-local electric-field contributions evaluated using a boundary-element method. Bifurcation diagrams of these solutions are constructed by pseudo-arclength continuation to characterise the dependence of bridge shapes on liquid volume and electric-field strength. In the absence of an electric field, the transient relaxation to equilibrium is analysed using a reduced-order model developed using Onsager's variational principle, with comparison to direct numerical simulations. The steady states predicted by the reduced-order model agree closely with those of the full formulation over a wide parameter range, and the dynamics is well captured in the overdamped regime.