A liquid bridge is a column of liquid, pinned at each end. Here we analyse the
stability of a bridge pinned between planar electrodes held at different potentials
and surrounded by a non-conducting, dielectric gas. In the absence of electric fields,
surface tension destabilizes bridges with aspect ratios (length/diameter) greater than
π. Here we describe how electrical forces counteract surface tension, using a linearized
model. When the liquid is treated as an Ohmic conductor, the specific conductivity
level is irrelevant and only the dielectric properties of the bridge and the surrounding
gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle
functions are used to formulate an eigenvalue problem. Numerical solutions
disclose that the most unstable axisymmetric deformation is antisymmetric with
respect to the bridge’s midplane. It is shown that whilst a bridge whose length
exceeds its circumference may be unstable, a sufficiently strong axial field provides
stability if the dielectric constant of the bridge exceeds that of the surrounding fluid.
Conversely, a field destabilizes a bridge whose dielectric constant is lower than that
of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is
sensitive to the presence of conduction along the surface and much higher fields are
required for stability when surface transport is present. The theoretical results are
compared with experimental work (Burcham & Saville 2000) that demonstrated how a
field stabilizes an otherwise unstable configuration. According to the experiments, the
bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as
the field is reduced. Agreement between theory and experiment for the field strength
at the pinch-off transition is excellent, but less so for the change from cylinder to
amphora. Using surface conductivity as an adjustable parameter brings theory and
experiment into agreement.
Free Vibration of Partially Supported Cylindrical Shells