Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges

Electrically conducting, cylindrical liquid bridges in a density-matched, electrically insulating bath were stabilized beyond the Rayleigh-Plateau (RP) limit using electrostatic stresses applied by concentric ring electrodes. A circular liquid cylinder of length L and radius R in real or simulated zero gravity becomes unstable when the slenderness S=L/2R exceeds pi. The initial instability involves the growth of the so-called (2, 0) mode of the bridge in which one side becomes thin and the other side rotund. A mode-sensing optical system detects the growth of the (2, 0) mode and an analog feedback system applies the appropriate voltages to a pair of concentric ring electrodes positioned near the ends of the bridge in order to counter the growth of the (2, 0) mode and prevent breakup of the bridge. The conducting bridge is formed between metal disks which are grounded. Three feedback algorithms were tested and each found capable of stabilizing a bridge well beyond the RP limit. All three algorithms stabilized bridges having S as great as 4.3 and the extended bridges broke immediately when feedback was terminated. One algorithm was suitable for stabilization approaching S=4.493... where the (3, 0) mode is predicted to become unstable for cylindrical bridges. For that algorithm the equilibrium shapes of bridges that were slightly under or over inflated corresponded to solutions of the Young-Laplace equation with negligible electrostatic stresses. The electrical conductivity of the bridge liquid need not be large. The conductivity was associated with salt added to the aqueous bridge liquid. (C) 2000 American Institute of Physics. [S1070-6631(00)00505-5].