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

Abstract

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 π. 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.

Stability of immersed viscous liquid threads under electric field

“…It would thus be interesting to understand the stability of these systems at different viscosity ratios. The present theory can also be used to study the stability of neutrally buoyant liquid bridges immersed in an outer bath of another immiscible liquid in the presence of electric field (Burcham & Saville, 2002;Marr-Lyon, Thiessen, & Blonigen, 2000).…”

Enhanced damping of capillary bridge oscillations using velocity feedback

“…Previous work has demonstrated the ability to stabilize small-scale bridges beyond the Rayleigh-Plateau limit by applying mode-coupled electrostatic or acoustic stresses in proportion to the measured modal amplitude. [4][5][6] This has the effect of stiffening the mode and can be thought of as increasing the spring constant of an oscillator. On the other hand, if the feedback stress is applied in proportion to the velocity of the instantaneous modal amplitude, it is possible to add artificial damping to the capillary wave mode.…”

“…4,5 Furthermore, it can be imagined that an array of electrodes could be used in order to control more than one mode at a time. The simultaneous control of both mode frequency and damping would be useful in a spacecraft environment with significant vibrations at discrete frequencies.…”

Electrical conductance study of θ-liquid bridges

“…Some traditional examples are the study of the distribution of phases in porous media with respect to oil recovery applications, capillary evaporation/condensation and binder induced agglomeration of particles which is of importance in operations such as flotation, coating, flocculation and granulation [1][2][3]. More modern applications are the stability of liquid bridges in flotation zones for producing high quality crystals [4][5][6], droplet squeezing flow between two plates for studying the dynamics of moving contact lines, e.g., in alignment of matched components during optoelectronics assembly [7,8] the stability of electrically conducting capillary bridges by control of electrostatic stresses [9,10] or even as a means to measure dynamic surface phenomena at short time scales such as wave damping and surfactant squeeze-out from the surface [11].…”