Active stabilization of liquid capillary bridges using optically sensed modal amplitudes

Abstract

Cylindrical capillary bridges consisting of liquid between two circular supports naturally become unstable and break when the length of the bridge exceeds its circumference for the situation where the weight or buoyancy of the bridge can be neglected. This is the Rayleigh–Plateau (RP) slenderness limit which is relevant to the management of liquids and to the formation of liquid drops. We have demonstrated methods of suppressing this instability based on the optical sensing of the instantaneous modal amplitude and the rapid adjustment of the axial distribution of applied radial stress. This applied stress may be the result of ultrasonic radiation pressure [M. J. Marr-Lyon et al., J. Fluid Mech. 351, 345–357 (1997)] or electrostatic stresses from an array of electrodes [M. J. Marr-Lyon et al., Phys. Fluids (accepted)]. We have stabilized bridges as much as 42% beyond the RP limit by phasing the stress so that the effective modal spring constant becomes positive; however, the modal damping is then decreased. The closed-loop response includes terms associated with boundary-layer damping and the sensor’s response time. The analysis indicates that damping of short bridges may be enhanced by reversing the feedback phase. [Work supported by NASA.]