Energy landscapes and bistability to finite-amplitude disturbances for the capillary bridge (original) (raw)

Axial and radial curvatures compete to destabilize the open catenoidal capillary bridge, and once destabilized, to influence its dynamical trajectory. The fates of finite-amplitude disturbances to the stable capillary shapes are mapped out by analysis of potential energy landscapes in combination with bounds on the total energy ͑kinetic plus potential͒ assuming viscous dissipation, following techniques from earlier work on the Rayleigh-Taylor problem. Energy landscapes ͑floor͒ and energy bounds ͑ceiling͒, in combination, form large trapping regions in the parameter space of bridge length l ͑scaled by contact radius R) and disturbance amplitude 2. Regions are identified within which disturbances must always return or can never return to the stable base state. Necessarily, sensitive competition between two or more directions in phase-space cannot occur in these regions. We find lϭ0.542 to be the location of a change in nature of saddle point in the landscape and discuss its implications for the dynamical behavior.