Finite-Amplitude Capillary Oscillations of Coupled Droplets
Eric A. Theisen1, Micheal J. Vogel1, Paul H. Steen1, Carlos A. Lopez2, and Amir H. Hirsa2. (1) School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, (2) Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy, NY
Predicting how surface-tension redistributes liquid volume is important for a number of small-scale applications. We consider a prototypical case. If a cylindrical hole drilled in a plate is overfilled with liquid, droplets will appear on either side of the plate. For small enough scale (so that gravity does not dominate shape) and for large enough total volume, one droplet will be bigger than the other. Big-droplet-up or big-droplet-down states are symmetric counterparts. ‘Kicking' one of the droplets with a prescribed pressure-pulse sets the system into motion. Depending on the amplitude of the kick, four different dynamical behaviors are observed in experiment: i) small vibrations about a static shape; ii) oscillations that go up and down n-times before coming to rest (where n=1,2,3); iii) deformations that break-off satellite droplets and iv) deformations that blow the liquid completely out of the hole. Observations are compared to a model that includes surface tension and inertia. Motion of the system center-of-mass is tracked in the model with interface deformation restricted to spherical-cap shapes. The resulting 2-d non-linear dynamical system can be written down in analytical form. The benefit of simplicity of model is the description of finite-amplitude behavior. The model predicts a phase-plane not unlike the simple pendulum which exhibits behaviors reminiscent of i) and ii). The focus of the talk will be a comparison of observations to model predictions.