Chaotic motions of a forced droplet-droplet oscillator

A model for the motion of two coupled spherical-cap droplets subject to periodic forcing is studied. The inviscid unforced model is a conservative second-order system, similar to Duffing’s equation. Surface tension resists the inertia of deformations from the spherical shape. Steady states of the system are parametrized by the total combined volume of the two droplet caps. The family of equilibria exhibits a classical pitchfork bifurcation, where a single lenslike symmetric steady state bifurcates into two dropletlike asymmetric states. The existence of homoclinic orbits in the unforced system suggests the possibility of chaotic dynamics in a forced, damped system. The forced damped extension is investigated for chaotic dynamics using Melnikov’s method and by calculating Lyapunov exponents. Observations are compared qualitatively to experimental results, confirming the existence of chaotic motions.