Oscillation dynamics of sessile droplets subjected to substrate vibration

• Used high speed imaging to study sessile droplets excited by support vibrations.
• Studied the effect of driving amplitude and frequency on oscillation level.
• Modal analysis on the droplet shape through proper orthogonal decomposition.
• Duffing oscillator analogy established for a sessile droplet for the first time.

Sessile droplets on a vibrating substrate are investigated focusing on axisymmetric oscillations with pinned contact line. Proper orthogonal decomposition is employed to identify the different modes of droplet shape oscillation and quantitatively assess the droplet oscillation and spectral response. We offer the first experimental evidence for the analogy of an oscillating sessile droplet with a non-linear spring mass damper system. The qualitative and quantitative agreement of amplitude-response and phase-response curves and limit cycles of the model dynamical system with that observed experimentally suggest that the bulk oscillations in the fundamental mode of a sessile droplet can be very well modeled by a Duffing oscillator with a hard spring, especially near the resonance. The red shift of the resonance peak with an increase in the glycerol concentration is clearly evidenced by both the experimental and predicted amplitude response curves. The influence of various operational parameters such as excitation frequency and amplitude and fluid properties on the droplet oscillation characteristics is adequately captured by the model.