Bouncing droplet dynamics above the Faraday threshold.

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Soft matter physics

Background:

• The Faraday instability in fluid interfaces is a well-studied phenomenon.
• Droplet dynamics on vibrating surfaces can exhibit complex, non-trivial behaviors.

Purpose of the Study:

• To experimentally investigate droplet bouncing dynamics on a vibrating fluid bath above the Faraday threshold.
• To characterize new dynamical regimes and their dependence on system parameters.

Main Methods:

• Experimental setup involving droplets on a vibrating fluid bath.
• System parameters varied: fluid viscosity (20 cS, 50 cS), vibrational frequency (80 Hz, 50 Hz), drop size, and vibrational acceleration.
• Observation and characterization of droplet trajectories and interactions.

Main Results:

• Identification of novel dynamical regimes: meandering, zig-zagging, erratic bouncing, coalescing, and trapped states.
• Detailed analysis of an erratic bouncing regime resembling Brownian motion.
• Demonstration that effective diffusivity increases with vibrational acceleration.
• Demonstration that effective diffusivity decreases with drop size.

Conclusions:

• Droplet bouncing on vibrating fluid baths presents rich and complex dynamics beyond simple oscillations.
• The observed Brownian-like motion is quantifiable and predictable via scaling arguments.
• Vibrational acceleration and drop size are key parameters controlling droplet diffusion on the fluid bath.