Bouncing droplet dynamics above the Faraday threshold.

We present the results of an experimental investigation of the dynamics of droplets bouncing on a vibrating fluid bath for forcing accelerations above the Faraday threshold. Two distinct fluid viscosity and vibrational frequency combinations (20 cS-80 Hz and 50 cS-50 Hz) are considered, and the dependence of the system behavior on drop size and vibrational acceleration is characterized. A number of new dynamical regimes are reported, including meandering, zig-zagging, erratic bouncing, coalescing, and trapped regimes. Particular attention is given to the regime in which droplets change direction erratically and exhibit a dynamics akin to Brownian motion. We demonstrate that the effective diffusivity increases with vibrational acceleration and decreases with drop size, as suggested by simple scaling arguments.

Faraday-Talbot effect: Alternating phase and circular arrays.

A hydrodynamic analog to the optical Talbot effect may be realized on the surface of a vertically shaken fluid bath when a periodic array of pillars protrudes from the fluid surface. When the pillar spacing is twice or one and a half times the Faraday wavelength, we observe repeated images of the pillars projected in front of the array. Sloshing inter-pillar ridges act as sources of Faraday waves, giving rise to self-images. Here, we explore the emergence of Faraday-Talbot patterns when the sloshing ridges between pillars have alternating phases. We present a simple model of linear wave superposition and use it to calculate the expected self-image locations, comparing them to experimental observations. We explore how alternating phase sources affect the Faraday-Talbot patterns for linear and circular arrays of pillars, where curvature allows for magnification and demagnification of the self-imaging pattern. The use of an underlying wavefield is a subject of current interest in hydrodynamic quantum analog experiments, as it may provide a means to trap walking droplets.