Droplet Dynamics on a Vibrating Fiber: A Numerical Study

We employ a phase-field lattice Boltzmann model to numerically
investigate the complex dynamics of droplets on a mechanically excited,
horizontally oriented fiber. Famously, the droplet can wet the fiber
in two distinct states: the barrel state and the clamshell state.
Initially, we characterize the natural oscillatory behavior of a droplet
sitting on a stationary fiber, finding that the clamshell state exhibits
a significantly higher natural frequency compared to the barrel state.
By systematically varying the vibration amplitude and frequency, we
uncover a diverse range of droplet response modes. For vertical fiber
vibration, these modes include the quasi-static motion, rigid motion,
regular pumping, up-and-down pumping, and subharmonic pumping modes.
Furthermore, at sufficiently high acceleration amplitudes, droplet
detachment occurs. Additionally, a swinging motion can be induced
by an initial disturbance within a specific frequency range. For horizontal
fiber vibration, the observed modes encompass regular swinging, combined
swinging and pumping, pure side-to-side pumping, and a slinging mode,
where the droplet orbits the fiber. We present comprehensive regime
maps that delineate the boundaries for each response mode in the parameter
space of frequency and acceleration amplitude. Our findings provide
valuable insights into the intricate interplay between a droplet and
a vibrating fiber, with potential applications in fog harvesting,
microfluidics, and droplet-based technologies.